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Automated computer-aided soft computing methods are presently used to detect the tumor regions in brain images. In this paper, the tumor cells are detected in the brain Magnetic Resonance Imaging (MRI) using the Extended Linear Boosting (ELB) classification method as one type of soft computing process. This paper proposes an effective brain tumor detection and segmentation method using the ELB classification method. The Curvelet transform is applied on the source brain MRI image to convert the spatial domain pixels into multi-resolution pixel. The spectral and linear discriminate features are computed from the Curvelet transformed coefficient matrix. The dimensionality of the computed features is reduced using the PCA method and the optimized features are then classified using the ELB classification method. The performance evaluation metrics, sensitivity, specificity, accuracy and detection rate, are used in this paper to evaluate the performance of the proposed brain tumor detection and segmentation system. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar (SAR) images depend on the dielectric properties of objects with certain incident angles. Thus, vessels and other metallic objects appear clear in SAR images however, they are difficult to be distinguished in optical images. Synergy of these two types of images leads to not only high spatial and spectral resolutions but also good explanation of the image scene. In this paper, a hybrid pixel-level image fusion method is proposed for integrating panchromatic (PAN), multispectral (MS) and SAR images. The fusion method is performed using Multi-stage guided filter (MGF) for optical images pansharpening, to get high preserving spatial details and nested Gram-Schmidt (GS) and Curvelet-Transform (CVT) methods for SAR and optical images,to increase the quality of the final fused image and benefit from the SAR image properties. The accuracy and performance of the proposed method are appraised using Landsat-8 Operational-Land-Imager (OLI) and Sentinel-1 images subjectively as well as objectively using different quality metrics. Moreover, the proposed method is compared to a number of state-of-the-art fusion techniques. The results show significant improvements in both visual quality and the spatial and spectral evaluation metrics. Consequently, the proposed method is capable of highlighting maritime activity for further processing. [ABSTRACT FROM AUTHOR]

Nullifying the noise and redundancy in the breast thermogram is still a critical challenge. In this paper, a framework is designed for the purpose of classification of noisy RGB thermal breast images. The proposed framework includes enhancement in frequency domain, advanced mixed denoising and color correction for thermal images. The enhancement of thermogram uses curvelet transform that is applied to the V component of the HSV derived from RGB thermogram. Gain-controlled bihistogram equalization operation is performed to the detailed component of V to enhance the image quality. The advanced mixed denoising algorithm is also presented using a combination of Gaussian and bilateral filter for denoising the enhanced thermogram. Spatially varying color correction (SVCC) technique is applied, which is based on an optimum linear color correction matrix that is calculated from the local blocks of enhanced image. The classification outcome of this proposed framework is more encouraging compared with the results of the existing methods for thermogram classification. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced a novel integral transform namely linear canonical curvelet transform (LCCT). Firstly, we established basic properties of LCCT including admissibility condition, Moyals principle, inversion formula and range theorem. Toward the culmination of the paper, we formulate a couple of Heisenberg-type inequalities associated with LCCT. [ABSTRACT FROM AUTHOR]

Breast cancer is the most serious type of diseases; hence, it requires an efficient diagnosis for an early cure. Thermography for breast screening has achieved breakthroughs in detecting the abnormalities at earlier stages. In this paper, breast thermograms acquired in lateral views are considered for applying transform-based feature extraction. It is necessary to transform the acquired thermograms into the frequency domain to pick out the detailed feature that delineates abnormal from the normal ones. This paper categorizes the features under three major types of transforms namely wavelet, curvelet and contourlet transform. The transformed thermograms are then subjected to feature extraction where statistical values are measured and compared with spatial domain gray level co-occurrence matrix values. By analyzing the features using ANOVA and independent t test, the result significantly shows that the lateral view thermograms outperform than the frontal views. Finally, the features are used to classify the normal and abnormal thermograms of frontal and lateral views using pattern classifiers. According to the results, the classification performance is measured with the highest accuracy of 91%, 87% of sensitivity rate and 90% of specificity rate using the AdaBoost algorithm. [ABSTRACT FROM AUTHOR]

Image processing covers a wide range of processing techniques. Image Fusion is one of those technique which plays a vital role with medical images since different imaging methods provide different set of clinical information for diagnosis. Advances in technology provide us with plenty of imaging modalities. Image fusion is essential for a joint analysis of these multimodality images since each of these modalities provide unique and complementary characterization of the underlying anatomy and tissue microstructure. This paper analyzes the image fusion methods based on multiscale transforms and implements using wavelet, contourlet, curvelet, and shearlet transform. The results are compared. [ABSTRACT FROM AUTHOR]

In order to overcome deficiency in wavelet analysis, people have proposed beyond wavelets based on wavelets transform, in which curvelets transform is a kind of commonly used method for signal processing. Because of directional sensitivity of its basis function, curvelets transform suggested more superior characteristics than that of wavelets in describing singularity for curve and image edges. Because the spatial distribution of stripe noise in hyperspectral image has clear directivity, so it is more reasonable that it uses Curvelet transform for image denosing. Combining with spectrum relation, curvelet transform was used in this paper for noise elimination of the hyperspectral image. The algorithm used in this paper includes three main steps. Step 1: Weighting sums of high frequency curvelet coefficients in bands containing less noise; Step 2: Replacing the high frequency curvelet transform to obtain reconstructed images with less noises. Experiments indicated that this method can carry on the effective denoising to hyperspectral image, and retained detail information well at the same time. The denoising images obtained by this method possessed a higher peak signal-to-noise ratio and better visual effects. [ABSTRACT FROM AUTHOR]

Due to the huge advancement in technology, digitizing the multimedia content like text, images and videos has become easier. Everyday huge amounts of multimedia content are shared through the social networks using internet. Sometimes this multimedia content can be hacked by the hackers. This will lead to the misuse of the data. On the other hand, the medical content needs high security and privacy. Motivated by this, joint secured medical image compression–encryption mechanisms are proposed in this paper using multiscale transforms and symmetric key encryption techniques. The multiscale transforms involved in this paper are wavelet transform, bandelet transform and curvelet transform. The encryption techniques involved in this paper are international data encryption algorithm (IDEA), Rivest Cipher (RC5) and Blowfish. The encoding technique used in this paper is embedded block coding with truncation (EBCOT). Experimental results are done for the proposed works and evaluated by using various parameters like Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), Image Quality Index (IQI) and Structural Similarity Index (SSIM), Average Difference (AD), Normalized Cross-correlation (NK), Structural Content (SC), Maximum difference (MD), Laplacian Mean Squared Error (LMSE) and Normalized Absolute Error (NAE). It is justified that the proposed approaches in this paper yield good results. [ABSTRACT FROM AUTHOR]

