Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed, and there have been efforts to use sparse models for regularizing blind deconvolution to promote signal identifiability. Part I of this two-part paper characterizes the ambiguity space of blind deconvolution and shows unidentifia...

We review some of the important results on deconvolution, particularly the multichannel deconvolution problem, for the setting of Euclidean space, focusing on the central role of the Hörmander strongly coprime condition in this area of analysis. We then address the problem of deconvolution in the Heisenberg group setting, beginning with the results of [16]. We also extend the results of [16] to...

Convolution and Deconvolution is having wide area of application in Digital Signal Processing. Convolution helps to estimate the output of a system with arbitrary input, with knowledge of impulse response of the system. Linear systems characteristics are completely specified by the systems impulse response, as governed by the mathematics of convolution. And with the knowledge of impulse respons...

Image deconvolution is a challenging ill-posed problem when only partial information of the blur kernel is available. Certain regularization on sharp images has to be imposed to constrain the estimation of true images during the blind deconvolution process. Based on the observation that an image of sharp edges tends to minimize the ratio between the `1 norm and the `2 norm of its wavelet frame ...

This paper addresses the blind deconvolution of multi-input– multi-output (MIMO) FIR systems driven by white non-Gaussian source signals. First, we present a weaker condition on source signals than the so-called i.i.d. condition so that blind deconvolution is possible. Then, under this condition, we provide a necessary and sufficient condition for blind deconvolution of MIMO FIR systems. Finall...

Multichannel blind deconvolution has received increasing attention during the last decade. Recently, Martone [3, 4] extended the super-exponential method proposed by Shalvi and Weinstein [1, 2] for single-channel blind deconvolution to multichannel blind deconvolution. However, the Martone extension suffers from two type of serious drawbacks. The objective of this paper is to obviate these draw...

Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed since signal identifiability is a key concern, and there have been efforts to use sparse models for regularizing blind deconvolution to promote signal identifiability. Part I of this two-part paper establishes a measure theoretica...

Time-domain bidirectional deconvolution methods show great promise for overcoming the minimum-phase assumption in blind deconvolution of signals containing a mixed-phase wavelet, such as seismic data. However, usually one timedomain method is slow to converge (the slalom method) and the other one is sensitive to the initial point or preconditioner (the symmetric method). Claerbout proposed a lo...