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Journal Publications
Leveraging Diversity and Sparsity in Blind Deconvolution
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…
Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming
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…
Bilinear Compressed Sensing Under Known Signs via Convex Programming
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…
Blind Image Deconvolution Using Deep Generative Priors
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…
Compressive Sampling of Ensembles
of Correlated Signals
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…
Blind Deconvolution Using Modulated Inputs
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…
Compressed Sensing based Robust Phase Retrieval
via Deep Generative Priors
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…
Blind Deconvolution Using Convex Programming
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…
Compressive Acquisition and Least-Squares Reconstruction of Correlated Signals
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…
A Convex Approach to Blind MIMO Communications
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…
Conference Publications
Cleaning up toxic waste: Removing nefarious contributions to recommendation systems
Recommendation systems are becoming increasingly important, as evidenced by the popularity of the Netflix prize and the sophistication of various online shopping systems. With this increase in interest, a new…
A convex approach to blind deconvolution with diverse inputs
This note considers the problem of blind identification of a linear, time-invariant (LTI) system when the input signals are unknown, but belong to sufficiently diverse, known subspaces. This problem can…
Invertible generative models for inverse problems: mitigating representation error and dataset bias
Trained generative models have shown remark-able performance as priors for inverse problems in imaging – for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements…
BranchHull: Convex Bilinear Inversion from the Entrywise Product of Signals with Known Signs
We consider the bilinear inverse problem of recovering two vectors, and , in from their entrywise product. For the case where the vectors have known signs and belong to known…
Compressive sampling of correlated signals
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…
Compressive Multiplexing of Correlated Signals
We propose two compressive multiplexers for the efficient sampling of ensembles of correlated signals. We show that we can acquire correlated ensembles, taking advantage of their (a priori-unknown) correlation structure,…
A convex program for bilinear inversion of sparse vectors
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…
Blind Deconvolutional Phase Retrieval via Convex Programming
We consider the task of recovering two real or complex -vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on…
Deep Ptych: Subsampled Fourier Ptychography Using Generative Priors
This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the…
Channel Protection Using Random Modulation
This paper shows that modulation protects a bandlimited signal against convolutive interference. A signal , bandlimited to BHz, is modulated (pointwise multiplied) with a known random sign sequence , alternating…