In order to better perform the characteristics of natural image curves and further improve the robustness of digital watermarking algorithms, this paper proposed a robust zero-watermarking algorithm based on Curvelet-DSVD and visual cryptography. Firstly, it performed Arnold scrambling on the original image, then obtained the low frequency domain information by Curvelet transform, segmented the low frequency domain information, and each block was double singular value decomposition(DSVD), by using the relationship between the maximum singular value of the block and the mean value of the global singular value structuring characteristic matrix. At the same time, this paper used the visual cryptography to generate two shared copies of the watermark information. Finally, it executed one of the shares to Arnold scramble and then xor operation with the feature matrix to generate a zero-watermark. Experimental results show that the proposed algorithm can effectively resist the conventional attacks and is more robust and more secure than the existing zero-watermarking algorithms. [ABSTRACT FROM AUTHOR]

Deblending of simultaneous-source seismic data is becoming more popular in seismic exploration since it can greatly improve the efficiency of seismic acquisition and reduce acquisition cost. At present, the deblending methods of simultaneous-source seismic data are mainly divided into two types: filtering method and sparse inversion method. Compared with the filtering method, the sparse inversion method has higher precision, but the selection of its parameter value mainly depends on experience, which is not suitable for large-scale seismic data processing. In this paper, an adaptive iterative deblending method based on sparse inversion is proposed. By improving the original iterative solution method of regularization inversion model, the effective signal and blending noise are weakened simultaneously in the iterative process, so that the energy intensity of blending noise is consistent with that of the effective signal in each iterative, so as to ensure the consistency of the regular parameter calculation method of each iteration. By analyzing the distribution of coefficients in the curvelet domain of pseudo-deblending data and blending noise, it is concluded that the value of regular parameters is the maximum amplitude of residual pseudo-deblending data in the curvelet domain multiplied by a coefficient between 0 and 1. In the process of iterative deblending, the regularized parameters are obtained adaptively from the data itself. It not only ensures the accuracy of the calculation results, but also improves the calculation efficiency, which is suitable for large-scale seismic data processing. [ABSTRACT FROM AUTHOR]

Odia is an old and recognized regional language of India and is spoken, read and written by almost 90% people of Odisha state and an appreciable part of the population of neighbouring states. Unfortunately, very little work on Odia language processing (OLP) has been carried out and reported in standard literature. Accordingly, in this paper, a sincere attempt has been made on the recognition of handwritten Odia numerals, as a part of OLP, by using a standard database (Bhowmik et al. in Proceedings of 9th international conference on information technology (ICIT’06), Bhubaneswar, 18-21 December, pp 105-110, 2006) of ISI Kolkata. In this investigation, we have chosen six different transforms like the discrete Fourier transform (DFT), short-time Fourier transform, discrete cosine transform, discrete wavelet transform, S-transform (ST) and curvelet transform (CT) for feature extraction from handwritten numerals and principal component analysis for feature reduction. The standard four adaptive classifiers such as multilayered perceptron (MLP), four types of functional link artificial neural network (FLANN), radial basis function network and probabilistic neural network (PNN) are used to classify the handwritten Odia digits using the reduced extracted features from transform as inputs. The investigation made in this paper reveals that the RBF network with CT-based features and the power series FLANN with DFT features provide the best and the worst recognition performance for handwritten Odia numerals, respectively. Further, the first five best accuracy-based combined recognition systems are RBF-CT, RBF-ST, RBF-WT, PNN-CT and MLP-CT which offers percentage classification accuracy of 98.70, 96.22, 95.12, 95.10 and 93.60, respectively. [ABSTRACT FROM AUTHOR]

Images captured under low light are noisy and consist of unidentifiable features. Low light noise problem occurs in imaging devices because of smaller sensor size or insufficient exposure. Low light image denoising is an exacting task in many image processing applications. This paper proposes a patch-based image denoising method for low light images in the curvelet domain with contrast enhancement. Curvelet transform is a directional transform and it gives the best sparse representation for images with edges. Here the Expectation–Maximization (EM) algorithm, based on the Gaussian mixture adaptation method is performed in the curvelet domain for denoising. EM Algorithm helps in computing the Gaussian mixture model (GMM) parameters from the patches which are used in maximum a posteriori estimation to update them. GMM parameters and patches are updated periodically until a satisfactory result is achieved. Simulation is performed on standard test data set, and then extended to natural low light noisy images. The results of the proposed technique are then compared using quality metrics such as Peak Signal to Noise Ratio and Structural Similarity Index. It is observed that the use of curvelet transform in denoising process helps to restore the structural information satisfactorily. [ABSTRACT FROM AUTHOR]

Diabetic retinopathy (DR) is the major reason of vision loss in the active population. It can usually be prevented by regulating the blood glucose and providing a timely treatment. DR has clinical features recognized by the experts including the blood vessel area, exudates, neovascularization, hemorrhages, and microaneurysm. Because DR has some varieties and complexities due to its geometrical and haemodynamic features, it is hard and time-consuming to detect DR in manual diagnosis. In Computer Aided Diagnosis (CAD) systems, the features of DR fundus images are detected using computer vision techniques. In this paper, a CAD system is proposed, which distinguishes automatically whether the fundus is normal or it suffers from diabetic retinopathy disease. As preprocess morphological operations like filtering, opening, and dilation are applied to the images firstly, then, Optic Disk (OD) segmentation is implemented using Greedy algorithm. Because of the intensity of an OD is similar to some DR intensities, OD regions are removed from the fundus images for an accurate feature extraction. The features extracted with Curvelet Transform (CT) and Scale Invariant Feature Transform (SIFT), respectively, are concatenated to provide a feature set that defines the fundus data optimally. Finally, the feature set is given to the Support Vector Machines (SVM), K-Nearest Neighborhood (KNN), and Naïve–Bayes (NB) classifiers for the DR identification purpose. The proposed method achieves the highest accuracy and sensitivity as 92.8% and 97.6%, respectively, with SVM and specificity as 92.5% with KNN classifier. [ABSTRACT FROM AUTHOR]

