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Image nonlocal self-similarity (NSS) property has been widely exploited via various sparsity models such as joint sparsity (JS) and group sparse coding (GSC). However, the existing NSS-based sparsity models are either too restrictive, e.g., JS enforces the sparse codes to share the same support, or too general, e.g., GSC imposes only plain sparsity on the group coefficients, which limit their effectiveness for modeling real images. In this paper, we propose a novel NSS-based sparsity model, namely, low-rank regularized group sparse coding (LR-GSC), to bridge the gap between the popular GSC and JS. The proposed LR-GSC model simultaneously exploits the sparsity and low-rankness of the dictionary-domain coefficients for each group of similar patches. An alternating minimization with an adaptive adjusted parameter strategy is developed to solve the proposed optimization problem for different image restoration tasks, including image denoising, image deblocking, image inpainting, and image compressive sensing. Extensive experimental results demonstrate that the proposed LR-GSC algorithm outperforms many popular or state-of-the-art methods in terms of objective and perceptual metrics. [ABSTRACT FROM AUTHOR]

Regularization-based image restoration is one of the most powerful tools in image processing and computer vision thanks to its flexibility for handling various inverse problems. However, designing an optimal regularization function still remains unsolved since natural images and related scene types have a complex structure. In this paper, we present a general and principled framework, called deeply aggregated alternating minimization (DeepAM). We design a convolutional neural network (CNN) to implicitly parameterize the regularizer of the alternating minimization (AM) algorithm. Contrary to the conventional AM algorithm based on a point-wise proximal mapping, the DeepAM projects intermediate estimate into a set of natural images via deep aggregation. Since the CNN is fully integrated into the AM procedure, all parameters can be jointly optimized through end-to-end training. These properties enable the DeepAM to converge with a small number of iterations, while maintaining an algorithmic simplicity. We show that the DeepAM outperforms state-of-the-art methods, including nonlocal-based methods, Plug-and-Play regularization, and recent data-driven approaches. The effectiveness of our framework is demonstrated in a variety of image restoration tasks: Guassian denoising, deraining, deblurring, super-resolution, color-guided depth upsampling, and RGB/NIR restoration. [ABSTRACT FROM AUTHOR]

We study the problem of image alignment for panoramic stitching. Unlike most existing approaches that are feature-based, our algorithm works on pixels directly, and accounts for errors across the whole images globally. Technically, we formulate the alignment problem as rank-1 and sparse matrix decomposition over transformed images, and develop an efficient algorithm for solving this challenging non-convex optimization problem. The algorithm reduces to solving a sequence of subproblems, where we analytically establish exact recovery conditions, convergence and optimality, together with convergence rate and complexity. We generalize it to simultaneously align multiple images and recover multiple homographies, extending its application scope toward vast majority of practical scenarios. The experimental results demonstrate that the proposed algorithm is capable of more accurately aligning the images and generating higher quality stitched images than the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are contaminated by multiplicative noise. Due to the edge-preserving feature of the total variation (TV), variational models with TV regularization have attracted much interest in removing multiplicative noise. However, the fidelity term of the variational model, based on maximum a posteriori estimation, is not convex, and so, it is usually difficult to find a global solution. Hence, the logarithmic function is used to transform the nonconvex variational model to the convex one. In this paper, instead of using the log, we exploit the mth root function to relax the nonconvexity of the variational model. An algorithm based on the augmented Lagrangian function, which has been applied to solve the log transformed convex variational model, can be applied to solve our proposed model. However, this algorithm requires solving a subproblem, which does not have a closed-form solution, at each iteration. Hence, we propose to adapt the linearized proximal alternating minimization algorithm, which does not require inner iterations for solving the subproblems. In addition, the proposed method is very simple and highly parallelizable; thus, it is efficient to remove multiplicative noise in huge SAR images. The proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation. [ABSTRACT FROM PUBLISHER]

The main aim of this paper is to develop an algorithm for blending of multiple images in the image-stitching process. Our idea is to propose a variational method containing an energy functional to determine both a stitched image and weighting mask functions of multiple input images for image blending. The existence of the solution of the proposed energy functional is shown. We also present an alternative minimizing algorithm to solve the proposed model numerically and show the convergence of this algorithm. Experimental results show that the proposed model works effectively and efficiently and that the proposed method is competitive with the tested existing methods under noisy conditions. [ABSTRACT FROM AUTHOR]

Speckles (multiplicative noise) in synthetic aperture radar (SAR) make it difficult to interpret the observed image. Due to the edge-preserving feature of total variation (TV), variational models with TV regularization have attracted much interest in reducing speckles. Algorithms based on the augmented Lagrangian function have been proposed to efficiently solve speckle-reduction variational models with TV regularization. However, these algorithms require inner iterations or inverses involving the Laplacian operator at each iteration. In this paper, we adapt Tseng's alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the Laplacian operator. The proposed method is very simple and highly parallelizable; therefore, it is very efficient to despeckle huge-size SAR images. Numerical results show that our proposed method outperforms the state-of-the-art algorithms for speckle-reduction variational models with a TV regularizer in terms of central-processing-unit time. [ABSTRACT FROM AUTHOR]

Blind deconvolution, which comprises simultaneous blur and image estimations, is a strongly ill-posed problem. It is by now well known that if multiple images of the same scene are acquired, this multichannel (MC) blind deconvolution problem is better posed and allows blur estimation directly from the degraded images. We improve the MC idea by adding robustness to noise and stability in the case of large blurs or if the blur size is vastly overestimated. We formulate blind deconvolution as an \ell1-regularized optimization problem and seek a solution by alternately optimizing with respect to the image and with respect to blurs. Each optimization step is converted to a constrained problem by variable splitting and then is addressed with an augmented Lagrangian method, which permits simple and fast implementation in the Fourier domain. The rapid convergence of the proposed method is illustrated on synthetically blurred data. Applicability is also demonstrated on the deconvolution of real photos taken by a digital camera. [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]

A wavelet inpainting problem refers to the problem of filling in missing wavelet coefficients in an image. A variational approach was used by Chan et al. The resulting functional was minimized by the gradient descent method. In this paper, we use an optimization transfer technique which involves replacing their univariate functional by a bivariate functional by adding an auxiliary variable. Our bivariate functional can be minimized easily by alternating minimization: for the auxiliary variable, the minimum has a closed form solution, and for the original variable, the minimization problem can be formulated as a classical total variation (TV) denoising problem and, hence, can be solved efficiently Using a dual formulation. We show that our bivariate functional is equivalent to the original univariate functional. We also show that Our alternating minimization is convergent. Numerical results show that the proposed algorithm is very efficient and outperforms that of Chan et al. [ABSTRACT FROM AUTHOR]