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In this paper, we study nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ ONTD on the image data sets from the real world applications including face recognition, image representation, and hyperspectral unmixing. Numerical results are shown to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Tone mapping methods aim to display a high-dynamic-range image on a common 8-bit liquid crystal display by compressing the dynamic range. We propose a simple but effective tone mapping operator (TMO) by using localized gamma correction. As the TMO involves the contrast and the color saturation components, our idea is to make use of gamma correction to adjust the values of these two components locally. The local weights can be determined according to the pixel values within local regions. Such an adaption can be handled more effectively for the contrast and color saturation in dark and bright regions of an image. Numerical examples are given to demonstrate the merit of the localized gamma correction scheme. The experiments reported in this paper illustrate that the proposed method can provide visually pleasing results, and it is also competitive with the other testing methods. [ABSTRACT FROM AUTHOR]

In this paper, we address the total variation (TV)-based nonlinear image restoration problems. In nonlinear image restoration problems, an original image is corrupted by a spatiallyinvariant blur, the build-in nonlinearity in imaging system, and the additive Gaussian white noise. We study the objective function consisting of the nonlinear least squares data-fitting term and the TV regularization term of the restored image. By making use of the structure of the objective function, an efficient alternating direction method of multipliers can be developed for solving the proposed model. The convergence of the numerical scheme is also studied. Numerical examples, including nonlinear image restoration and high-dynamic range imaging are reported to demonstrate the effectiveness of the proposed model and the efficiency of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study image enhancement by using sparse and redundant representations of the reflectance component in the Retinex model over a learned dictionary. This approach is different from existing variational methods, and the advantage of this approach is that the reflectance component in the Retinex model can be represented with more details by the dictionary. A variational method based on the dynamic dictionaries is adopted here, where it changes with respect to iterations of the enhancement algorithm. Numerical examples are also reported to demonstrate that the proposed methods can provide better visual quality of the enhanced high-contrast images than the other variational methods, i.e., revealing more details in the low-light part. [ABSTRACT FROM AUTHOR]

The JPEG compression method is among the most successful compression schemes since it readily provides good compressed results at a rather high compression ratio. However, the decompressed result of the standard JPEG decompression scheme usually contains some visible artifacts, such as blocking artifacts and Gibbs artifacts (ringing), especially when the compression ratio is rather high. In this paper, a novel artifact reducing approach for the JPEG decompression is proposed via sparse and redundant representations over a learned dictionary. Indeed, an effective two-step algorithm is developed. The first step involves dictionary learning and the second step involves the total variation regularization for decompressed images. Numerical experiments are performed to demonstrate that the proposed method outperforms the total variation and weighted total variation decompression methods in the measure of peak of signal to noise ratio, and structural similarity. [ABSTRACT FROM AUTHOR]

In many sparsity-based image processing problems, compared with the convex ℓ 1 norm approximation of the nonconvex ℓ 0 quasi-norm, one can often preserve the structures better by taking full advantage of the nonconvex ℓ p quasi-norm (0 ≤ p < 1). In this paper, we propose a nonconvex ℓ p quasi-norm approximation in the total generalized variation (TGV)-shearlet regularization for image reconstruction. By introducing some auxiliary variables, the nonconvex nonsmooth objective function can be solved by an efficient alternating direction method of multipliers with convergence analysis. Especially, we use a generalized iterated shrinkage operator to deal with the ℓ p quasi-norm subproblem, which is easy to implement. Extensive experimental results show clearly that the proposed nonconvex sparsity approximation outperforms some state-of-the-art algorithms in both the visual and quantitative measures for different sampling ratios and noise levels. [ABSTRACT FROM AUTHOR]