With the availability of multi-sensor, multi-temporal, multi-resolution and multi-spectral images from operational Earth observation satellites, remote sensing image fusion has become a valuable tool. The goal of remote sensing image fusion is to integrate complementary information from multi-source data such that the new images are more suitable for human visual perception and computer-processing tasks such as segmentation, feature extraction, and object recognition. In this paper, a pixel-level remote sensing image fusion method is proposed, which is based on combining the principal component analysis (PCA) and the curvelet transformation (CT). First, the multi-spectral image with low-spatial-resolution is transformed by PCA and principal components are obtained. Second, the panchromatic image with high-spatial-resolution and the principal components of the multi-spectral image are respectively merged with the curvelet transform. Finally, the fused image is obtained by inverse CT and inverse PCA. The experiments using Landsat-8 OLI multi-spectral and panchromatic image show that, compared with the traditional methods such as the WT-based method, the IHS-based method, the HPF-based method, the BT-based method, the PCA-based method and the CT-based method, the results of the proposed method preserve the spatial details while preserving more spectral information of the original image. [ABSTRACT FROM AUTHOR]

[Display omitted] • An image SR method is proposed to improve the accuracy of vision measurement. • Curvelet transform is formulated to feature extraction in neural network. • Curvelet loss is built to evaluate the recovery quality of Curvelet coefficients. • Loss function is built to measure the localization accuracy of reconstructed edges. • The reconstructed images have sharp edges and high accuracy of edge localization. The precision of image-based measurements is mainly limited by the resolution of the camera hardware. Currently, increasing the resolution of measurement images by super-resolution method is an effective way to improve the precision of vision measurement. However, most image super-resolution methods are only based on the prediction of spatial information, therefore the reconstruction quality and localization accuracy of the edge regions are often insufficient to meet the requirements of precision measurements. For this reason, a Curvelet coefficient prediction method for image super-resolution (CPSR) is proposed to achieve accurate super-resolution results of edge regions in this paper. Firstly, the image is decomposed into sub-bands of Curvelet coefficients at different scale to extract frequency features. Then, deep residual networks are built and trained to fit the mapping function between low- and high-resolution coefficient sub-bands. In addition, Curvelet loss and edge localization loss functions are designed to obtain Curvelet coefficient errors of each scale and edge localization errors of sub-pixel level. The proposed method is evaluated using public super-resolution datasets and actual precision measurement images. Experimental results show that CPSR generates images with better visual effects, and has strong generalization ability for the reconstruction of different edge patterns. Furthermore, compared with the common super-resolution method based on deep learning, vision measurements on the reconstructed image of CPSR achieve smaller measurement errors, indicating that CPSR achieves more accurate edge localization. Experimental results verified the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a joint image encryption and compression scheme based on a new hyperchaotic system and curvelet transform. A new five-dimensional hyperchaotic system based on the Rabinovich system is presented. By means of the proposed hyperchaotic system, a new pseudorandom key stream generator is constructed. The algorithm adopts diffusion and confusion structure to perform encryption, which is based on the key stream generator and the proposed hyperchaotic system. The key sequence used for image encryption is relation to plain text. By means of the second generation curvelet transform, run-length coding, and Huffman coding, the image data are compressed. The joint operation of compression and encryption in a single process is performed. The security test results indicate the proposed methods have high security and good compression effect. [ABSTRACT FROM AUTHOR]

Hyperspectral imaging (HSI) classification has become a popular research topic in recent years, and effective feature extraction is an important step before the classification task. Traditionally, spectral feature extraction techniques are applied to the HSI data cube directly. This paper presents a novel algorithm for HSI feature extraction by exploiting the curvelet-transformed domain via a relatively new spectral feature processing technique—singular spectrum analysis (SSA). Although the wavelet transform has been widely applied for HSI data analysis, the curvelet transform is employed in this paper since it is able to separate image geometric details and background noise effectively. Using the support vector machine classifier, experimental results have shown that features extracted by SSA on curvelet coefficients have better performance in terms of classification accuracy over features extracted on wavelet coefficients. Since the proposed approach mainly relies on SSA for feature extraction on the spectral dimension, it actually belongs to the spectral feature extraction category. Therefore, the proposed method has also been compared with some state-of-the-art spectral feature extraction techniques to show its efficacy. In addition, it has been proven that the proposed method is able to remove the undesirable artifacts introduced during the data acquisition process. By adding an extra spatial postprocessing step to the classified map achieved using the proposed approach, we have shown that the classification performance is comparable with several recent spectral–spatial classification methods. [ABSTRACT FROM PUBLISHER]

To reduce the magnetic resonance imaging (MRI) data acquisition time and improve the MR image reconstruction performance, reconstruction algorithms based on the iterative shrinkage thresholding algorithm (ISTA) are widely used. However, these traditional algorithms use global threshold shrinkage, which is not efficient. In this paper, a novel algorithm based on local threshold shrinkage, which is called the local shrinkage thresholding algorithm (LSTA), was proposed. The LSTA can shrink differently for different elements from the residual matrix to adjust the shrinkage speed for each element of the image during the iterative process. Then, by taking advantage of the sparser characteristics of the curvelet transform, the LSTA combined with the curvelet transform (CLSTA) can make the construction process more efficient. Finally, compared with ISTA, the generalized thresholding iterative algorithm (GTIA) and the fast iterative shrinkage threshold algorithm (FISTA), when analysing human (brain and cervical) MR images, a conclusion can be drawn that the proposed method has better reconstruction performance in terms of the mean square error (MSE), the peak signal to noise ratio (PNSR), the structural similarity index measure (SSIM), the normalized mutual information (NMI), the transferred edge information (TEI) and the number of iterations. The proposed method can better maintain the detailed information of the reconstructed images and effectively decrease the blurring of the images edges. Graphical abstract. [ABSTRACT FROM AUTHOR]

Given that the price signal in the electricity market is highly volatile or otherwise uncertain, short-term forecasting is significantly affected. Since time-series methods cannot estimate such nonlinear models appropriately with high accuracy, we need to provide an efficient model. For this reason, in this paper, a new hybrid algorithm for day-ahead electricity price forecasting is proposed. In order to achieve this model, we first divide the forecasting problem into three main layers: preprocessor, training, and regulator. In the first layer, we use the curvelet transform to reduce possible noise in the price signal. Then, using the extended data selection model based on increasing correlation and decreasing redundancy, we eliminate the unnecessary data and reduce the volume of computation significantly. Then the regularized data is entered into the learning layer which is a developed Extreme Learning Machine (ELM) to obtain and extract the best pattern from the input data. Since adjusting the control parameters of the proposed ELM can maximize its ability to derive a nonlinear pattern from the price signal, a new developed Virus Colony Search (VCS) method based on the time-varying coefficients theory is proposed in the last layer. The proposed algorithm is a novel optimization method based on the function of viruses to destroy host cells and penetrate the best ones into a cell for replication. The proposed method is applied to existing real electricity markets and the results are compared based on prediction error rates and error-based criteria. The obtained results show the appropriate and acceptable performance of the proposed forecasting method. [ABSTRACT FROM AUTHOR]

