Method and apparatus for compressed sensing

摘要

Method and apparatus for compressed sensing yields acceptable quality reconstructions of an object from reduced numbers of measurements. A component x of a signal or image is represented as a vector having m entries. Measurements y, comprising a vector with n entries, where n is less than m, are made. An approximate reconstruction of the m-vector x is made from y. Special measurement matrices allow measurements y=Ax+z, where y is the measured m-vector, x the desired n-vector and z an m-vector representing noise. “A” is an n by m matrix, i.e. an array with fewer rows than columns. “A” enables delivery of an approximate reconstruction, x#, of x. An embodiment discloses approximate reconstruction of x from the reduced-dimensionality measurement y. Given y, and the matrix A, approximate reconstruction x# of x is possible. This embodiment is driven by the goal of promoting the approximate sparsity of x#.

主权项

1. A method, comprising:
reconstructing a compressible digital image or a digital acoustic signal that is represented as a vector x with m entries, wherein the reconstructing is based on a vector y with n entries, wherein n is less than m, and wherein the reconstructing comprises:
a processor taking n traditional measurements to obtain the vector x;a processor compressing the measured vector x by a known matrix B to create a vector Bx, wherein the vector Bx is a vector that is approximated by one or more amplitude entries, with remaining entries that are smaller in amplitude;a processor delivering among approximate solutions y=Ax+e, with e being a reconstruction error, a delivered approximate solution x# for which Bx# is sparse or substantially sparse; anda processor applying post processing filtering to the delivered approximate solution to reduce a noise level of the delivered approximate solution,wherein at least one of the processors comprises a hardware implementation.