Variational Bayesian Blind Deconvolution Using a Total Variation Prior

In this paper, we present novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Using a hierarchical Bayesian model, the unknown image, blur, and hyperparameters for the image, blur, and noise priors are estimated simultaneously. A variational inference approach is utilized so that approximations of the posterior distributions of the unknowns are obtained, thus providing a measure of the uncertainty of the estimates. Experimental results demonstrate that the proposed approaches provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.      

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.     

Variational Bayesian Image Restoration With a Product of Spatially Weighted Total Variation Image Priors

In this paper, a new image prior is introduced and used in image restoration. This prior is based on products of spatially weighted total variations (TV). These spatial weights provide this prior with the flexibility to better capture local image features than previous TV based priors. Bayesian inference is used for image restoration with this prior via the variational approximation. The proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms. Numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state-of-the-art restoration algorithms.      

基于变分方法的超分辨率

基于全变分先验和变分分布.提出一个新颖的超分辨率算法,使用分级的贝叶斯框架,能够同时计算出重建的高分辨率图像和模型参数.本算法利用变分推论给出变量的后验分布近似.因为能够同时估计出模型参数,是自动的过程,无需对参数人工调节.实验结果表明所提算法在重建质量上优于当前主流的算法.     

Kronecker product approximation for preconditioning in three-dimensional imaging applications.

We derive Kronecker product approximations, with the help of tensor decompositions, to construct approximations of severely ill-conditioned matrices that arise in three-dimensional (3-D) image processing applications. We use the Kronecker product approximations to derive preconditioners for iterative regularization techniques; the resulting preconditioned algorithms allow us to restore 3-D images in a computationally efficient manner. Through examples in microscopy and medical imaging, we show that the Kronecker approximation preconditioners provide a powerful tool that can be used to improve efficiency of iterative image restoration algorithms.     

Hierarchical Bayesian image restoration from partially known blurs

We examine the restoration problem when the point-spread function (PSF) of the degradation system is partially known. For this problem, the PSF is assumed to be the sum of a known deterministic and an unknown random component. This problem has been examined before; however, in most previous works the problem of estimating the parameters that define the restoration filters was not addressed. In this paper, two iterative algorithms that simultaneously restore the image and estimate the parameters of the restoration filter are proposed using evidence analysis (EA) within the hierarchical Bayesian framework. We show that the restoration step of the first of these algorithms is in effect almost identical to the regularized constrained total least-squares (RCTLS) filter, while the restoration step of the second is identical to the linear minimum mean square-error (LMMSE) filter for this problem. Therefore, in this paper we provide a solution to the parameter estimation problem of the RCTLS filter. We further provide an alternative approach to the expectation-maximization (EM) framework to derive a parameter estimation algorithm for the LMMSE filter. These iterative algorithms are derived in the discrete Fourier transform (DFT) domain; therefore, they are computationally efficient even for large images. Numerical experiments are presented that test and compare the proposed algorithms.     

基于低秩先验非局部匹配的高光谱图像恢复北大核心CSCD

为了实现未知退化类型条件下的图像恢复,提出了一种基于低秩先验非局部匹配的高光谱图像恢复方法。该恢复策略将结构相似性指数度量作为数据保真度项,核范数作为正则化项,从而能够使用单一算法解决延迟和信号相关的退化形式,能够处理加性高斯噪声、与信号相关的泊松噪声、混合泊松-高斯噪声,并且能够恢复被截止期和条纹损坏的高光谱图像。通过多个数据集实验结果证明了提出方法具有较好的恢复效果。     

Unsupervised learning of multi-task deep variational model

We propose a general deep variational model (reduced version, full version as well as the extension) via a comprehensive fusion approach in this paper. It is able to realize various image tasks in a completely unsupervised way without learning from samples. Technically, it can properly incorporate the CNN based deep image prior (DIP) architecture into the classic variational image processing models. The minimization problem solving strategy is transformed from iteratively minimizing the sub-problem for each variable to automatically minimizing the loss function by learning the generator network parameters. The proposed deep variational (DV) model contributes to the high order image edition and applications such as image restoration, inpainting, decomposition and texture segmentation. Experiments conducted have demonstrated significant advantages of the proposed deep variational model in comparison with several powerful techniques including variational methods and deep learning approaches.     