Nonsmooth nonconvex regularization has remarkable advantages for the restoration of piecewise constant images. Constrained optimization can improve the image restoration using a priori information. In this paper, we study regularized nonsmooth nonconvex minimization with box constraints for image restoration. We present a computable positive constant \theta for using nonconvex nonsmooth regularization, and show that the difference between each pixel and its four adjacent neighbors is either 0 or larger than \theta in the recovered image. Moreover, we give an explicit form of \theta for the box-constrained image restoration model with the non-Lipschitz nonconvex \ellp-norm (0

SUMMARY A crucial aspect of spectral image analysis is the identification of the materials present in the object or scene being imaged and to quantify their abundance in the mixture. An increasingly useful approach to extracting such underlying structure is to employ image classification and object identification techniques to compressively represent the original data cubes by a set of spatially orthogonal bases and a set of spectral signatures. Owing to the increasing quantity of data usually encountered in hyperspectral data sets, effective data compressive representation is an important consideration, and noise and blur can present data analysis problems. In this paper, we develop image segmentation methods for hyperspectral space object material identification. We also couple the segmentation with a hyperspectral image data denoising/deblurring model and propose this method as an alternative to a tensor factorization methods proposed recently for space object material identification. The model provides the segmentation result and the restored image simultaneously. Numerical results show the effectiveness of our proposed combined model in hyperspectral material identification. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the image processing community, there have recently been many restoration and reconstruction problems that can be reformulated into linearly constrained convex programming models whose objective functions have separable structures. These favorable reformulations have promoted impressive applications of the alternating direction method (ADM) in the field of image processing. At each iteration, the computation of ADM is dominated by solving two subproblems exactly. However, in many restoration and reconstruction applications, it is cither impossible or extremely expensive to obtain exact solutions of these ADM subproblems. This fact urges the development on inexact versions of ADM, which allow the generated ADM subproblems to be solved approximately subject to certain inexactness criteria. In this paper, we develop some truly implementable inexact ADMs whose inexactness criteria controlling the accuracy of the ADM subproblems are easily implementable. The convergence of the new inexact ADMs will be proved. Numerical results on several image processing problems will be given to illustrate the effectiveness of the proposed inexact ADMs. [ABSTRACT FROM AUTHOR]

In this paper, we propose and present an algorithm for total variation (TV)-based blind deconvolution. Both the unknown image and blur can be estimated within an alternating minimization framework. With the generalized cross-validation (GCV) method, the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps. Experimental results confirm that the performance of the proposed algorithm is better than variational Bayesian blind deconvolution algorithms with Student's-t priors or a total variation prior. [ABSTRACT FROM AUTHOR]

The goal of this paper is to provide a theoretical study of a total variation (TV) dictionary model. Based on the properties of convex analysis and bounded variation functions, the existence of solutions of the TV dictionary model is proved. We then show that the dual form of the model can be given by the minimization of the sum of the l¹-norm of the dual solution and the Bregman distance between the curvature of the primal solution and the subdifferential of TV norm of the dual solution. This theoretical result suggests that the dictionary must represent sparsely the curvatures of solution image in order to obtain a better denoising performance. [ABSTRACT FROM AUTHOR]

Abstract: We consider the iterative solution of unconstrained minimization problems arising from nonlinear image restoration. Our approach is based on a novel generalized BFGS method for such large-scale image restoration minimization problems. The complexity per step of the method is of operations and only memory allocations are required, where is the number of image pixels. Based on the results given in [Carmine Di Fiore, Stefano Fanelli, Filomena Lepore, Paolo Zellini, Matrix algebras in quasi-Newton methods for unconstrained minimization, Numer. Math. 94 (2003) 479–500], we show that the method is globally convergent for our nonlinear image restoration problems. Experimental results are presented to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: The main aim of this paper is to employ the total variation (TV) inpainting model to superresolution imaging problems. We focus on the problem of reconstructing a high-resolution image from several decimated, blurred and noisy low-resolution versions of the high-resolution image. We propose a general framework for multiple shifted and multiple blurred low-resolution image frames which subsumes several well-known superresolution models. Moreover, our framework allows an arbitrary pattern of missing pixels and in particular missing frames. The proposed model combines the TV inpainting model with the framework to formulate the superresolution image reconstruction problem as an optimization problem. A distinct feature of our model is that in regions without missing pixels, the reconstruction process is regularized by TV minimization whereas in regions with missing pixels or missing frames, they are reconstructed automatically by means of TV inpainting. A fast algorithm based on fixed-point iterations and preconditioning techniques is investigated to solve the associated Euler–Lagrange equations. Experimental results are given to show that the proposed TV superresolution imaging model is effective and the proposed algorithm is efficient. [Copyright &y& Elsevier]

