Single Image Blind Deconvolution with Higher-Order Texture Statistics

Abstract

Abstract. We present a novel method for solving blind deconvolution, i.e., the task of recovering a sharp image given a blurry one. We focus on blurry images obtained from a coded aperture camera, where both the camera and the scene are static, and allow blur to vary across the image domain. As most methods for blind deconvolution, we solve the problem in two steps: First, we estimate the coded blur scale at each pixel; second, we deconvolve the blurry image given the estimated blur. Our approach is to use linear high-order priors for texture and second-order priors for the blur scale map, i.e., constraints involving two pixels at a time. We show that by incorporating the texture priors in a least-squares energy minimization we can transform the initial blind deconvolution task in a simpler optimization problem. One of the striking features of the simplified optimization problem is that the parameters that define the functional can be learned offline directly from natural images via singular value decomposition. We also show a geometrical interpretation of image blurring and explain our method from this viewpoint. In doing so we devise a novel technique to design optimally coded apertures. Finally, our coded blur identification results in computing convolutions, rather than deconvolutions, which are stable operations. We will demonstrate in several experiments that this additional stability allows the method to deal with large blur. We also compare our method to existing algorithms in the literature and show that we achieve state-of-the-art performance with both synthetic and real data.

Theoretical performance model for single image depth from defocus

“…In this respect, SIDFD is strongly related to blind deconvolution [22]. SIDFD algorithms are thus usually based on some assumption on the unknown scene: a scene with sharp edges is assumed in [7], while learning from a database is proposed in [8], and parametric statistical models of the scene gradients are used in [5,6,9]. To study the performance, it is preferable to use a generic model of the scene, in order to broaden the range of validity of the model.…”

“…Finally, note that criteria related to SIDFD performance have been proposed in [6,8] for the comparison and optimization of coded apertures. However, these criteria return a global score for an aperture shape.…”

“…However, acquisition of several images requires the scene to remain still during the whole acquisition process, which is a strong hypothesis in practice, unless sophisticated imaging systems are used to separate the input beam [3,4]. More recently, Single Image DFD (SIDFD) alternatives have been proposed [5][6][7][8][9]. Acquisition is then simpler, while the processing becomes more complex, since only a single image of an unknown scene is available to infer the depth map.…”

“…Acquisition is then simpler, while the processing becomes more complex, since only a single image of an unknown scene is available to infer the depth map. However, several algorithms have been proposed to deal with this problem [5][6][7][8][9], and SIDFD can now be considered as a candidate approach for designing a RGB-D camera, i.e., a camera, associated to a processing stage, which provides both a color image and a depth map.…”

The Algorithm for Compensating Distortion of Images of Type “Blur”

“…Existing methods for reconstruction of blurred images have a number of advantages, such as ease of use (inverse filtering, Wiener filter, filtering with least squares method, recursive Kalman filter, forced deconvolution iterative methods [2][3][4][5]) or high enough quality of recovery (regularisation methods [2,6,7]). However, they do not take into account the physical processes of blur forming during the image acquisition.…”