A variational approach for Bayesian blind image deconvolution

In this paper, the blind image deconvolution (BID) problem is addressed using the Bayesian framework. In order to solve for the proposed Bayesian model, we present a new methodology based on a variational approximation, which has been recently introduced for several machine learning problems, and can be viewed as a generalization of the expectation maximization (EM) algorithm. This methodology reaps all the benefits of a "full Bayesian model" while bypassing some of its difficulties. We present three algorithms that solve the proposed Bayesian problem in closed form and can be implemented in the discrete Fourier domain. This makes them very cost effective even for very large images. We demonstrate with numerical experiments that these algorithms yield promising improvements as compared to previous BID algorithms. Furthermore, the proposed methodology is quite general with potential application to other Bayesian models for this and other imaging problems.     

A wavelet-laplace variational technique for image deconvolution and inpainting.

We construct a new variational method for blind deconvolution of images and inpainting, motivated by recent PDE-based techniques involving the Ginzburg-Landau functional, but using more localized wavelet-based methods. We present results for both binary and grayscale images. Comparable speeds are achieved with better sharpness of edges in the reconstruction.     

A cartoon-plus-texture image decomposition model for blind deconvolution

In this paper, we study a blind deconvolution problem by using an image decomposition technique. Our idea is to make use of a cartoon-plus-texture image decomposition procedure into the deconvolution problem. Because cartoon and texture components can be represented differently in images, we can adapt suitable regularization methods to restore their components. In particular, the total variational regularization is used to describe the cartoon component, and Meyer’s G-norm is employed to model the texture component. In order to obtain the restored image automatically, we also use the generalized cross validation method efficiently and effectively to estimate their corresponding regularization parameters. Experimental results are reported to demonstrate that the visual quality of restored images by using the proposed method is very good, and is competitive with the other testing methods.     

Blind image deconvolution using a robust GCD approach

In this correspondence, a new viewpoint is proposed for estimating an image from its distorted versions in presence of noise without the a priori knowledge of the distortion functions. In z-domain, the desired image can be regarded as the greatest common polynomial divisor among the distorted versions. With the assumption that the distortion filters are finite impulse response (FIR) and relatively coprime, in the absence of noise, this becomes a problem of taking the greatest common divisor (GCD) of two or more two-dimensional (2-D) polynomials. Exact GCD is not desirable because even extremely small variations due to quantization error or additive noise can destroy the integrity of the polynomial system and lead to a trivial solution. Our approach to this blind deconvolution approximation problem introduces a new robust interpolative 2-D GCD method based on a one-dimensional (1-D) Sylvester-type GCD algorithm. Experimental results with both synthetically blurred images and real motion-blurred pictures show that it is computationally efficient and moderately noise robust.     

Blind image deconvolution for single motion-blurred image

Motion blur due to camera shake during exposure is one of the most common reasons of image degradation,which usually reduces the quality of photographs seriously.Based on the statistical properties of the natural image's gradient and the blur kernel,a blind deconvolution algorithm is proposed to restore the motion-blurred image caused by camera shake,adopting the variational Bayesian estimation theory.In addition,the ring effect is one problem that is not avoided in the process of image deconvolution,and usually makes the visual effect of the restored image badly.So a dering method is put forward based on the sub-region detection and fuzzy filter.Tested on the real blurred photographs,the experimental results show that the proposed algorithm of blind image deconvolution can remove the camera-shake motion blur from the degraded image effectively,and can eliminate the ring effect better,while preserve the edges and details of the image well.     

A segmentation-based regularization term for image deconvolution.

This paper proposes a new and original inhomogeneous restoration (deconvolution) model under the Bayesian framework for observed images degraded by space-invariant blur and additive Gaussian noise. In this model, regularization is achieved during the iterative restoration process with a segmentation-based a priori term. This adaptive edge-preserving regularization term applies a local smoothness constraint to pre-estimated constant-valued regions of the target image. These constant-valued regions (the segmentation map) of the target image are obtained from a preliminary Wiener deconvolution estimate. In order to estimate reliable segmentation maps, we have also adopted a Bayesian Markovian framework in which the regularized segmentations are estimated in the maximum a posteriori (MAP) sense with the joint use of local Potts prior and appropriate Gaussian conditional luminance distributions. In order to make these segmentations unsupervised, these likelihood distributions are estimated in the maximum likelihood sense. To compute the MAP estimate associated to the restoration, we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration. The experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state-of-the-art methods in benchmark tests.     

An image pixel based variational model for histogram equalization

In this paper, we develop an image pixel based histogram equalization model for image contrast enhancement. The approach is to propose a variational model containing an energy functional to adjust the pixel values of an input image directly so that the resulting histogram can be redistributed to be uniform. This idea is different from existing histogram equalization algorithms where a histogram based on the input image is constructed, a mapping is determined to output a uniform histogram and then the pixel values of the input image are adjusted based on the mapping. In the variational model, a mean brightness term is incorporated to preserve the brightness of the input image, and a geometry constraint can also be added to keep the geometry structure of the input image. Theoretically, the existence of the minimizer of the proposed model, and the convergence of the proposed algorithm are given. Experimental results are reported to demonstrate that the performance of the proposed model are competitive with the other testing histogram equalization methods for several testing images.     

Complex spatial filters for image deconvolution

The history and principles of image distortion correction by means of holographic spatial filtering are reviewed. Both predetection and postdetection filtering are considered. These and other principle applications of complex spatial filtering are assessed. The major problem areas are discussed, along with possible solutions.     