We address the minimization of regularized convex cost functions which are customarily used for edge-preserving restoration and reconstruction of signals and images. In order to accelerate computation, the multiplicative and the additive half-quadratic reformulation of the original cost-function have been pioneered in Geman and Reynolds [IEEE Trans. Pattern Anal. Machine Intelligence, 14 (1992), pp. 367--383] and Geman and Yang IEEE Trans. Image Process., 4 (1995), pp. 932--946]. The alternate minimization of the resultant (augmented) cost-functions has a simple explicit form. The goal of this paper is to provide a systematic analysis of the convergence rate achieved by these methods. For the multiplicative and additive half-quadratic regularizations, we determine their upper bounds for their root-convergence factors. The bound for the multiplicative form is seen to be always smaller than the bound for the additive form. Experiments show that the number of iterations required for convergence for the multiplicative form is always less than that for the additive form. However, the computational cost of each iteration is much higher for the multiplicative form than for the additive form. The global assessment is that minimization using the additive form of half-quadratic regularization is faster than using the multiplicative form. When the additive form is applicable, it is hence recommended. Extensive experiments demonstrate that in our MATLAB implementation, both methods are substantially faster (in terms of computational times) than the standard MATLAB Optimization Toolbox routines used in our comparison study. [ABSTRACT FROM AUTHOR]

Super-resolution image reconstruction refers to obtaining an image at a resolution higher than that of a camera (sensor) used in recording the image. In this paper, we present a new joint minimization model in which an objective function is set up consisting of three terms: the data fitting term, the regularization terms for the reconstructed image and the observed low-resolution images. An alternating minimization iterative algorithm is proposed and developed to reconstruct the image. We give a convergence analysis of the alternating minimization iterative algorithm and show that it converges for H1-norm regularization functional. Numerical examples are given to illustrate the effectiveness of the joint minimization model and the efficiency of the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Blur removal is an important problem in signal and image processing. In this article, we formulate the deblurring problem within a wavelet framework and design a methodology to find deblurring filters. Using these deblurring filters, we derive an iterative deblurring algorithm and prove its convergence. Simulation results are reported to illustrate the proposed framework and methodology. © 2004 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 113–121, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20014 [ABSTRACT FROM AUTHOR]

Many image processing applications require computing approximate solutions of very large, ill-conditioned linear systems. Physical assumptions of the imaging system usually dictate that the matrices in these linear systems have exploitable structure. The specific structure depends on (usually simplifying) assumptions of the physical model and other considerations such as boundary conditions. When reflexive (Neumann) boundary conditions are used, the coefficient matrix is a combination of Toeplitz and Hankel matrices. Kronecker products also occur, but this structure is not obvious from measured data. In this paper we discuss a scheme for computing a (possibly approximate) Kronecker product decomposition of structured matrices in image processing, which extends previous work by Kamm and Nagy [SIAM J. Matrix Anal. Appl., 22 (2000), pp. 155–172] to a wider class of image restoration problems. [ABSTRACT FROM AUTHOR]

