Regularization For Image Restoration Research Articles

Kronecker product approximation for the total variation regularization in image restoration

In this paper, we propose a new algorithm to restore blurred and noisy images based on the total variation regularization, where the discrete associated Euler-Lagrange problem is solved by exploiting the structure of the matrices and transforming the initial problem to a generalized Sylvester linear matrix equation by using a special Kronecker product approximation. Afterwards, global Krylov subspace methods are used to solve the linear matrix equation. Numerical experiments are given to illustrate the effectiveness of the proposed method.

Improved block preconditioners for linear systems arising from half-quadratic image restoration

In this paper, the minimization problem with a half-quadratic (HQ) regularization for image restoration is studied. For the structured linear system arising at each step of the Newton method for solving the minimization problem, we propose improved block preconditioners based on approximate inversion of the Schur complement and matrix decomposition of the Hessian matrix. The approximate inverse of the Schur complement is constructed by the Taylor expansion. We analyze the spectral properties of the preconditioned matrix and present eigenvalue bounds. Numerical results illustrate the efficiency of the proposed preconditioners.

Patch-Based Nonlocal Adaptive Gradient Regularization for Image Restoration in Sensor Networks

In this paper, we propose a novel patch-based adaptive nonlocal gradient regularization method for image restoration in sensor networks. It formulates the hyper-Laplacian distribution to regularize the global gradient distribution. The patch-based nonlocal gradient prior is utilized to regularize the nonlocal self-similarity of image gradients. Firstly, the L0-norm smoothing scheme is used innovatively as the preprocessing step to preserve strong edges, which are critical to improve the accuracy of clustering the similar image patches. Then, adaptive weights for each patches are developed from a set of clustered nonlocal self-similarity patches by learning the the expectation and variance for sparse gradient distribution at each pixel. Comparing with several recent state-of-the-art methods, experimental results show that the proposed method has better performance in alleviating block effects and preserving image details.

Alternating method based on framelet l0-norm and TV regularization for image restoration

ABSTRACTThis paper presents an efficient alternating method for image deblurring and denoising, it is based on our new model with TV norm to denoise the deblurred image which is penalized by norm of the framelet transform. Our combinational algorithm performs deblurring and denoising alternately. We apply the proximity algorithm to solve the TV regularization for denoising part, and the mean doubly augmented Lagrangian (MDAL) method is used to solve minimization in the analysis-based sparsity for the deblurring part. Experimental results show that the proposed alternating minimization method is robust for a different type of blur and noise. We also do some comparisons with related existing methods to demonstrate that our method has a more significant effect.

Adaptive Order Non-Convex Lp-norm Regularization in Image Restoration

The optimization formulations of sparse signal recovery problems use a regularizer term which encourages the solution to be sparse or piece-wise smooth. Of special interest are the ℓp norms with 0 ≤ p ≤ 1 which penalize large values and encourage the solution of the optimization problem to be sparse. In this work, we propose a new regularizer in which the exponent p, 0 ≤ p ≤ 1 of the ℓp–norm is a function of the signal element amplitude, leading to a function which is smooth and convex over non-negative values. This formulation adapts the value of the exponent p according to a sigmoid function applied on the signal values, to restrict its values to between 0 and 1. Experiments show that this formulation is more accurate in denoising, than the ℓ1 and ℓ0.5 norm regularizers, and is more accurate than the ℓ1-norm when used iteratively for deblurring or inpainting.

Multiple Degree Total Variation (MDTV) Regularization for Image Restoration.

We introduce a novel image regularization termed as multiple degree total variation (MDTV). This type of regularization combines the first and second degree directional derivatives, thus providing a good balance between preservation of edges and region smoothness. In order to solve the resulting optimization problem, we proposed a fast majorize minimize algorithm. We demonstrate the utility of the MDTV regularization in the context of image denoising and compressed sensing. We compare the proposed method with standard TV, and the state of the art higher degree methods, including higher degree total variation (HDTV) and total generalized variation (TGV) based schemes. Numerical results indicate that MDTV penalty provides improved image recovery performance.

