First, notice that the smallest value1 of r is minx∈[−L,L−1] r[x] = r[−1] = δ0 + δ1 − UL and occurs at x = −1. Next, consider solving the taut string problem by enforcing only the constraint |s[−1] − r[−1]| ≤ λ. The cost of the taut string problem is minimum for the shortest path s through a point at x = −1. We can decompose such path into the concatenation of the shortest path from x = −L− 1 t...

We propose a total variation based model for simultaneous image inpainting and blind deconvolution. We demonstrate that the tasks are inherently coupled together and that solving them individually will lead to poor results. The main advantages of our model are that (i) boundary conditions for deconvolution required near the interface between observed and occluded regions are naturally generated...

We have been investigating ways to restore images of objects obtained with a telescope under anisoplanatic atmospheric conditions. Anisoplanatic means that the point spread function due to atmospheric turbulence is position dependent. We began by looking at extended astronomical objects, such as craters on the moon but have turned our attention to extended objects on the earth’s surface imaged ...

—We developed novel conditional expressions (CEs) for Lane and Bates' blind deconvolution. The CEs are given in term of the derivatives of the zero-values of the z-transform of given images. The CEs make it possible to automatically detect multiple blur convolved in the given images all at once without performing any analysis of the zero-sheets of the given images. We illustrate the multiple bl...

In this paper, we present an algorithm for multichannel blind deconvolution of seismic signals, which exploits lateral continuity of earth layers by dynamic programming approach. We assume that reflectors in consecutive channels, related to distinct layers, form continuous paths across channels. We introduce a quality measure for evaluating the quality of a continuous path, and iteratively appl...

In this paper, we present novel algorithms for multichannel blind deconvolution under output whitening constraints. The algorithms are inspired by recently-developed procedures for gradient adaptive paraunitary filter banks. Several algorithms are developed, including one algorithm that successfully deconvolves mixtures of arbitrary non-zero kurtosis source signals. We provide detailed local st...

Based on a Gaussian mixture model for the reflectivity sequence, we present a new technique for blind deconvolution of seismic data. The method obtains a deconvolution filter that maximizes at its output a measure of the relative entropy between the proposed Gaussian mixture and a pure Gaussian distribution. A new updating procedure for the mixture parameters is included in the algorithm: it al...

Camera shake during exposure leads to objectionable image blur and ruins many photographs. Conventional blind deconvolution methods typically assume frequency-domain constraints on images, or overly simplified parametric forms for the motion path during camera shake. Real camera motions can follow convoluted paths, and a spatial domain prior can better maintain visually salient image characteri...

We consider the general issue of estimating a nonparametric function φ from the inverse problem r = Tφ given estimates of the function r and of the linear transform T . Two typical examples include the estimation of a probability density function from data contaminated by a noise whose distribution is unknown (blind deconvolution) and the nonparametric instrumental regression. We provide a unif...