Superresolution image reconstruction refers to obtaining an image at a resolution higher than that of the camera (sensor) used in recording the image. In this article, we present a joint minimization model with an objective function setup that comprises three terms: the data-fitting term (DFT), the regularization term for the reconstructed image, and the observed low-resolution images. An alternating minimization iterative algorithm is presented to reconstruct the image. We also analyze the alternating minimization iterative algorithm and show that it converges globally for H1-norm or total-variation regularization that are functional for the reconstructed image. Numeric examples are given to illustrate the effectiveness of the joint minimization model and the efficiency of the algorithm. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 13, 153–160, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10053 [ABSTRACT FROM AUTHOR]

Multiple undersampled images of a scene are often obtained by using a charge-coupled device (CCD) detector array of sensors that are shifted relative to each other by subpixel displacements. This geometry of sensors, where each sensor has a subarray of sensing elements of suitable size, has been popular in the task of attaining spatial resolution enhancement from the acquired low-resolution degraded images that comprise the set of observations. With the objective of improving the performance of the signal processing algorithms in the presence of the ubiquitous perturbation errors of displacements around the ideal subpixel locations (because of imperfections in fabrication), in addition to noisy observation, the errors-in-variables or the total least-squares method is used in this paper. A regularized constrained total least-squares (RCTLS) solution to the problem is given, which requires the minimization of a nonconvex and nonlinear cost functional. Simulations indicate that the choice of the regularization parameter influences significantly the quality of the solution. The L-curve method is used to select the theoretically optimum value of the regularization parameter instead of the unsound but expedient trial-and-error approach. The expected superiority of this RCTLS approach over the conventional least-squares theory-based algorithm is substantiated by example. © 2002 John Wiley & Sons, Inc. Int J Imaging Syst Technol 12, 35–42, 2002 [ABSTRACT FROM AUTHOR]

Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for one-dimensional problems and block-Toeplitz­Toeplitz- block matrices for two-dimensional cases. They are computationally intensive to invert especially in the block case. If the periodic boundary condition is used, the matrices become (block) circulant and can be diagonalized by discrete Fourier transform matrices. In this paper, we consider the use of the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary). The resulting matrices are (block) Toeplitz-plus-Hankel matrices. We show that for symmetric blurring functions, these blurring matrices can always be diagonalized by discrete cosine transform matrices. Thus the cost of inversion is significantly lower than that of using the zero or periodic boundary conditions. We also show that the use of the Neumann boundary condition provides an easy way of estimating the regularization parameter when the generalized cross-validation is used. When the blurring function is nonsymmetric, we show that the optimal cosine transform preconditioner of the blurring matrix is equal to the blurring matrix generated by the symmetric part of the blurring function. Numerical results are given to illustrate the efficiency of using the Neumann boundary condition. [ABSTRACT FROM AUTHOR]

