Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First, from the perspective of image statistics, a joint statistical modeling (JSM) in an adaptive hybrid space-transform domain is established, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Second, a new form of minimization functional for solving image inverse problem is formulated using JSM under regularization-based framework. Finally, in order to make JSM tractable and robust, a new Split-Bregman based algorithm is developed to efficiently solve the above severely underdetermined inverse problem associated with theoretical proof of convergence. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions on Circuits System and Video Technology (TCSVT). High resolution pdf version and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM

Residual-Sparse Fuzzy CC-Means Clustering Incorporating Morphological Reconstruction and Wavelet frames

Instead of directly utilizing an observed image including some outliers, noise or intensity inhomogeneity, the use of its ideal value (e.g. noise-free image) has a favorable impact on clustering. Hence, the accurate estimation of the residual (e.g. unknown noise) between the observed image and its ideal value is an important task. To do so, we propose an $\ell_0$ regularization-based Fuzzy $C$-Means (FCM) algorithm incorporating a morphological reconstruction operation and a tight wavelet frame transform. To achieve a sound trade-off between detail preservation and noise suppression, morphological reconstruction is used to filter an observed image. By combining the observed and filtered images, a weighted sum image is generated. Since a tight wavelet frame system has sparse representations of an image, it is employed to decompose the weighted sum image, thus forming its corresponding feature set. Taking it as data for clustering, we present an improved FCM algorithm by imposing an $\ell_0$ regularization term on the residual between the feature set and its ideal value, which implies that the favorable estimation of the residual is obtained and the ideal value participates in clustering. Spatial information is also introduced into clustering since it is naturally encountered in image segmentation. Furthermore, it makes the estimation of the residual more reliable. To further enhance the segmentation effects of the improved FCM algorithm, we also employ the morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, the segmented image is reconstructed by using a tight wavelet frame reconstruction operation. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.Comment: 12 pages, 11 figur

Variable-Wise Diagonal Preconditioning for Primal-Dual Splitting: Design and Applications

This paper proposes a method of designing appropriate diagonal preconditioners for a preconditioned primal-dual splitting method (P-PDS). P-PDS can efficiently solve various types of convex optimization problems arising in signal processing and image processing. Since the appropriate diagonal preconditioners that accelerate the convergence of P-PDS vary greatly depending on the structure of the target optimization problem, a design method of diagonal preconditioners for PPDS has been proposed to determine them automatically from the problem structure. However, the existing method has two limitations: it requires direct access to all elements of the matrices representing the linear operators involved in the target optimization problem, and it is element-wise preconditioning, which makes certain types of proximity operators impossible to compute analytically. To overcome these limitations, we establish an Operator-norm-based design method of Variable-wise Diagonal Preconditioning (OVDP). First, the diagonal preconditioners constructed by OVDP are defined using only the operator norm or its upper bound of the linear operator thus eliminating the need for their explicit matrix representations. Furthermore, since our method is variable-wise preconditioning, it keeps all proximity operators efficiently computable. We also prove that our preconditioners satisfy the convergence conditions of PPDS. Finally, we demonstrate the effectiveness and utility of our method through applications to hyperspectral image mixed noise removal, hyperspectral unmixing, and graph signal recovery.Comment: Submitted to IEEE Transactions on Signal Processin

Mixed noise removal using adaptive median based non-local rank minimization

publishedVersio

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS