NIPS Poster Learning without the Phase: Regularized PhaseMax Achieves Optimal Sample Complexity

Poster

Learning without the Phase: Regularized PhaseMax Achieves Optimal Sample Complexity

Fariborz Salehi · Ehsan Abbasi · Babak Hassibi

Room 210 #64

Keywords: [ Convex Optimization ] [ Gaussian Processes ] [ Structured Prediction ] [ Sparsity and Compressed Sensing ] [ Regularization ] [ Signal Processing ] [ Information Retrieval ]

[ Abstract ]

Abstract: The problem of estimating an unknown signal,

$\mathbf x_0\in \mathbb R^n$ , from a vector

$\mathbf y\in \mathbb R^m$ consisting of

$m$ magnitude-only measurements of the form

$y_i=|\mathbf a_i\mathbf x_0|$ , where

$\mathbf a_i$ 's are the rows of a known measurement matrix

$\mathbf A$ is a classical problem known as phase retrieval. This problem arises when measuring the phase is costly or altogether infeasible. In many applications in machine learning, signal processing, statistics, etc., the underlying signal has certain structure (sparse, low-rank, finite alphabet, etc.), opening of up the possibility of recovering

$\mathbf x_0$ from a number of measurements smaller than the ambient dimension, i.e., $m

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