City University of Hong Kong

Wen-Jun Zeng

Hing Cheung So

Jiayi Chen

Abdelhak M Zoubir

A method for processing electronic data includes the steps of transforming the electronic data to a matrix representation including a plurality of matrices; decomposing the matrix representation into a series of matrix approximations; and processing, with an approximation process, the plurality of matrices thereby obtaining a low-rank approximation of the plurality of matrices.

Method for processing electronic data

The present disclosure relates to methods and systems for signal processing using coordinate descent technique for solving technical implementation problems that are expressed as unit-modulus least squares (UMLS) and unit-modulus quadratic program (UMQP) problems. Embodiments provide for iteratively minimizing an objective function of a signal vector associated with a UMLS/UMQP problem expression over a set of coordinates of the signal vector to a convergence point. The objective function is minimized with respect to a vector element corresponding to a selected coordinate index, while other vector elements that do not correspond to the selected coordinate index are fixed. Accordingly, at each iteration, minimizing the objective function involves a solution to a one-dimensional univariate quadratic minimization. Embodiments also provide various coordinate index selection rules that include a cyclic CD rule (CCD), a randomized CD rule (RCD), randomly permuted CD rule (RPCD), and a greedy CD rule (CCD).

Systems and methods for signal processing using coordinate descent techniques for unit modulus least squares (UMLS) and unit-modulus quadratic program (UMQP)

Coordinate descent is applied to recover a signal-of-interest from only magnitude information. In doing so, a single unknown value is solved at each iteration, while all other variables are held constant. As a result, only minimization of a univariate quartic polynomial is required, which is efficiently achieved by finding the closed-form roots of a cubic polynomial. Cyclic, randomized, and/or a greedy coordinate descent technique can be used. Each coordinate descent technique globally converges to a stationary point of the nonconvex problem, and specifically, the randomized coordinate descent technique locally converges to the global minimum and attains exact recovery of the signal-of-interest at a geometric rate with high probability when the sample size is sufficiently large. The cyclic and randomized coordinate descent techniques can also be modified via minimization of the l-regularized quartic polynomial for phase retrieval of sparse signals-of-interest, i.e., those signals with only a few nonzero elements.

Phase retrieval using coordinate descent techniques

Systems and methods which provide robust low-rank matrix approximation using low-rank matrix factorization in the l-norm space, where p&#x3c;2 (e.g., 1&#x2264;p&#x3c;2), providing a l-PCA technique are described. For example, embodiments are configured to provide robust low-rank matrix approximation using low-rank matrix factorization in the least absolute deviation (l-norm) space providing a l-PCA technique. Embodiments minimize the l-norm of the residual matrix in the subspace factorization of an observed data matrix, such as to minimize the l-norm of the residual matrix where p=1. The alternating direction method of multipliers (ADMM) is applied according to embodiments to solve the subspace decomposition of the low-rank matrix factorization with respect to the observed data matrix. Iterations of the ADMM may comprise solving a l-subspace decomposition and calculating the proximity operator of the l-norm.

Growing community of inventors

Hong Kong, China

Wen-Jun Zeng