This paper proposed a synchronous processing method using random noise suppression and high-frequency compensation for GPR data in curvelet domain. First, the GPR data were transformed into curvelet domain in order to use its multi-angle and multi-scale sparsity. The random noise thus could be suppressed by the adaptive threshold function changed with angle and scale. Second, according to the propagation laws of electromagnetic waves in elastic medium and the curvelet multi-scale feature, the time-varying compensation factor could be calculated so as to inverse weighting the corresponding scale and angle for compensation of the high-frequency absorption. Finally, inverse curvelet transformation was conducted thus the GPR data after random noise suppression and high-frequency compensation could be obtained. This method is totally a data-driven method thus can overcome the influence from artificial factors in traditional method. [ABSTRACT FROM AUTHOR]

This paper presents a new feature descriptor for iris recognition. The descriptor makes use of the wedge-shaped sub-bands of the curvelet transform, which allow it to cover the complete frequency spectrum, to characterize the iris images. The texture present in each of the curvelet sub-band is further represented by fitting a 2D polynomial of appropriate degree. Coefficients of polynomials fitted to each of the curvelet sub-bands are further collected to form the complete feature vector. The proposed approach is investigated with benchmark IITD and CASIA-v4-Interval iris databases to prove its usefulness. Results calculated in terms of area under receiver operator characteristics (ROC) curves (AUC) and equal error rates (EER) clearly display the outperforming nature of the proposed descriptor. [ABSTRACT FROM AUTHOR]

Nowadays, a number of scripts are used for writing. Script identification finds many applications like sorting and preparing an online database of documents. Identifying these scripts, especially with different orientations and scales, is an important and challenging problem in document image analysis. This paper proposed a new scheme for script identification from word images using skew and scale robust log-polar curvelet features. These word images are first extracted in the form of text-patches from documents using Gaussian filtering. Thereafter, texture features are calculated using curvelet transform in log-polar domain. Log-polar domain is independent of rotation and scale variations, whereas curvelet transform exhibits directional and anisotropic properties. This helps in the extraction of significant features. For experiments, k-nearest neighbor classifier is employed to identify the scripts, as it has zero training time and is simple to implement. Further, statistical significance test is performed by using two more classifiers, namely random forest and support vector machine. Comprehensive experimentations are carried out on ALPH-REGIM, Pati and Ramakrishnan, PHDIndic_11, and proprietary databases containing printed as well as handwritten texts. Here, bi-script, tri-script, and multi-script identification results are reported. Benchmarking analysis illustrated the effectiveness of the proposed method, where a maximum recall rate of 98.76% has been achieved. [ABSTRACT FROM AUTHOR]

In the process of catenary failure diagnosis system based on image processing technique, some catenary images present low contrast, which need to be enhanced. Curvelet transform has the high directional sensitivity and anisotropy, which is suitable for image enhancement because of its optimal sparse representation of image with rich details and edges. First, the catenary image is decomposed by Curvelet transform to get its high and low frequency coefficients, then adjust the high frequency coefficients using the enhancement function. Afterwards, combine the high frequency coefficients and low frequency coefficients by the inverse Curvelet transform, and thus to get the enhanced catenary image. In this paper, Curvelet transform is compared with the traditional enhancement methods. The experimental results show that the proposed method can effectively enhance the low contrast catenary images, the catenary insulator, arm, hanger, pillar and locator part become visible, the details become more obvious. Moreover, as for the online application of catenary failure diagnosis system, efficiency is another important consideration. The experimental results also show that the cost time of catenary image enhancement is within a few tens of seconds, which meets the requirements of catenary failure diagnosis system. [ABSTRACT FROM AUTHOR]

In many practical situations, magnetic resonance imaging (MRI) needs reconstruction of images at low measurements, far below the Nyquist rate, as sensing process may be very costly and slow enough so that one can measure the coefficients only a few times. Segmentation of such subsampled reconstructed MR images for medical analysis and diagnosis becomes a challenging task due to the inherent complex characteristics of the MR images. This paper considers reconstruction of MR images at compressive sampling (or compressed sensing (CS)) paradigm followed by its segmentation in an integrated platform. Image reconstruction is done from incomplete measurement space with random noise injection iteratively. A weighted linear prediction is done for the unobserved space followed by spatial domain denoising through adaptive recursive filtering. The reconstructed images, however, suffer from imprecise and/or missing edges, boundaries, lines, curvatures etc. and residual noise. Curvelet transform (CT) is purposely used for removal of noise and for edge enhancement through hard thresholding and suppression of approximate subbands, respectively. Then a fuzzy entropy-based clustering, using genetic algorithms (GAs), is done for segmentation of sharpen MR Image. Extensive simulation results are shown to highlight performance improvement of both image reconstruction and segmentation of the reconstructed images along with relative gain over the existing works. [ABSTRACT FROM AUTHOR]

Pedestrian detection is a key problem in night vision processing with a dozen of applications that will positively impact the performance of autonomous systems. Despite significant progress, our study shows that performance of state-of-the-art thermal image pedestrian detectors still has much room for improvement. The purpose of this paper is to overcome the challenge faced by the thermal image pedestrian detectors, which employ intensity based Region Of Interest (ROI) extraction followed by feature based validation. The most striking disadvantage faced by the first module, ROI extraction, is the failed detection of cloth insulted parts. To overcome this setback, this paper employs an algorithm and a principle of region growing pursuit tuned to the scale of the pedestrian. The statistics subtended by the pedestrian drastically vary with the scale and deviation from normality approach facilitates scale detection. Further, the paper offers an adaptive mathematical threshold to resolve the problem of subtracting the background while extracting cloth insulated parts as well. The inherent false positives of the ROI extraction module are limited by the choice of good features in pedestrian validation step. One such feature is curvelet feature, which has found its use extensively in optical images, but has as yet no reported results in thermal images. This has been used to arrive at a pedestrian detector with a reduced false positive rate. This work is the first venture made to scrutinize the utility of curvelet for characterizing pedestrians in thermal images. Attempt has also been made to improve the speed of curvelet transform computation. The classification task is realized through the use of the well known methodology of Support Vector Machines (SVMs). The proposed method is substantiated with qualified evaluation methodologies that permits us to carry out probing and informative comparisons across state-of-the-art features, including deep learning methods, with six standard and in-house databases. With reference to deep learning, our algorithm exhibits comparable performance. More important is that it has significant lower requirements in terms of compute power and memory, thus making it more relevant for depolyment in resource constrained platforms with significant size, weight and power constraints. [ABSTRACT FROM AUTHOR]

