Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

A Logarithmic Image Prior for Blind Deconvolution

Blind Deconvolution consists in the estimation of a sharp image and a blur kernel from an observed blurry image. Because the blur model admits several solutions it is necessary to devise an image prior that favors the true blur kernel and sharp image. Many successful image priors enforce the sparsity of the sharp image gradients. Ideally the L0 “norm” is the best choice for promoting sparsity, but because it is computationally intractable, some methods have used a logarithmic approximation. In this work we also study a logarithmic image prior. We show empirically how well the prior suits the blind deconvolution problem. Our analysis confirms experimentally the hypothesis that a prior should not necessarily model natural image statistics to correctly estimate the blur kernel. Furthermore, we show that a simple Maximum a Posteriori formulation is enough to achieve state of the art results. To minimize such formulation we devise two iterative minimization algorithms that cope with the non-convexity of the logarithmic prior: one obtained via the primal-dual approach and one via majorization-minimization.

Deconvolution-based deblurring of reconstructed images in photoacoustic/thermoacoustic tomography

Photoacoustic/thermoacoustic tomography is an emerging hybrid imaging modality combining optical/microwave imaging with ultrasound imaging. Here, a k-wave MATLAB toolbox was used to simulate various configurations of excitation pulse shape, width, transducer types, and target object sizes to see their effect on the photoacoustic/thermoacoustic signals. A numerical blood vessel phantom was also used to demonstrate the effect of various excitation pulse waveforms and pulse widths on the reconstructed images. Reconstructed images were blurred due to the broadening of the pressure waves by the excitation pulse width as well as by the limited transducer bandwidth. The blurring increases with increase in pulse width. A deconvolution approach is presented here with Tikhonov regularization to correct the photoacoustic/thermoacoustic signals, which resulted in improved reconstructed images by reducing the blurring effect. It is observed that the reconstructed images remain unaffected by change in pulse widths or pulse shapes, as well as by the limited bandwidth of the ultrasound detectors after the use of the deconvolution technique. (C) 2013 Optical Society of America

Total Variation Blind Deconvolution: The Devil Is in the Details

In this paper we study the problem of blind deconvolution. Our analysis is based on the algorithm of Chan and Wong [2] which popularized the use of sparse gradient priors via total variation. We use this algorithm because many methods in the literature are essentially adaptations of this framework. Such algorithm is an iterative alternating energy minimization where at each step either the sharp image or the blur function are reconstructed. Recent work of Levin et al. [14] showed that any algorithm that tries to minimize that same energy would fail, as the desired solution has a higher energy than the no-blur solution, where the sharp image is the blurry input and the blur is a Dirac delta. However, experimentally one can observe that Chan and Wong's algorithm converges to the desired solution even when initialized with the no-blur one. We provide both analysis and experiments to resolve this paradoxical conundrum. We find that both claims are right. The key to understanding how this is possible lies in the details of Chan and Wong's implementation and in how seemingly harmless choices result in dramatic effects. Our analysis reveals that the delayed scaling (normalization) in the iterative step of the blur kernel is fundamental to the convergence of the algorithm. This then results in a procedure that eludes the no-blur solution, despite it being a global minimum of the original energy. We introduce an adaptation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the state of the art.

Bilayer Blind Deconvolution with the Light Field Camera

In this paper we propose a solution to blind deconvolution of a scene with two layers (foreground/background). We show that the reconstruction of the support of these two layers from a single image of a conventional camera is not possible. As a solution we propose to use a light field camera. We demonstrate that a single light field image captured with a Lytro camera can be successfully deblurred. More specifically, we consider the case of space-varying motion blur, where the blur magnitude depends on the depth changes in the scene. Our method employs a layered model that handles occlusions and partial transparencies due to both motion blur and out of focus blur of the plenoptic camera. We reconstruct each layer support, the corresponding sharp textures, and motion blurs via an optimization scheme. The performance of our algorithm is demonstrated on synthetic as well as real light field images.

A Clearer Picture of Total Variation Blind Deconvolution

Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort resulted in the deployment of effective algorithms, the theoretical findings generated contrasting views on why these approaches worked. On the one hand, one could observe experimentally that alternating energy minimization algorithms converge to the desired solution. On the other hand, it has been shown that such alternating minimization algorithms should fail to converge and one should instead use a so-called Variational Bayes approach. To clarify this conundrum, recent work showed that a good image and blur prior is instead what makes a blind deconvolution algorithm work. Unfortunately, this analysis did not apply to algorithms based on total variation regularization. In this manuscript, we provide both analysis and experiments to get a clearer picture of blind deconvolution. Our analysis reveals the very reason why an algorithm based on total variation works. We also introduce an implementation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the top performing algorithms.

Features-pooling blind jpeg image steganalysis

In this research, we introduce a new blind steganalysis in detecting grayscale JPEG images. Features-pooling method is employed to extract the steganalytic features and the classification is done by using neural network. Three different steganographic models are tested and classification results are compared to the five state-of-the-art blind steganalysis.

Constrained high-order statistical blind deconvolution of spectral data

A constrained high-order statistical algorithm is proposed to blindly deconvolute the measured spectral data and estimate the response function of the instruments simultaneously. In this algorithm, no prior-knowledge is necessary except a proper length of the unit-impulse response. This length can be easily set to be the width of the narrowest spectral line by observing the measured data. The feasibility of this method has been demonstrated experimentally by the measured Raman and absorption spectral data.