Robust low-rank tensor completion plays an important role in multidimensional data analysis against different degradations, such as Gaussian noise, sparse noise, and missing entries, and has a variety of applications in image processing and computer vision. In this paper, we investigate the problem of low-rank tensor completion with different degradations for third-order tensors, and propose a transformed tensor nuclear norm method combined the tensor ℓ 1 norm with total variational (TV) regularization. Our model is based on a recently proposed algebraic framework in which the transformed tensor nuclear norm is introduced to capture lower transformed multi-rank by using suitable unitary transformations. We adopt the tensor ℓ 1 norm to detect the sparse noise, and the TV regularization to preserve the piecewise smooth structure along the spatial and tubal dimensions. Moreover, a symmetric Gauss–Seidel based alternating direction method of multipliers is developed to solve the resulting model and its global convergence is established under very mild conditions. Extensive numerical examples on both hyperspectral images and video datasets are carried out to demonstrate the superiority of the proposed model compared with several existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The robust tensor recovery problem consists in reconstructing a tensor from a sample of entries corrupted by noise, which has attracted great interest in a wide range of practical situations such as image processing and computer vision. In this paper, we study robust tensor recovery for third-order tensors with different degradations, which aims to recover a tensor from partial observations corrupted by Gaussian noise and sparse noise simultaneously. In contrast to traditional approaches based on the tensor nuclear norm penalty for the low-rank component and the tensor ℓ1 norm penalty for the sparse component, we propose a nonlocal robust low-rank tensor recovery model with nonconvex regularization (NRTRM) to explore the global low-rankness and nonlocal self-similarity of the underlying tensor. The NRTRM method is first to extract similar patched-tubes to form a third-order sub-tensor. Then a class of nonconvex low-rank penalties and nonconvex sparse penalties are employed to explore the low-rank component and the sparse corruptions for such sub-tensor, respectively. Moreover, a proximal alternating linearized minimization algorithm is developed to solve the resulting model in each group and its convergence is established under very mild conditions. Extensive numerical experiments on both multispectral images and video datasets demonstrate the superior performance of NRTRM in comparison with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a spatially variant total variational model to correct chromatic aberration (CA) that causes false color artifacts near edges in captured images. In general, it may be very difficult to determine suitably CA regions in captured images. Instead of using local image processing methods, our idea is to make use of spatially variant model to control the gradient and intensity matching between the red and blue color channels and the green color channel at the edges. The total variation regularization is also employed to constraint the change of the intensity of red and blue color channels during the gradient and intensity matching. We present both theoretical results and algorithms for the proposed model. Experimental results are given to illustrate the effectiveness of the proposed model and algorithm and show that their corrected images are visually better than those corrected by the other testing methods. [ABSTRACT FROM AUTHOR]

As an important pre-processing step for many related computer vision tasks, color image denoising has attracted considerable attention in image processing. However, traditional methods often regard the red, green, and blue channels of color images independently without considering the correlations among the three channels. In order to overcome this deficiency, this paper proposes a novel dictionary method for color image denoising based on pure quaternion representation, which efficiently deals with both single-channel and cross-channel information. The pure quaternion constraint is firstly used to force the sparse representations of color images to contain only red, green, and blue color information. Moreover, a total variation regularization is proposed in the quaternion domain and embedded into the pure quaternion-based representation model, which is effective to recover the sharp edges of color images. To solve the proposed model, a new numerical scheme is also developed based on the alternating minimization method (AMM). Experimental results demonstrate that the proposed model has better denoising results than the state-of-the-art methods, including a deep learning approach DnCNN, in terms of PSNR, SSIM, and visual quality. [ABSTRACT FROM AUTHOR]

Heterogeneous transfer learning has recently gained much attention as a new machine learning paradigm in which the knowledge can be transferred from source domains to target domains in different feature spaces. Existing works usually assume that source domains can provide accurate and useful knowledge to be transferred to target domains for learning. In practice, there may be noise appearing in given source (text) and target (image) domains data, and thus, the performance of transfer learning can be seriously degraded. In this paper, we propose a robust and non-negative collective matrix factorization model to handle noise in text-to-image transfer learning, and make a reliable bridge to transfer accurate and useful knowledge from the text domain to the image domain. The proposed matrix factorization model can be solved by an efficient iterative method, and the convergence of the iterative method can be shown. Extensive experiments on real data sets suggest that the proposed model is able to effectively perform transfer learning in noisy text and image domains, and it is superior to the popular existing methods for text-to-image transfer learning. [ABSTRACT FROM AUTHOR]

Comments on an article about matrix formulation arising from the constrained optimization of the least squares restoration of multichannel images. Equation for the degradation of multichannel images.