In this paper, a denoising scheme based on curvelet transform is proposed to improve the signal-to-noise ratio (SNR) for vibration sensing in phase-sensitive optical time-domain reflectometry (Φ -OTDR) systems. The noise level can be estimated based on non-vibration images, which can be used to set the threshold for curvelet coefficients. We further optimize the threshold according to the amplitude distribution of the curvelet coefficients. In the experimental demonstration, when the optical pulse width is 100 ns, the SNR of location information of the 100 Hz vibration events can be increased by 6.93 dB, which proves the effectiveness of the proposed method. • We propose to estimate the level of the noise using non-vibration images in distributed fiber sensing schemes, which can be used to set the threshold for curvelet coefficients. • An efficient denoising method with adaptive threshold is proposed to improve the denoising performance of Φ -OTDR system. • Experimental results show that the SNR of location information for the vibration source of 100 Hz increases from 5.69 dB to 12.62 dB, indicating a large improvement when compared with the traditional curvelet denoising method. The proposed denoising method eliminates the requirement of estimating the noise level and reduces noise effectively, which shows great potential in improving the performance of Φ -OTDR system. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to detect and classify the power quality disturbance (PQD) signals based on singular spectrum analysis (SSA), curvelet transform (CT) and deep convolutional neural networks (DCNNs). SSA is a non-parametric technique, does not require any supposition to generate the observed signal, and provides an effective way to recognize weak transient PQ signal. Fast discrete curvelet transform (FDCT) is an efficient method compared to wavelet transforms. Firstly, PQD signals are decomposed using SSA and FDCT methods. Initial six and three levels decomposition of the SSA and FDCT are used as features of PQD respectively. Finally, DCNNs based classifier and multiclass support vector machines (SVMs) classifier are used for classification of single and complex PQDs. For validation of the proposed algorithm, thirty-one categories of real and synthetic PQD waveforms are considered. The proposed scheme is tested and the results are recorded. The results of proposed SSA-FDCT-DCNN (SFD) based classifier are compared to the results of multiclass SVM based and other existing methods The achieved results show that the SFD classifier is more proficient than the multiclass SVM and other present methods. In addition, the proposed SFD based classifier can be efficiently used to classify the single and complex PQ disturbances. [ABSTRACT FROM AUTHOR]

As a result of the acquisition of environment and instrument performance constraints, seismic data collected are often irregular and incomplete.Thus it is necessary to reconstruct the complete seismic data before proceeding to the next step in the seismic data analysis. The authors present a modified Curvelet algorithm for image reconstruction based on seismic compression.First in the framework of compressed sensing theory, using the sparse characteristic of Curvelet, a missing data reconstruction model is built, and then using the CRSI(Curvelet Recovery by sparsity-promoting Inversion, CRSI) algorithm framework,adopting improved exponential threshold algorithm, the missing seismic data are restored and reconstructed. In this paper, the authors use four level homogeneous medium model and the seismic data simulated by Marmousi model to carry out numerical experiments of random sparse sampling and reconstruction. The result of the experiment shows that compared with the traditional recon-struction algorithm, the proposed method not only accelerates the convergence speed of the original algorithm, but also guarantees a high SNR of the reconstructed data, which verifies the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Ground roll is a type of coherent noise in land seismic data that has low frequency, low velocity and high amplitude. It damages reflection events that contain important information about subsurface structures, hence the removal of ground roll is a crucial step in seismic data processing. A suitable transform is needed for removal of ground roll. Curvelet transform is an effective sparse transform that optimally represents seismic events. In addition, the curvelets can provide a multiscale and multidirectional decomposition of the input data in time-frequency and angular domain, which can help distinguish between ground roll and useful signals. In this paper, we apply synchrosqueezed curvelet transform (SSCT) for ground roll attenuation. The synchrosqueezing technique in SSCT is used to precisely reallocate the energy of local wave vectors in order to separate ground roll from the original data with higher resolution and higher fidelity. Examples of synthetic and field seismic data reveal that SSCT performs well in the suppression of aliased and non-aliased ground roll while preserving reflection waves, in comparison with high-pass filtering, wavelet and curvelet methods. [ABSTRACT FROM AUTHOR]

With the growth of various image-capturing devices, image acquisition is no longer a difficult task. As this technology is flourishing, various types of complex images are being produced. In order to access a large number of images stored in database easily, the images must be properly organized. Field of image retrieval attempts to solve this problem. As the complex images are being produced, processing them using single-resolution techniques is not sufficient as these images may contain varying levels of details. This paper proposes a novel multiresolution descriptor, local binary curvelet co-occurrence pattern, to achieve the task of content-based image retrieval. Curvelet transform of grayscale image is computed followed by computation of local binary pattern of resulting curvelet coefficients. Finally, feature vector is constructed using grey-level co-occurrence matrix which is matched with the feature vector of database images. The proposed descriptor combines the properties of local pattern and multiresolution technique of curvelet transform, and efficiently covers curvilinear and geometrical structures present in the image. Performance of the proposed method is measured in terms of precision and recall and is tested on five benchmark datasets consisting of natural images. The proposed method has been compared with single and multiresolution techniques as well as with some of the other state-of-the-art image retrieval methods. The experimental results clearly demonstrate that the proposed method produces high retrieval accuracy and outperforms other techniques in terms of precision and recall. [ABSTRACT FROM AUTHOR]