An iterative algorithm for L1-TV constrained regularization in image restoration

We consider the problem of restoring blurred images affected by impulsive noise. The adopted method restores the images by solving a sequence of constrained minimization problems where the data fidelity function is the ℓ1 norm of the residual and the constraint, chosen as the image Total Variation, is automatically adapted to improve the quality of the restored images. Although this approach is general, we report here the case of vectorial images where the blurring model involves contributions from the different image channels (cross channel blur). A computationally convenient extension of the Total Variation function to vectorial images is used and the results reported show that this approach is efficient for recovering nearly optimal images.

Nonlocal Total Variation Based Image Deblurring Using Split Bregman Method and Fixed Point Iteration

Nonlocal regularization for image restoration is extensively studied in recent years. However, minimizing a nonlocal regularization problem is far more difficult than a local one and still challenging. In this paper, a novel nonlocal total variation based algorithm for image deblurring is presented. The core idea of this algorithm is to consider the latent image as the fixed point of the nonlocal total variation regularization functional. And a split Bregman method is proposed to solve the minimization problem in each fixed point iteration efficiently. By alternatively reconstructing a sharp image and updating the nonlocal gradient weights, the recovered image becomes more and more sharp. Experimental results on the benchmark problems are presented to show the efficiency and effectiveness of our algorithm.

Gradient-based image deconvolution

Image restoration and deconvolution from blurry and noisy observation is known to be ill-posed. To stabilize the recovery, total variation (TV) regularization is often utilized for its beneficial edge in preserving the image's property. We take a different approach of TV regularization for image restoration. We first recover horizontal and vertical differences of images individually through some successful deconvolution algorithms. We restore horizontal and vertical difference images separately so that each is more sparse or compressible than the corresponding original image with a TV measure. Then we develop a novel deconvolution method that recovers the horizontal and vertical gradients, respectively, and then estimate the original image from these gradients. Various experiments that compare the effectiveness of the proposed method against the traditional TV methods are presented. Experimental results are provided to show the improved performance of our method for deconvolution problems. 2013 SPIE and IS and T.

A hybrid-optimization method for large-scale non-negative full regularization in image restoration

We describe a new hybrid-optimization method for solving the full-regularization problem of computing both the regularization parameter and the corresponding regularized solution in 1-norm and 2-norm Tikhonov regularizations with additional non-negativity constraints. The approach combines the simulated annealing technique for global optimization and the low-cost spectral projected gradient method for the minimization of large-scale smooth functions on convex sets. The new method is matrix-free in the sense that it relies on matrix–vector multiplications only. We describe the method and discuss some of its properties. Numerical results indicate that the new approach is a promising tool for solving large-scale image restoration problems.

Poisson Noise Removal Scheme Based on Fourth‐Order PDE by Alternating Minimization Algorithm

To overcome the staircasing effects introduced by the TV regularization in image restoration, this paper investigates a fourth‐order partial differential equation (PDE) filter for removing Poisson noise. In consideration of the slow convergence property of the classical gradient descent method, we adopt the alternating minimization algorithm for realizing this scheme. Compared with the corresponding total variation based one, numerical simulations distinctly indicate the superiority of our proposed strategy in handling smooth regions of Poissonian images and improving the computational speed.

Multiscale total variation regularization in image restoration

AbstractA total variation model for image restoration is introduced. The model utilizes a spatially dependent regularization parameter in order to enhance image regions containing details while still sufficiently smoothing homogeneous features. A local variance estimator is used to automatically adjust the regularization parameter. A generalized hierarchical decomposition of the restored image is integrated to the algorithm in order to speed‐up the performance of the update scheme. The corresponding subproblems are solved by a superlinearly convergent algorithm based on Fenchel‐duality and inexact semismooth Newton techniques. Numerical tests illustrate the performance of the algorithm. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Minimization Problems and Associated Flows Related to Weighted p Energy and Total Variation

Motivated by the problem of edge preserving regularization in image restoration, in this paper we investigate the relations between weighted p energy based and total variation based minimization problems and their associated flows. We prove that the weighted total variation based minimization and its associated flow in a weakened formulation can be approximated by the weighted p energy based minimization and its associated flows, respectively. Moreover, we show that the flow of the weighted total variation based minimization converges weakly in BV and strongly in L2 to the minimizer as $t\rightarrow \infty$.