Multiplicative noise removal is a challenging image processing problem, and most existing methods are based on the maximum a posteriori formulation and the logarithmic transformation of multiplicative denoising problems into additive denoising problems. Sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, in this paper, we propose to learn a dictionary from the logarithmic transformed image, and then to use it in a variational model built for noise removal. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio, and mean absolute deviation error, the proposed algorithm outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel supervised nonnegative matrix factorization-based framework for both image classification and annotation. The framework consists of two phases: training and prediction. In the training phase, two supervised nonnegative matrix factorizations for image descriptors and annotation terms are combined to identify the latent image bases, and to represent the training images in the bases space. These latent bases can capture the representation of the images in terms of both descriptors and annotation terms. Based on the new representation of training images, classifiers can be learnt and built. In the prediction phase, a test image is first represented by the latent bases via solving a linear least squares problem, and then its class label and annotation can be predicted via the trained classifiers and the proposed annotation mapping model. In the algorithm, we develop a three-block proximal alternating nonnegative least squares algorithm to determine the latent image bases, and show its convergent property. Extensive experiments on real-world image data sets suggest that the proposed framework is able to predict the label and annotation for testing images successfully. Experimental results have also shown that our algorithm is computationally efficient and effective for image classification and annotation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of segmentation of large collections of images. We propose a semisupervised optimization model that determines an efficient segmentation of many input images. The advantages of the model are twofold. First, the segmentation is highly controllable by the user so that the user can easily specify what he/she wants. This is done by allowing the user to provide, either offline or interactively, some (fully or partially) labeled pixels in images as strong priors for the model. Second, the model requires only minimal tuning of model parameters during the initial stage. Once initial tuning is done, the setup can be used to automatically segment a large collection of images that are distinct but share similar features. We will show the mathematical properties of the model such as existence and uniqueness of solution and establish a maximum/minimum principle for the solution of the model. Extensive experiments on various collections of biological images suggest that the proposed model is effective for segmentation and is computationally efficient. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors from multisensors. Preconditioned conjugate gradient methods with cosine transform based preconditioners and incomplete factorization based preconditioners are applied to solve this image reconstruction problem. Numerical examples are given to demonstrate the efficiency of these preconditioners. We find that cosine transform based preconditioners are effective when the number of shifted low-resolution frames are large, but are less effective when the number is small. However, incomplete factorization based preconditioners work quite well independent of the number of shifted low-resolution frames. [Copyright &y& Elsevier]

Abstract Most of existing image categorizations assume that the given datasets have a good resolution and quality. However, the assumption is often violated in real applications. In this paper, we study the low-resolution (LR) image categorization. By utilizing labeled high-resolution (HR) images as auxiliary information, we formulate the problem as a heterogeneous domain adaptation problem and propose a Discriminative Joint Distribution Adaptation (DJDA) model to solve it. The DJDA model projects both LR and HR images into an intermediate subspace with a well-designed objective function, where the distance between classes is expected to be enlarged and the distribution divergence to be reduced. As a result, the discriminative knowledge for HR images can be transferred effectively to LR images. Experimental results demonstrate the proposed DJDA method produces significantly superior categorization accuracies against state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

• We propose a new nonconvex l 2 − l p approximation of the Mumford–Shah model for image segmentation. • Our model adopts a two-stage image segmentation strategy and we use a closed-form p -shrinkage operator to deal with the l p quasi-norm subproblem in the first stage. • We utilize the K-means method to select the thresholds automatically and get good segmentation results both qualitatively and quantitatively. Image segmentation is of great importance in image processing. In this paper, we propose a two-stage image segmentation strategy based on the nonconvex ℓ 2 − ℓ p approximation of the Mumford–Shah (MS) model, where we use the nonconvex ℓ p (0 < p < 1) regularizer to approximate the Hausdorff measure and to extract more boundary information. In the first stage, we solve the nonconvex variant of the MS model efficiently via the split-Bregman algorithm. Moreover, we use a closed-form p -shrinkage operator to deal with the ℓ p quasi-norm subproblem, which is easy to implement. The second stage is segmenting the u obtained in the first stage into different phases with thresholds determined by the K-means clustering method. We compare our method with several state-of-the-art methods both qualitatively and quantitatively to demonstrate the effectiveness and advantages of our strategy. [ABSTRACT FROM AUTHOR]

Introduces several articles on high-resolution imaging published in the March 1, 2004 issue of "International Journal of Imaging Systems and Technology."