The most recent face recognition systems are mainly dependent on feature representations obtained using either local handcrafted-descriptors, such as local binary patterns (LBP), or use a deep learning approach, such as deep belief network (DBN). However, the former usually suffers from the wide variations in face images, while the latter usually discards the local facial features, which are proven to be important for face recognition. In this paper, a novel framework based on merging the advantages of the local handcrafted feature descriptors with the DBN is proposed to address the face recognition problem in unconstrained conditions. Firstly, a novel multimodal local feature extraction approach based on merging the advantages of the Curvelet transform with Fractal dimension is proposed and termed the Curvelet-Fractal approach. The main motivation of this approach is that the Curvelet transform, a new anisotropic and multidirectional transform, can efficiently represent the main structure of the face (e.g., edges and curves), while the Fractal dimension is one of the most powerful texture descriptors for face images. Secondly, a novel framework is proposed, termed the multimodal deep face recognition (MDFR) framework, to add feature representations by training a DBN on top of the local feature representations instead of the pixel intensity representations. We demonstrate that representations acquired by the proposed MDFR framework are complementary to those acquired by the Curvelet-Fractal approach. Finally, the performance of the proposed approaches has been evaluated by conducting a number of extensive experiments on four large-scale face datasets: the SDUMLA-HMT, FERET, CAS-PEAL-R1, and LFW databases. The results obtained from the proposed approaches outperform other state-of-the-art of approaches (e.g., LBP, DBN, WPCA) by achieving new state-of-the-art results on all the employed datasets. [ABSTRACT FROM AUTHOR]

The simultaneous seismic interpolation and denoising problem can be solved as a sparse inversion problem by using the sparseness of seismic data in a transformed domain as the a priori information, where the properties of the sparse transform will significantly influence the numerical results and computational efficiency. Curvelet transform has nearly optimal sparse expression for seismic data, thus seismic signal processing based on this transform tends to result in preferable results. However, the redundancy of this transform can be 24-32 for three dimensional data which is not computationally cost efficient. This paper introduces a low redundancy curvelet transform to simultaneously interpolate and denoise. The redundancy of the proposed transform can be reduced to 10 for three dimensional data, and this property will improve the computational efficiency of the curvelet transform-based signal processing. The iterative soft thresholding method was chosen to solve the sparse inversion problem. Some practical principles on how to choose the regularisation parameters are discussed, due to the crucial nature of the regularisation parameter for simultaneous interpolation and denoising. Numerical experiments on synthetic and field data demonstrate that the low redundancy transform can provide reliable results while at the same time improving the computational efficiency. [ABSTRACT FROM AUTHOR]

Offline handwritten signature identification has received less attention in comparison with the offline signature verification, despite its crucial applications such as in law-enforcements, automatic bank check and historical documents processing. In this paper, an Open Handwritten Signature Identification System (OHSIS) is proposed by using conjointly the Curvelet Transform (CT) and the One-Class classifier based on Principal Component Analysis (OC-PCA). CT is explored for feature generation due to its efficient characterization of curves contained into the local orientations within the signature image. While, OC-PCA is used for its effectiveness to absorb the high feature size generated by the CT and allows achieving at the same time an open system. Then, in order to improve the robustness of the OHSIS when few reference signatures are available, a new combination approach based on Choquet fuzzy integral is proposed to combine multiple individual OHSISs. Furthermore, a designing protocol with limited number of writers and reference signatures is proposed to perform a parameter-independent OHSIS. Experimental results conducted on standard CEDAR and GPDS handwritten signature datasets report 97.99% and 94.96% correct identification rate, respectively, which highlights the effectiveness of the proposed OHSIS since it can comfortably outperform the state-of-the-art when using few reference signatures. [ABSTRACT FROM AUTHOR]

This paper proposes two different methods for fusing multispectral (MS) and panchromatic (PAN) satellite images using the nonsubsampled contourlet transform (NSCT). The NSCT decomposes the images into several directional subbands at flexible resolutions. The finer subbands of the MS image decomposition, which represent the high frequency details, are modified with the subbands from PAN image. The inverse transform gives a high resolution MS representation of the given low resolution MS image. The paper also proposes the use of the parameters mean structural similarity index measure (MSSIM) and edge stability mean square error (ESMSE) to measure the quality of the fused image, in addition to standard parameters like correlation coefficient, PSNR, RASE and ERGAS. Experiments show that the proposed methods outperform standard fusion techniques in terms of both visual quality and quantitative error measures. The fused images obtained using the proposed methods show good structural similarity and better edge stability as the contourlet transform very well extracts the oriented edge details from the high resolution PAN image. [ABSTRACT FROM AUTHOR]

In X-ray computed tomography (CT), the presence of metal objects in a patient's body produces streak artifacts in the reconstructed images. During the past decades, many different methods were proposed for the reduction or elimination of the streaking artifacts. When scanning a patient, the projection data affected by metal objects (missing projections) appear as regions with high intensities in the sinogram. In spiral fan beam CT, these regions are sinusoid-like curves on sinogram. During the first time, if the metal curves are detected carefully, then, they can be replaced by corresponding unaffected projections using other slices or opposite views; therefore, the CT slices regenerated by the modified sonogram will be imaged with high quality. In this paper, a new method of the segmentation of metal traces in spiral fan-beam CT sinogram is proposed. This method is based on a sinogram curve detection using a curvelet transform followed by 2D Hough transform. The initial enhancement of the sinogram using modified curvelet transform coefficients is performed by suppressing all the coefficients of one band and applying 2D Hough transform to detect more precisely metal curves. To evaluate the performance of the proposed method for the detection of metal curves in a sinogram, precision and recall metrics are calculated. Compared with other methods, the results show that the proposed method is capable of detecting metal curves, with better precision and good recovery. [ABSTRACT FROM AUTHOR]

Correct mammography evaluation demands great expertise and rigorous interpretation of some radiographic features. The Breast Imaging Reporting and Data System (BI-RADS) is accepted as a standardized method to communicate mammographic findings. This report assigns a detailed description to breast masses in terms of their shape, margin, and density, a process highly dependent on the observer experience. This paper proposes a new automatic BI-RADS characterization of breast masses contained in a Regions of Interest (RoI). For doing so, the proposed approach learns relevant radiological characteristics from several multiscale decomposition of the visual information, the Zernike polynomials and Curvelet bases, which are optimally fused by a Multiple Kernel Learning (MKL) strategy. The method first assesses the presence of masses in the RoI by training a conventional support vector machine (SVM) classifier. Once a RoI is identified as mass-positive, it feeds a bank of SVM binary classifiers that selects the type of shape from the BI-RADS terms. The mass margin and density are then set by combining the BI-RADS labels of the five most similar shapes in the database. Evaluation was conducted using a set of 980 RoIs extracted from the Digital Database for Screening Mammography (DDSM) and 216 RoIs extracted from the INBreast database. Both database descriptions were updated to meet the fifth version of the BI-RADS lexicon. Masses were recognized with a sensitivity of 96.2% and a specificity of 93.1%, while shape, margin and density descriptions showed averaged sensitivity rates between 87.4% and 96.7% and specificity between 85.6% and 96.7%. This results outperformed the obtained when non-fused multiresolution features were used. These results suggest the proposed strategy may be useful in clinical scenarios and may contribute to the training of new radiologists as a second reader. [ABSTRACT FROM AUTHOR]

