Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

In this article, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the epigraph set of Total Variation (TV) function. This set does not need a prescribed upper bound on the total variation of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both of these two closed and convex sets can be used as a part of any blind deconvolution algorithm. Simulation examples are presented.Comment: Submitted to IEEE Selected Topics in Signal Processin

Regularization of RIF blind image deconvolution

Blind image restoration is the process of estimating both the true image and the blur from the degraded image, using only partial information about degradation sources and the imaging system. Our main interest concerns optical image enhancement, where the degradation often involves a convolution process. We provide a method to incorporate truncated eigenvalue and total variation regularization into a nonlinear recursive inverse filter (RIF) blind deconvolution scheme first proposed by Kundar, and by Kundur and Hatzinakos (1996, 1998). Tests are reported on simulated and optical imaging problems.published_or_final_versio

Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

In this paper, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the Epigraph Set of Total Variation (ESTV) function. This set does not need a prescribed upper bound on the Total Variation (TV) of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both the TV of the image and the blurring filter are regularized using the ESTV set. Both the phase information set and the ESTV are closed and convex sets. Therefore they can be used as a part of any blind deconvolution algorithm. Simulation examples are presented. © 2015 IEEE

An Enhanced Visualization of DBT Imaging Using Blind Deconvolution and Total Variation Minimization Regularization

Digital Breast Tomosynthesis (DBT) presents out-of-plane artifacts caused by features of high intensity. Given observed data and knowledge about the point spread function (PSF), deconvolution techniques recover data from a blurred version. However, a correct PSF is difficult to achieve and these methods amplify noise. When no information is available about the PSF, blind deconvolution can be used. Additionally, Total Variation (TV) minimization algorithms have achieved great success due to its virtue of preserving edges while reducing image noise. This work presents a novel approach in DBT through the study of out-of-plane artifacts using blind deconvolution and noise regularization based on TV minimization. Gradient information was also included. The methodology was tested using real phantom data and one clinical data set. The results were investigated using conventional 2D slice-by-slice visualization and 3D volume rendering. For the 2D analysis, the artifact spread function (ASF) and Full Width at Half Maximum (FWHMMASF) of the ASF were considered. The 3D quantitative analysis was based on the FWHM of disks profiles at 90°, noise and signal to noise ratio (SNR) at 0° and 90°. A marked visual decrease of the artifact with reductions of FWHMASF (2D) and FWHM90° (volume rendering) of 23.8% and 23.6%, respectively, was observed. Although there was an expected increase in noise level, SNR values were preserved after deconvolution. Regardless of the methodology and visualization approach, the objective of reducing the out-of-plane artifact was accomplished. Both for the phantom and clinical case, the artifact reduction in the z was markedly visible

Understanding Kernel Size in Blind Deconvolution

Most blind deconvolution methods usually pre-define a large kernel size to guarantee the support domain. Blur kernel estimation error is likely to be introduced, yielding severe artifacts in deblurring results. In this paper, we first theoretically and experimentally analyze the mechanism to estimation error in oversized kernel, and show that it holds even on blurry images without noises. Then to suppress this adverse effect, we propose a low rank-based regularization on blur kernel to exploit the structural information in degraded kernels, by which larger-kernel effect can be effectively suppressed. And we propose an efficient optimization algorithm to solve it. Experimental results on benchmark datasets show that the proposed method is comparable with the state-of-the-arts by accordingly setting proper kernel size, and performs much better in handling larger-size kernels quantitatively and qualitatively. The deblurring results on real-world blurry images further validate the effectiveness of the proposed method.Comment: Accepted by WACV 201