A coupled variational model for image denoising using a duality strategy and split Bregman

To reduce the staircase effect, high-order diffusion equations are used with high computational cost. Recently, a two-step method with two energy functions has been introduced to alleviate the staircase effect successfully. In the two-step method, firstly, the normal vector of noisy image is smoothed, and then the image is reconstructed from the smoothed normal field. In this paper, we propose a new image restoration model with only one energy function. When the alternating direction method is used, the estimation of the vector field and the reconstruction of the image are interlaced, which makes the new vector field can utilize sufficiently the information of the restored image, thus the constructed vector field is more accurate than that generated by the two-step method. To speed up the computation, the dual approach and split Bregman are employed in our numerical algorithm. The experimental results show that the new model is more effective to filter out the Gaussian noise than the state-of-the-art models.     

A robust nonlinear filter for image restoration

A class of nonlinear regression filters based on robust estimation theory is introduced. The goal of the filtering is to recover a high-quality image from degraded observations. Models for desired image structures and contaminating processes are employed, but deviations from strict assumptions are allowed since the assumptions on signal and noise are typically only approximately true. The robustness of filters is usually addressed only in a distributional sense, i.e., the actual error distribution deviates from the nominal one. In this paper, the robustness is considered in a broad sense since the outliers may also be due to inappropriate signal model, or there may be more than one statistical population present in the processing window, causing biased estimates. Two filtering algorithms minimizing a least trimmed squares criterion are provided. The design of the filters is simple since no scale parameters or context-dependent threshold values are required. Experimental results using both real and simulated data are presented. The filters effectively attenuate both impulsive and nonimpulsive noise while recovering the signal structure and preserving interesting details.     

Blind deconvolution using a variational approach to parameter, image, and blur estimation.

Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods.     

A variational Bayesian approach to number of sources estimation for multichannel blind deconvolution

Most traditional multichannel blind deconvolution algorithms rely on some assumptions on the mixing model, e.g. the number of sources is known a priori; and the mixing environment is noise-free. Unfortunately, these assumptions are not necessarily true in practice. In this paper, we will relax the assumption placed on the number of sources by studying a state space mixing model where the number of sources is assumed to be unknown but not greater than the number of sensors. Based on this mixing model, we will formulate the estimation of the number of sources problem as a model order selection problem. Model comparison, as a common method of model order selection, usually involves the evaluation of multi-variable integrals which is computationally intractable. A variational Bayesian method is therefore used to overcome this multi-variable integral issue. The problem is solved by approximating the true, complicated posteriors with a set of independent, simple, tractable posteriors. To realize the objective of optimal approximation, we maximize an objective function called negative free energy. We will derive a variational Bayesian algorithm, in which the number of sources will be estimated through two approaches: automatic relevance determination and comparison of the optimized negative free energy. The proposed variational Bayesian algorithm will be evaluated on both artificially generated examples, and practical signals.     

A novel blind deconvolution scheme for image restoration usingrecursive filtering

We present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function. The technique applies to situations in which the scene consists of a finite support object against a uniformly black, grey, or white background. This occurs in certain types of astronomical imaging, medical imaging, and one-dimensional (1-D) gamma ray spectra processing, among others. The only information required are the nonnegativity of the true image and the support size of the original object. The restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function. We prove convexity of the cost function, establish sufficient conditions to guarantee a unique solution, and examine the performance of the technique in the presence of noise. The new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods. For situations in which the exact object support is unknown, we propose a novel support-finding algorithm     

An adaptive two phase blind image deconvolution algorithm for an iterative regularization model

This paper proposes a blind image deconvolution method which consists of two sequential phases, i.e., blur kernel estimation and image restoration. In the first phase, we adopt the L₀-norm of image gradients and total variation (TV) to regularize the latent image and blur kernel, respectively. Then we design an alternating optimization algorithm which jointly incorporates the estimation of intermediately restored image, blur kernel and regularization parameters into account. In the second phase, we propose to take the mixture of L₀-norm of image gradients and TV to regularize the latent image, and design an efficient non-blind deconvolution algorithm to achieve the restored image. Experimental results on both a benchmark image dataset and real-world blurred images show that the proposed method can effectively restore image details while suppress noise and ringing artifacts, the result is of high quality which is competitive with some state of the art methods.     

Blind image deconvolution revisited

The article discusses the major approaches, such as projection based blind deconvolution and maximum likelihood restoration, we overlooked previously (see ibid., no.5, 1996). We discuss them for completeness along with some other works found in the literature. As the area of blind image restoration is a rapidly growing field of research, new methods are constantly being developed     

A generalized divergence measure for robust image registration

Entropy-based divergence measures have shown promising results in many areas of engineering and image processing. We define a new generalized divergence measure, namely, the Jensen-Renyi (1996, 1976) divergence. Some properties such as convexity and its upper bound are derived. Based on the Jensen-Renyi divergence, we propose a new approach to the problem of image registration. Some appealing advantages of registration by Jensen-Renyi divergence are illustrated, and its connections to mutual information-based registration techniques are analyzed. As the key focus of this paper, we apply Jensen-Renyi divergence for inverse synthetic aperture radar (ISAR) image registration. The goal is to estimate the target motion during the imaging time. Our approach applies Jensen-Renyi divergence to measure the statistical dependence between consecutive ISAR image frames, which would be maximal if the images are geometrically aligned. Simulation results demonstrate that the proposed method is efficient and effective.     

应用变分法的极化SAR图像分类方法研究

提出了一种用于图像分类的变分模型,该模型结合正则化过程,可以较好地保持图像边缘信息,同时可以用于图像恢复.利用模拟和真实SAR图像的分类仿真试验表明,基于变分法的极化SAR图像分类方法不仅能够实现SAR图像的正确分类,克服SAR图像中相干斑噪声的影响,并且算法快速,易于实现.