The process of interpretation of high-speed optical coherence tomography (OCT) images is restricted due to the large speckle noise. To address this problem, this paper proposes a new method using two-dimensional (2D) curvelet-based K-SVD algorithm for speckle noise reduction and contrast enhancement of intra-retinal layers of 2D spectral-domain OCT images. For this purpose, we take curvelet transform of the noisy image. In the next step, noisy sub-bands of different scales and rotations are separately thresholded with an adaptive data-driven thresholding method, then, each thresholded sub-band is denoised based on K-SVD dictionary learning with a variable size initial dictionary dependent on the size of curvelet coefficients' matrix in each sub-band. We also modify each coefficient matrix to enhance intra-retinal layers, with noise suppression at the same time. We demonstrate the ability of the proposed algorithm in speckle noise reduction of 100 publically available OCT B-scans with and without non-neovascular age-related macular degeneration (AMD), and improvement of contrast-to-noise ratio from 1.27 to 5.12 and mean-to-standard deviation ratio from 3.20 to 14.41 are obtained. [ABSTRACT FROM AUTHOR]

Seismic data contain random noise interference and are affected by irregular subsampling. Presently, most of the data reconstruction methods are carried out separately from noise suppression. Moreover, most data reconstruction methods are not ideal for noisy data. In this paper, we choose the multiscale and multidirectional 2D curvelet transform to perform simultaneous data reconstruction and noise suppression of 3D seismic data. We introduce the POCS algorithm, the exponentially decreasing square root threshold, and soft threshold operator to interpolate the data at each time slice. A weighing strategy was introduced to reduce the reconstructed data noise. A 3D simultaneous data reconstruction and noise suppression method based on the curvelet transform was proposed. When compared with data reconstruction followed by denoizing and the Fourier transform, the proposed method is more robust and effective. The proposed method has important implications for data acquisition in complex areas and reconstructing missing traces. [ABSTRACT FROM AUTHOR]

In this paper, we extend the continuous curvelet transform to the space of quaternion valued functions using convolution. We prove that the quaternionic curvelet transform is consistent with the continuous curvelet transform of complex valued functions. Also it satisfies the inversion formula, Parseval's formula and linearity property. Finally, we derive a convolution theorem for quaternionic curvelet transform and extend it to a suitable Boehmian space. [ABSTRACT FROM AUTHOR]

Traditional MRI technology may easily generate artifact due to slow imaging speed, therefore, MRI has low imagining quality and over-long sampling duration. Since wavelet transform cannot achieve the best approximation, image block theory is introduced in compressed sensing image reconstruction. In combination of the advantage of curvelet transform – it is suitable for expressing edge detail information and curve information, curvelet transform is utilized to conduct sparse representation of MRI image and proposed compressed sensing reconstruction algorithm of MRI image based on curvelet transform of image block. Signal to Noise Ratio (SNR), Relative L2 norm error (RLNE) and matching degree served as the evaluation indexes, and 4 groups of experiments about the influence of noise-free image, noised image, different sampling frequencies and different regularization parameters on the quality of reconstructed image were done. The results show that during image reconstruction, the algorithm proposed in this paper is superior to SIDCT and PBDCT in terms of three evaluation indexes. Besides, the algorithm owns strong ability to resist noise and good effects on keeping image detail and edge. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the minimax properties of Stein block thresholding in any dimension d with a particular emphasis on . Towards this goal, we consider a frame coefficient space over which minimaxity is proved. The choice of this space is inspired by the characterization provided in [L. Borup, M. Nielsen, Frame decomposition of decomposition spaces, J. Fourier Anal. Appl. 13 (1) (2007) 39–70] of family of smoothness spaces on , a subclass of so-called decomposition spaces [H.G. Feichtinger, Banach spaces of distributions defined by decomposition methods, II, Math. Nachr. 132 (1987) 207–237]. These smoothness spaces cover the classical case of Besov spaces, as well as smoothness spaces corresponding to curvelet-type constructions. Our main theoretical result investigates the minimax rates over these decomposition spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax (up to a log factor) in the least favorable situation. Another contribution is that the minimax rates given here are stated for a noise sequence model in the transform coefficient domain satisfying some mild assumptions. This covers for instance the Gaussian case with frames where the noise is not white in the coefficient domain. The choice of the threshold parameter is theoretically discussed and its optimal value is stated for some noise models such as the (non-necessarily i.i.d.) Gaussian case. We provide a simple, fast and a practical procedure. We also report a comprehensive simulation study to support our theoretical findings. The practical performance of our Stein block denoising compares very favorably to the BLS-GSM state-of-the art denoising algorithm on a large set of test images. A toolbox is made available for download on the Internet to reproduce the results discussed in this paper. [Copyright &y& Elsevier]

This paper presents new developments of directional filterbanks (DFBs). The motivation for the paper is the existence of multiresolution and multidirection orthogonal transform for two-dimensional (2-D) discrete signals. Based on the frequency supports of the ideal transform, a new uniformly, maximally decimated DFB with six highpass directional subbands and two lowpass subands is introduced. The uniform DFB (uDFB) can be implemented by a binary tree structure of two-channel filterbanks. The filterbank employed in the tree is shown to be alias-free decimation and permissible. The uDFB is then extended to a nonuniform case (nuDFB), which is still maximally decimated, by combining the two lowpass subbands. The nuDFB yields nonuniform frequency division, which composes of one lowpass filter with a decimation factor of one fourth and six highpass directional filters with a decimation factor of one eighth. The new DFBs offer alternative image decompositions, which overcome the limited directional selectivity of the separable wavelets and the limited multiresolution of the conventional DFB. The lowpass subband of the nuDFB can be used to obtain a multiresolution representation by simply reiterating the same nuDFB decomposition. On the other hand, the directional subbands can also be further refined by simply applying a two-channel conventional DFB at each highpass component. A simple design method yielding near orthogonal uniform and nonuniform multidimensional filterbanks is presented. Finally, the performances of the newly proposed nuDFB are compared with other conventional transforms in non-linear approximation, image denoising, and texture classification to demonstrate its potential. [ABSTRACT FROM AUTHOR]

