This paper considers recovering L-dimensional vectors , and from their circular convolutions The vector is assumed to be S-sparse in a known basis that is spread out in the Fourier domain, and each input xn is a member of a known K-dimensional random subspace. We prove that whenever , the problem can be solved effectively […]
We consider the task of recovering two real or complexm-vectors from phase less Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a non-trivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belongto […]
We consider the bilinear inverse problem of recovering two vectors, and , from their entrywise product. We consider the case where and have known signs and are sparse with respect to known dictionaries of size and , respectively. Here, and may be larger than, smaller than, or equal to . We introduce -BranchHull, which is […]
This article proposes a novel approach to regularize the ill-posed and non-linear blind image deconvolution (blind deblurring) using deep generative networks as priors. We employ two separate pretrained generative networks — given lower-dimensional Gaussian vectors as input, one of the generative models samples from the distribution of sharp images, while the other from that of […]
The recently developed theory of Compressive sensing (CS) has shown that sparse signals can be reconstructed from a much smaller number of measurements than their bandwidth suggests. In this paper we present a sampling scheme to acquire ensembles of correlated signals at a sub-Nyquist rate. The sampling architecture uses simple analog building blocks including analog […]
This paper considers the blind deconvolution of multiple modulated signals/filters, and an arbitrary filter/signal. Multiple inputs are modulated (pointwise multiplied) with random sign sequences , respectively, and the resultant inputs are convolved against an arbitrary input to yield the measurements , where and denote pointwise multiplication, and circular convolution. Given , we want to recover […]
Algorithmic phase retrieval offers an alternative means to recover the phase of optical images without requiring sophisticated measurement setups such as holography. This paper proposes a framework to regularize the highly ill-posed and nonlinear phase retrieval problem through deep generative priors by simply using gradient descent algorithm. We experimentally show effectiveness of the proposed approach […]
We consider the problem of recovering two unknown vectors, and , of length from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension and the other with dimension . Although the observed convolution is nonlinear in both and , it is linear in the […]
This letter presents a framework for the compressive acquisition of correlated signals. We propose an implementable sampling architecture for the acquisition of ensembles of correlated (lying in an a priori unknown subspace) signals at a sub-Nyquist rate. The sampling architecture acquires structured compressive samples of the signals after preprocessing them with easy-toimplement components. Quantitatively, we […]
This letter considers the blind separation of convolutive mixtures in a multi-in-multi-out (MIMO) communication system. Multiple source signals are transmitted simultaneously over a shared communication medium (modeled as linear convolutive channels) to multiple receivers. We recast the joint recovery of the source signals, and the channel impulse responses as a block-rank-one matrix recovery problem, which […]