A neural learning approach for adaptive image restoration using a fuzzy model-based network architecture

We address the problem of adaptive regularization in image restoration by adopting a neural-network learning approach. Instead of explicitly specifying the local regularization parameter values, they are regarded as network weights which are then modified through the supply of appropriate training examples. The desired response of the network is in the form of a gray level value estimate of the current pixel using weighted order statistic (WOS) filter. However, instead of replacing the previous value with this estimate, this is used to modify the network weights, or equivalently, the regularization parameters such that the restored gray level value produced by the network is closer to this desired response. In this way, the single WOS estimation scheme can allow appropriate parameter values to emerge under different noise conditions, rather than requiring their explicit selection in each occasion. In addition, we also consider the separate regularization of edges and textures due to their different noise masking capabilities. This in turn requires discriminating between these two feature types. Due to the inability of conventional local variance measures to distinguish these two high variance features, we propose the new edge-texture characterization (ETC) measure which performs this discrimination based on a scalar value only. This is then incorporated into a fuzzified form of the previous neural network which determines the degree of membership of each high variance pixel in two fuzzy sets, the EDGE and TEXTURE fuzzy sets, from the local ETC value, and then evaluates the appropriate regularization parameter by appropriately combining these two membership function values.

Application of evolutionary programming to adaptive regularization in image restoration

Image restoration is a difficult problem due to the ill-conditioned nature of the associated inverse filtering operation, which requires regularization techniques. The choice of the corresponding regularization parameter is thus an important issue since an incorrect choice would either lead to noisy appearances in the smooth regions or excessive blurring of the textured regions. In addition, this choice has to be made adaptively across, different image regions to ensure the best subjective quality for the restored image. We employ evolutionary programming (EP) to solve this adaptive regularization problem by generating a population of potential regularization strategies, and allowing them to compete under a new error measure which characterizes a large class of images in terms of their local correlational properties. The nonavailability of explicit gradient information for this measure motivates the adoption of EP techniques for its optimization, which allows efficient search at multiple error surface points. The adoption of EP also allows the broadening of the range of possible cost functions for image processing so that we can choose the most relevant function rather than the most tractable one for a particular image processing application.

Adaptive regularization in image restoration by unsupervised learning

The <i>Journal of Electronic Imaging</i> (JEI), copublished bimonthly with the Society for Imaging Science and Technology, publishes peer-reviewed papers that cover research and applications in all areas of electronic imaging science and technology.

Adaptive regularization in image restoration using a model-based neural network

Regularization parameter estimation is an important issue in the overall optimization of image restoration systems. The parameter controls the relative weightings of the data- and model-conformance terms in the restoration cost function. In general, we should adopt small parameter values for highly textured image regions to emphasize detail and should use large values to suppress noise in smooth regions. In spite of this qualitative knowledge, the exact value of the parameter is normally difficult to estimate due to the nonintuitiveness of the parameter value as an indicator of the resulting image quality. In view of this problem, we propose a regionally adaptive regularization approach that first specifies the desired image regional quality in terms of a specific predictive filter mask and then establishes a correspondence between the filter mask and a regional regularization parameter value using a modelbased neural network. Due to the ease of tailoring local image quality using a filter mask by judiciously specifying the mask coefficients, we can define separate filter masks for different image regions to indicate different preferences for detail preservation. We can then relate the prediction given by each filter mask to a specific parameter value through the function approximation capability of the model-based neural network and fine-tune this value through training. As a result, the current assignment is more relevant in relation to the local spatial characteristics of the image than with the usual practice of using an arbitrary function of the SNR to determine the parameter value.

Optimal space-varying regularization in iterative image restoration

It has been shown that space-variant regularization in image restoration provides better results than space-invariant regularization. However, the optimal choice of the regularization parameter is usually unknown a priori. In previous work, the generalized cross-validation (GCV) criterion was shown to provide accurate estimates of the optimal regularization parameter. The author introduces a modified form of the GCV criterion that incorporates space-variant regularization and data error terms. Furthermore, he presents an efficient method for estimating the GCV criterion for the space-variant case using iterative image restoration techniques. This method performs nearly as well as the exact criterion for the image restoration problem. In addition, he proposes a Wiener filter interpretation for choosing the local weighting of the regularization. This interpretation suggests the use of a multistage estimation procedure to estimate the optimal choice of the local regularization weights. Experiments confirm the value of the modified GCV estimation criterion as well as the multistage procedure for estimating the local regularization weights.