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 problem of nefarious or false rankings that compromise a recommendation system’s integrity has surfaced. We consider such purposefully erroneous rankings to be a form of […]
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 be recast as the recovery of a rank-1 matrix, and is effectively relaxed using a semidefinite program (SDP). We show that exact recovery of both […]
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 than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training […]
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 subspaces, we introduce the convex program BranchHull, which is posed in the natural parameter space and does not require an approximate solution or initialization in […]
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 […]
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, at a sub-Nyquist rate using simple modulation and filtering architectures. We recast the reconstruction of the ensemble as a low-rank matrix recovery problem from generalized […]
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 […]
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 a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong […]
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 existing Fourier ptychography techniques, in terms of quality of reconstruction and robustness against noise, using far fewer samples. We further modify the proposed approach to […]
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 at a rate , and the resultant spread spectrum signal is convolved against an M-tap channel impulse response to yield the observed signal , where […]