Simultaneous image classification and annotation based on probabilistic model

The paper proposes a novel probabilistic generative model for simultaneous image classification and annotation.The model considers the fact that the category information can provide valuable information for image annotation.Once the category of an image is ascertained,the scope of annotation words can be narrowed,and the probability of generating irrelevant annotation words can be reduced.To this end,the idea that annotates images according to class is introduced in the model.Using variational methods,the approximate inference and parameters estimation algorithms of the model are derived,and efficient approximations for classifying and annotating new images are also given.The power of our model is demonstrated on two real world datasets:a 1 600-images LabelMe dataset and a 1 791-images UIUC-Sport dataset.The experiment results show that the classification performance is on par with several state-of-the-art classification models,while the annotation performance is better than that of several state-of-the-art annotation models.     

Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging

The nonparametric multiscale platelet algorithms presented in this paper, unlike traditional wavelet-based methods, are both well suited to photon-limited medical imaging applications involving Poisson data and capable of better approximating edge contours. This paper introduces platelets, localized functions at various scales, locations, and orientations that produce piece-wise linear image approximations, and a new multiscale image decomposition based on these functions. Platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries. For smoothness measured in certain H?lder classes, it is shown that the error of m-term platelet approximations can decay significantly faster than that of m-term approximations in terms of sinusoids, wavelets, or wedgelets. This suggests that platelets may outperform existing techniques for image denoising and reconstruction. Fast, platelet-based, maximum penalized likelihood methods for photon-limited image denoising, deblurring and tomographic reconstruction problems are developed. Because platelet decompositions of Poisson distributed images are tractable and computationally efficient, existing image reconstruction methods based on expectation-maximization type algorithms can be easily enhanced with platelet techniques. Experimental results suggest that platelet-based methods can outperform standard reconstruction methods currently in use in confocal microscopy, image restoration, and emission tomography.     

Robust classification of blurred imagery

We present two novel approaches for the classification of blurry images. It is assumed that the blur is linear and space invariant, but that the exact blurring function is unknown. The proposed fusion-based approaches attempt to perform the simultaneous tasks of blind image restoration and classification. We call such a problem blind image fusion. The techniques are implemented using the nonnegativity and support constraints recursive inverse filtering (NAS-RIF) algorithm for blind image restoration and the Markov random field (RIRF)-based fusion method for classification by Schistad-Solberg et al. (see IEEE Trans. Geosci. Remote Sensing, vol.32, p.768-78, 1994). Simulation results on synthetic and real photographic data demonstrate the potential of the approaches. The algorithms are compared with one another and to situations in which blind blur removal is not attempted.     

交替使用小波去噪和全变差正则化的盲图像恢复算法

盲图像恢复就是在点扩散函数未知情况下从降质观测图像恢复出原图像.该文提出了一种交替使用小波去噪和全变差正则化的盲图像恢复算法.观测模型首先被分解成两个相互关联的子模型,这种分解转化盲恢复问题成为图像去噪和图像恢复两个问题,可以交替采用图像去噪和图像恢复算法求解.模糊辨识阶段,使用全变差正则化算法估计点扩散函数;图像恢复阶段,使用小波去噪和全变差正则化相结合的算法恢复图像.实验结果和与其它方法的比较表明该文算法能够获得更好的恢复效果.     

A VQ-based blind image restoration algorithm

Learning-based algorithms for image restoration and blind image restoration are proposed. Such algorithms deviate from the traditional approaches in this area, by utilizing priors that are learned from similar images. Original images and their degraded versions by the known degradation operator (restoration problem) are utilized for designing the VQ codebooks. The codevectors are designed using the blurred images. For each such vector, the high frequency information obtained from the original images is also available. During restoration, the high frequency information of a given degraded image is estimated from its low frequency information based on the codebooks. For the blind restoration problem, a number of codebooks are designed corresponding to various versions of the blurring function. Given a noisy and blurred image, one of the codebooks is chosen based on a similarity measure, therefore providing the identification of the blur. To make the restoration process computationally efficient, the principal component analysis (PCA) and VQ-nearest neighbor approaches are utilized. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms.     

