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Hyper-wavelet transforms, such as a non-subsampled shearlet transform (NSST), are one of the mainstream algorithms for removing random noise from ground-penetrating radar (GPR) images. Because GPR image noise is non-uniform, the use of a single fixed threshold for noisy coefficients in each sub-band of hyper-wavelet denoising algorithms is not appropriate. To overcome this problem, a novel NSST-based GPR image denoising grey wolf optimisation (GWO) algorithm is proposed. First, a time-varying threshold function based on the trend of noise changes in GPR images is proposed. Second, an edge area recognition and protection method based on the Canny algorithm is proposed. Finally, GWO is employed to select appropriate parameters for the time-varying threshold function and edge area protection method. The Natural Image Quality Evaluator is utilised as the optimisation index. The experiment results demonstrate that the proposed method provides excellent noise removal performance while protecting edge signals.

Highlights • This paper makes use of a deep CNN for image denoising. • The network is trained using edges given by the canny algorithm. • The proposed method can better recover edges of noisy images. Abstract This paper introduces a novel denoising approach making use of a deep convolutional neural network to preserve image edges. The network is trained by using the edge map obtained from the well-known Canny algorithm and aims at determining if a noisy patch in non-subsampled shearlet domain corresponds to the location of an edge. In the first step of the proposed denoising algorithm, we use the non-subsampled shearlet transform to decompose the noisy image into a low-frequency subband and a series of high-frequency subbands. Subsequently, 3D blocks are formed by stacking 2D blocks of high-frequency subbands along a specific direction. Each 3D patch is then fed to the trained deep convolutional neural network to determine if it belongs to the edge-related class or not. Finally, the NSST (non-subsampled shearlet transform) coefficients belonging to the edge-related class remain unchanged, and those not belonging to the edge-related class are denoised by the shrinkage method using an adaptive threshold. Experimental results on various test images including benchmark grayscale images and medical ultrasound images demonstrate that the proposed method achieves better performance compared to some state-of-the-art denoising approaches. [ABSTRACT FROM AUTHOR]

Blind image denoising and edge-preserving are two primary challenges to recover an image from low-level vision to high-level vision. Blind denoising requires a single denoiser can denoise images with any intensity of noise, and it has practical utility since accurate noise levels cannot be acquired from realistic images. On the other hand, edge preservation can provide more image features for subsequent processing which is also important for the denoising. In this paper, we propose a novel blind universal image denoiser to remove synthesis and realistic noise while preserving the image texture. The denoiser consists of noise network and prior network parallelly, and then a fusion block is used to give the weight between these two networks to balance computation cost and denoising performance. We also use the Non-subsampled Shearlet Transform (NSST) to enlarge the size of receptive field to obtain more detailed information. Extensive denoising experiments on synthetic images and realistic images show the effectiveness of our denoiser. [ABSTRACT FROM AUTHOR]

Many algorithms to enhance low-light images have been proposed. They often assume that low-light images are clean. However, images acquired in low-light environments often contain noise. Consequently, those enhancement algorithms often simultaneously amplify the noise. For the purpose of overcoming the above-mentioned shortcoming, we propose a framework of joint enhancement and denoising. It is accomplished using the non-subsampled shearlet transform with adaptive soft-threshold shrinkage. The multi-scale feature of the proposed model can better represent edge textures in an image and decomposes an image into two parts of low frequency and high frequency for separate processing. Experimental results show that, compared with state-of-the-art methods, the proposed algorithm can achieve better quality in terms of objective assessment and subjective assessment. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the traditional denoising algorithms still exist some residual noise when removing large noise from noisy images, this paper proposed an improved image denoising algorithm based on normal inverse Gaussian model. The algorithm decomposed image into frequency coefficients in the non-subsampled shearlet transform, and used the optimal linear threshold interpolation shrink function to improve normal inverse Gaussian model as the coefficient distribution model. Then the algorithm built a statistic model using the high frequency subband decomposition coefficients, and finally achieved the noise removal using Bayesian maximum a posterior probability. Experimental results show that corrupted ima-ges with additive Gaussian noise over a wide range of noise variance. The proposed method can effectively preserve the image details and texture information, and a state-of-the-art performance in terms of peak signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

