4 accepted papers
Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure. Variants of this problem arise in applications such as image deblurring, microscopy, neural spike sorting, and more. The problem is challenging in both theory…
We study the Short-and-Sparse (SaS) deconvolution problem of recovering a short signal a0 and a sparse signal x0 from their convolution. We propose a method based on nonconvex optimization, which under certain conditions recovers the target short and sparse signals, up to a signed shift symmetry whi…
Blind deconvolution is a ubiquitous problem of recovering two unknown signals from their convolution. Unfortunately, this is an ill-posed problem in general. This paper focuses on the {\em short and sparse} blind deconvolution problem, where the one unknown signal is short and the other one is spars…
Blind deconvolution is the problem of recovering a convolutional kernel and an activation signal from their convolution. This problem is ill-posed without further constraints or priors. This paper studies the situation where the nonzero entries in the activation signal are sparsely and randomly popu…