Iterative tomographic image reconstruction using Fourier-based forward and back-projectors

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.     

Radon变换和全变分相融合的图像复原算法

图像复原的核心是点扩散函数的估计和直接去卷积算法,针对拍照过程中,相机和被拍摄物体由于相对运动而导致的图像退化问题,提出一种基于Radon变换和全变分相融合的图像复原算法。首先利用radon变换对图像退化模型参数进行估计,然后采用全变分算法复原退化图像,最后在Matlab 2012平台进行仿真实验对算法的性能检验。仿真结果表明,相对于其它图像复原算法,本文算法可以准确估计退化模型参数,获得了更加理想的图像复原效果,具有一定的实际利用价值。     

Synthetic aperture radar autofocus based on a bilinear model

Autofocus algorithms are used to restore images in nonideal synthetic aperture radar imaging systems. In this paper, we propose a bilinear parametric model for the unknown image and the nuisance phase parameters and derive an efficient maximum-likelihood autofocus (MLA) algorithm. In the special case of a simple image model and a narrow range of look angles, MLA coincides with the successful multichannel autofocus (MCA). MLA can be interpreted as a generalization of MCA to a larger class of models with a larger range of look angles. We analyze its advantages over previous extensions of MCA in terms of identifiability conditions and noise sensitivity. As a byproduct, we also propose numerical approximations to the difficult constant modulus quadratic program that lies at the core of these algorithms. We demonstrate the superior performance of our proposed methods using computer simulations in both the correct and mismatched system models. MLA performs better than other methods, both in terms of the mean squared error and visual quality of the restored image.     

Efficient blind image restoration using discrete periodic Radon transform

Restoring an image from its convolution with an unknown blur function is a well-known ill-posed problem in image processing. Many approaches have been proposed to solve the problem and they have shown to have good performance in identifying the blur function and restoring the original image. However, in actual implementation, various problems incurred due to the large data size and long computational time of these approaches are undesirable even with the current computing machines. In this paper, an efficient algorithm is proposed for blind image restoration based on the discrete periodic Radon transform (DPRT). With DPRT, the original two-dimensional blind image restoration problem is converted into one-dimensional ones, which greatly reduces the memory size and computational time required. Experimental results show that the resulting approach is faster in almost an order of magnitude as compared with the traditional approach, while the quality of the restored image is similar.     

Arbitrary resizing of images in DCT space

Using the spatial relationship of the block discrete cosine transform (DCT) coefficients and subband approximations, algorithms for image halving and doubling operations are presented. The computational steps identified in the process provide a general framework for image resizing operations. Some of the previously reported image halving and doubling algorithms are shown to be special cases. The proposed approach is general enough to accommodate resizing operations with arbitrary factors, namely with integral and rational factors. The application of these methods to the conversion in the compressed domain of images (video frames) from one format to another is demonstrated.     

A nonlinear least square technique for simultaneous image registration and super-resolution.

This paper proposes a new algorithm to integrate image registration into image super-resolution (SR). Image SR is a process to reconstruct a high-resolution (HR) image by fusing multiple low-resolution (LR) images. A critical step in image SR is accurate registration of the LR images or, in other words, effective estimation of motion parameters. Conventional SR algorithms assume either the estimated motion parameters by existing registration methods to be error-free or the motion parameters are known a priori. This assumption, however, is impractical in many applications, as most existing registration algorithms still experience various degrees of errors, and the motion parameters among the LR images are generally unknown a priori. In view of this, this paper presents a new framework that performs simultaneous image registration and HR image reconstruction. As opposed to other current methods that treat image registration and HR reconstruction as disjoint processes, the new framework enables image registration and HR reconstruction to be estimated simultaneously and improved progressively. Further, unlike most algorithms that focus on the translational motion model, the proposed method adopts a more generic motion model that includes both translation as well as rotation. An iterative scheme is developed to solve the arising nonlinear least squares problem. Experimental results show that the proposed method is effective in performing image registration and SR for simulated as well as real-life images.