In this paper, an image denoising method is proposed which uses sparse un-mixing by variable splitting and augmented Lagrangian (SUnSAL) classifier in the non-subsampled shearlet transform (NSST) domain. To this aim, the noisy image is decomposed into various scales and directional components using the NSST and then the feature vector for a pixel is constituted by the spatial regularity in the NSST domain. Subsequently, the NSST detail coefficients are labeled as edge-related coefficients or noise-related ones by using the SUnSAL classifier. The noisy coefficients of the NSST subbands are then denoised by the shrink method, which uses the adaptive Bayesian threshold for denoising. Finally, the inverse NSST transform is applied to the denoised coefficients. Our experiments demonstrate that the proposed approach improves the image quality in terms of both subjective and objective inspections, compared with some other state-of-the-art denoising techniques. [ABSTRACT FROM AUTHOR]

In this work, a non-subsampled shearlet transform (NSST) based anisotropic diffusion method is proposed. In the proposed method, the NSST transform is firstly applied to the noisy image to provide several scale and directional components. Then, the NSST coefficients are classified into textured regions and noise-related ones by using Sparse Un-mixing by the variable Splitting and Augmented Lagrangian (SUnSAL) classifier. Subsequently, an energy function is formed by the noise-related coefficients to be minimized by diffusion equations. The noisy free image is approximated from the denoised coefficients obtained by the anisotropic diffusion method and textured coefficients which are remained unchanged. Visual and quantitative assessments demonstrate that the proposed method outperforms the state-of-art denoising methods in terms of noise removal and detail preservation. [ABSTRACT FROM AUTHOR]

To overcome the problem of image de-noising, a novel technique based on non-subsampled shearlet transform (NSST) and intuitionistic fuzzy entropy (IFE) is proposed in this paper. Firstly, as a recently developed geometric analysis tool, NSST is utilized to decompose the noised image into multi-scale and multi-directional sub-band images. Secondly, the basic model of intuitionistic fuzzy entropy (IFE) is updated to be an improved IFE, with which each pixel in the noised image is adaptively defined by a pair of membership degree and non-membership degree, and each pixel's weight value can be figured out via improved IFE. Thirdly, the final de-noising image can be obtained by using inverse NSST. Besides, the algorithm for image de-noising is devised and concrete steps are also given. By following the above steps, the noising pixels in the image can be filtered well. Moreover, experimental results indicate that the technique is much more effective compared with other traditional filter ones. [ABSTRACT FROM AUTHOR]

Abstract: The denoising of a natural image corrupted by additive Gaussian white noise is a classical problem in image processing. A new image denoising method is proposed by using the dependencies between the non-subsampled shearlet transform (NSST) coefficients and their neighbors. The NSST is well known for its approximate shift invariance and better directional selectivity, which are very important in image denoising. In order to take account of the dependency between the current NSST coefficient and its neighbors, a new multivariate probability density function (pdf) is exploited, and a multivariate shrinkage function for image denoising is derived from it by using the maximum a posteriori (MAP) estimator. Then, the blend of the proposed multivariate shrinkage function and its method noise thresholding using NSST is proposed for image denoising. Experimental results demonstrate that the proposed method is very competitive when compared with other existing denoising methods in the literature. [Copyright &y& Elsevier]

Hyper-wavelet transforms, such as a non-subsampled shearlet transform (NSST), are one of the mainstream algorithms for removing random noise from ground-penetrating radar (GPR) images. Because GPR image noise is non-uniform, the use of a single fixed threshold for noisy coefficients in each sub-band of hyper-wavelet denoising algorithms is not appropriate. To overcome this problem, a novel NSST-based GPR image denoising grey wolf optimisation (GWO) algorithm is proposed. First, a time-varying threshold function based on the trend of noise changes in GPR images is proposed. Second, an edge area recognition and protection method based on the Canny algorithm is proposed. Finally, GWO is employed to select appropriate parameters for the time-varying threshold function and edge area protection method. The Natural Image Quality Evaluator is utilised as the optimisation index. The experiment results demonstrate that the proposed method provides excellent noise removal performance while protecting edge signals. [ABSTRACT FROM AUTHOR]

In this paper, we propose an advanced framework for image denoising using bilateral filtering based non-subsampled shearlet transform (NSST). Initially, we apply the NSST to decompose noisy input image into high and low frequency coefficients. The weighted bilateral filter (WBF) is then used to remove the noise from the low frequency coefficients while; thresholding is used to remove noise from the high frequency coefficients. The outputs of both the process are combined to form the resultant image. Finally, the inverse NSST is applied on the resultant output to estimate the final denoised image. To ensure validity of the proposed model, we conduct several experiments by considering different grayscale images with various noise variances. The qualitative and quantitative comparison is illustrated and it shows the improved performance of the proposed method as compared to the other conventional image denoising methods. Mathematical and simulation results are presented to show the validity of our work. [ABSTRACT FROM AUTHOR]