Abdomen related diseases are responsible of many deaths every year. These deaths can be reduced by early diagnosis of abdomen diseases. Computer aided diagnosis (CAD) can play vital role in early detection of diseases. Hence, a novel CAD is proposed in this paper that can diagnose abdomen diseases like Hepatocellular carcinoma, cysts and Calculi using statistical curvelet texture descriptors. The proposed CAD is divided into four stages: (a) Image segmentation using active contours, (b) feature extraction, (c) feature selection and (d) abdomen disease classification. The regions of interest (ROIs) are segmented from 120CT images using active contour models. The statistical features are extracted from segmented ROIs. Further, the classifiers are used to evaluate the ability of feature set in diagnosis various diseases of abdomen. The performance metrics indicates that the proposed CAD achieves accuracy of 87.9% using curvelet coefficient features and neural network as classifier. [ABSTRACT FROM AUTHOR]

Purpose: Automatic measurement of the intima-media thickness (IMT) from ultrasound carotid images is an important task in clinical diagnosis. Many computer-based techniques for IMT measurement have been proposed to overcome the limits of manual segmentation. However, the robustness of the algorithms would be influenced by the inherent specklenoise of ultrasoundimage. This paper proposed a curvelet guided ant colony optimization (CGACO) strategy that could achieve satisfied accuracy for IMT measurement with improved robustness to noise. Methods: The curvelet-based orientation-selective (CBOS) filter was first introduced for speckle removal and edge enhancement. Different from conventional methods, CBOS filter processes the curvelet coefficients by orientations rather than by magnitude. Then, a specially designed two-leg ant colony optimization technique, combined with Otsu thresholding and Sobel edge detector, was proposed as a novel segmentation method to extract the media-adventitia (MA) and the lumen-intima (LI) boundaries. Finally, a coupled snake model was employed to further smooth the contours of MA and LI. Results: In addition to 224 carotid arteryimages acquired from 34 participants, simulated speckled images with nine levels of noise were also included in the database. The mean absolute distance errors of CGACO for LI interface tracings, MA interface tracings, and IMT measurements were 0.030 ± 0.027, 0.039 ± 0.036, and 0.041 ± 0.036 mm, respectively. Besides, CGACO had a correlation coefficient as high as 0.992 and a bias as low as -0.008. All these measures were comparable to or better than a previous technique and the manual segmentation. On the other hand, CGACO had the highest success rate of 98.7% in the segmentation of real data. It also maintained a much higher success rate in the segmentation of simulated images with different levels of specklenoise. Conclusions: The proposed technique showed accurate IMT measurement results. Furthermore, benefiting from the CBOS filter, the robustness to noise of the algorithm was substantially improved. Therefore, CGACO could provide a reliable way to segment the carotid artery from ultrasoundimages and could be used in clinical practice of IMT measurement, particularly in early atherosclerotic stages. [ABSTRACT FROM AUTHOR]

Introduction: Dermoscopy is a non-invasive in vivo imaging technique, used in dermatology in feature identification, among pigmented melanocytic neoplasms, from suspicious skin lesions. Often, in the skin exam is possible to ascertain markers, whose identification and proper characterization is difficult, even when it is used a magnifying lens and a source of light. Dermoscopic images are thus a challenging source of a wide range of digital features, frequently with clinical correlation. Among these markers, one of particular interest to diagnosis in skin evaluation is the reticular pattern. Methods: This paper presents a novel approach (avoiding pre-processing, e.g. segmentation and filtering) for reticular pattern detection in dermoscopic images, using texture spectral analysis. The proposed methodology involves a Curvelet Transform procedure to identify features. Results: Feature extraction is applied to identify a set of discriminant characteristics in the reticular pattern, and it is also employed in the automatic classification task. The results obtained are encouraging, presenting Sensitivity and Specificity of 82.35% and 76.79%, respectively. Conclusions: These results highlight the use of automatic classification, in the context of artificial intelligence, within a computer-aided diagnosis strategy, as a strong tool to help the human decision making task in clinical practice. Moreover, the results were obtained using images from three different sources, without previous lesion segmentation, achieving to a rapid, robust and low complexity methodology. These properties boost the presented approach to be easily used in clinical practice as an aid to the diagnostic process. [ABSTRACT FROM AUTHOR]

Classification of clustered breast microcalcifications into benign and malignant categories is an extremely challenging task for computerized algorithms and expert radiologists alike. In this paper we apply a multi-view-classifier for the task. We describe a two-step classification method that is based on a view-level decision, implemented by a logistic regression classifier, followed by a stochastic combination of the two view-level indications into a single benign or malignant decision. The proposed method was evaluated on a large number of cases from a standardized digital database for screening mammography (DDSM). Experimental results demonstrate the advantage of the proposed multi-view classification algorithm that automatically learns the best way to combine the views. [ABSTRACT FROM PUBLISHER]

Seismic interpolation, as an efficient strategy of providing reliable wavefields, belongs to large-scale computing problems. The rapid increase of data volume in high dimensional interpolation requires highly efficient methods to relieve computational burden. Most methods adopt the L[sub 1] norm as a sparsity constraint of solutions in some transformed domain: however, the L[sub 1] norm is non-differentiable and gradient-type methods cannot be applied directly. On the other hand, methods for unconstrained L[sub 1] norm optimisation always depend on the regularisation parameter which needs to be chosen carefully. In this paper, a fast gradient projection method for the smooth L[sub 1] problem is proposed based on the tight frame property of the curvelet transform that can overcome these shortcomings. Some smooth L[sub 1] norm functions are discussed and their properties are analysed, then the Huber function is chosen to replace the L[sub 1] norm. The novelty of the proposed method is that the tight frame property of the curvelet transform is utilised to improve the computational efficiency. Numerical experiments on synthetic and real data demonstrate the validity of the proposed method which can be used in large-scale computing. [ABSTRACT FROM AUTHOR]

In recent years, many studies have been performed to reconstruct traces missing from irregularly undersampled seismic data. In this paper, we introduce a new curvelet-transform-based projection onto convex sets (POCS) algorithm that applies the curvelet transform to 2D Fourier-transformed data in the f – k domain instead of data in the t – x domain for each iteration of the POCS algorithm. To verify the efficiency of the suggested method, it was applied to synthetic data generated using the Marmousi2 and Hess vertically transverse isotropy (VTI) models. The results clearly demonstrate that the presented algorithm, which applies the curvelet transform to data in the f – k domain, is superior to conventional POCS and curvelet-transform-based POCS in the t – x domain, especially for reconstructing events with diverse directions and various amplitudes. [ABSTRACT FROM AUTHOR]