Efficient Iterative Regularization Method for Total Variation-Based Image Restoration

Total variation (TV) regularization has received much attention in image restoration applications because of its advantages in denoising and preserving details. A common approach to address TV-based image restoration is to design a specific algorithm for solving typical cost function, which consists of conventional ℓ2 fidelity term and TV regularization. In this work, a novel objective function and an efficient algorithm are proposed. Firstly, a pseudoinverse transform-based fidelity term is imposed on TV regularization, and a closely-related optimization problem is established. Then, the split Bregman framework is used to decouple the complex inverse problem into subproblems to reduce computational complexity. Finally, numerical experiments show that the proposed method can obtain satisfactory restoration results with fewer iterations. Combined with the restoration effect and efficiency, this method is superior to the competitive algorithm. Significantly, the proposed method has the advantage of a simple solving structure, which can be easily extended to other image processing applications.

Weighted Group Sparsity-Constrained Tensor Factorization for Hyperspectral Unmixing

Recently, unmixing methods based on nonnegative tensor factorization have played an important role in the decomposition of hyperspectral mixed pixels. According to the spatial prior knowledge, there are many regularizations designed to improve the performance of unmixing algorithms, such as the total variation (TV) regularization. However, these methods mostly ignore the similar characteristics among different spectral bands. To solve this problem, this paper proposes a group sparse regularization that uses the weighted constraint of the L2,1 norm, which can not only explore the similar characteristics of the hyperspectral image in the spectral dimension, but also keep the data smooth characteristics in the spatial dimension. In summary, a non-negative tensor factorization framework based on weighted group sparsity constraint is proposed for hyperspectral images. In addition, an effective alternating direction method of multipliers (ADMM) algorithm is used to solve the algorithm proposed in this paper. Compared with the existing popular methods, experiments conducted on three real datasets fully demonstrate the effectiveness and advancement of the proposed method.

A Remote Sensing Image Destriping Model Based on Low-Rank and Directional Sparse Constraint

Stripe noise is a common condition that has a considerable impact on the quality of the images. Therefore, stripe noise removal (destriping) is a tremendously important step in image processing. Since the existing destriping models cause different degrees of ripple effects, in this paper a new model, based on total variation (TV) regularization, global low rank and directional sparsity constraints, is proposed for the removal of vertical stripes. TV regularization is used to preserve details, and the global low rank and directional sparsity are used to constrain stripe noise. The directional and structural characteristics of stripe noise are fully utilized to achieve a better removal effect. Moreover, we designed an alternating minimization scheme to obtain the optimal solution. Simulation and actual experimental data show that the proposed model has strong robustness and is superior to existing competitive destriping models, both subjectively and objectively.

Denoising Diffusion MRI via Graph Total Variance in Spatioangular Domain

Diffusion MRI (DMRI) plays an essential role in diagnosing brain disorders related to white matter abnormalities. However, it suffers from heavy noise, which restricts its quantitative analysis. The total variance (TV) regularization is an effective noise reduction technique that penalizes noise-induced variances. However, existing TV-based denoising methods only focus on the spatial domain, overlooking that DMRI data lives in a combined spatioangular domain. It eventually results in an unsatisfactory noise reduction effect. To resolve this issue, we propose to remove the noise in DMRI using graph total variance (GTV) in the spatioangular domain. Expressly, we first represent the DMRI data using a graph, which encodes the geometric information of sampling points in the spatioangular domain. We then perform effective noise reduction using the powerful GTV regularization, which penalizes the noise-induced variances on the graph. GTV effectively resolves the limitation in existing methods, which only rely on spatial information for removing the noise. Extensive experiments on synthetic and real DMRI data demonstrate that GTV can remove the noise effectively and outperforms state-of-the-art methods.

A multi-stage algorithm for image denoising based on PCA and adaptive TV-regularization

In this paper, we present an image denoising algorithm comprising three stages. In the first stage, Principal Component Analysis (PCA) is used to suppress the noise. PCA is applied to image blocks to characterize localized features and rare image patches. In the second stage, we use the Gaussian curvature to develop an adaptive total-variation-based (TV) denoising model to effectively remove visual artifacts and noise residual generated by the first stage. Finally, the denoised image is sharpened in order to enhance the contrast of the denoising result. Experimental results on natural images and computed tomography (CT) images demonstrated that the proposed algorithm yields denoising results better than competing algorithms in terms of both qualitative and quantitative aspects.

Strip-Map SAR Image Formulation Based on the Modified Alternating Split Bregman Method

Conventional compressive sensing (CS)-based imaging methods allow images to be reconstructed from a small amount of data, while they suffer from high computational burden even for a moderate scene. To address this problem, this paper presents a novel two-dimensional (2D) CS imaging algorithm for strip-map synthetic aperture radars (SARs) with zero squint angle. By introducing a 2D separable formulation to model the physical procedure of the SAR imaging, we separate the large measurement matrix into two small ones, and then the induced algorithm can deal with 2D signal directly instead of converting it into 1D vector. As a result, the computational load can be reduced significantly. Furthermore, thanks to its superior performance in maintaining contour information, the gradient space of the SAR image is exploited and the total variation (TV) constraint is incorporated to improve resolution performance. Due to the non-differentiable property of the TV regularizer, it is difficult to directly solve the induced TV regularization problem. To overcome this problem, an improved split Bregman method is presented by formulating the TV minimization problem into a sequence of unconstrained optimization problem and Bregman updates. It yields an accurate and simple solution. Finally, the synthesis and real experiment results demonstrate that the proposed algorithm remains competitive in terms of high resolution and high computational efficiency.

Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization

Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.

Hybrid Regularization Algorithm for Efficient Image Deblurring

Image deblurring is a challenging illposed problem with widespread applications. Most existing deblurring methods make use of image priors or priors on the PSF to achieve accurate results. The performance of these methods depends on various factors such as the presence of well-lit conditions in the case of dark image priors and in case of statistical image priors the assumption the image follows a certain distribution might not be fully accurate. This holds for statistical priors used on the blur kernel as well. The aim of this paper is to propose a novel image deblurring method which can be readily extended to various applications such that it effectively deblurs the image irrespective of the various factors affecting its capture. A hybrid regularization method is proposed which uses a TV regularization framework with varying sparsity inducing priors. The edges of the image are accurately recovered due to the TV regularization. The sparsity prior is implemented through a dictionary such that varying weights of sparsity is induced based on the different image regions. This helps in smoothing the unwanted artifacts generated due to blur in the uniform regions of the image.