Signal reconstruction using total-variation primal-dual hybrid gradient (TV-PDHG) algorithm

摘要

A mechanism for reconstructing a signal (e.g., an image) based on a vector s, which includes measurements of the signal. The measurements have been acquired using at least a portion of a measurement vector set represented by a matrix H. Each of the measurements corresponds to a respective row of the matrix H. (For example, each of the measurements may correspond to an inner product between the signal and a respective row of the matrix product HD, wherein D is a generalized permutation matrix.) A total-variation primal-dual hybrid gradient (TV-PDHG) algorithm is executed based on data including the matrix H and the vector s, to determine an estimate for the signal. The TV-PDHG algorithm is implemented in fixed-point arithmetic.

主权项

1. A method for reconstructing a signal based on a vector s, wherein the vector s includes measurements of the signal, wherein the measurements have been acquired using at least a portion of a measurement vector set represented by a matrix H, wherein each of the measurements corresponds to a respective row of the matrix H, the method comprising:
executing a total-variation primal-dual hybrid gradient (TV-PDHG) algorithm based on data including the matrix H and the vector s, to determine an estimate for the signal, wherein said executing is performed by digital circuitry, wherein the total-variation primal-dual hybrid algorithm is implemented in fixed-point arithmetic; and storing the signal estimate in a memory, wherein said data also includes a matrix D, where D is a generalized permutation matrix, wherein said executing the TV-PDHG algorithm determines the estimate for the signal by determining a vector umin that at least approximates the solution to the problem given by:maxp≤M′⁢minu⁢{p·∇u+μ2⁢RHDu-s2}, wherein the minimization is over a space of signals corresponding to a vector variable u, wherein p is a vector variable, wherein M′ is a positive constant, wherein R is a diagonal matrix whose diagonal elements are selected from the set {0,1}, wherein R is not equal to the zero matrix, wherein μ is a non-negative scalar value, wherein the signal is an image, wherein the vector s is acquired by an imaging device including a light modulation unit and a light sensing device, wherein the light modulation unit is configured to modulate an incident light stream with a temporal sequence of spatial patterns in order to obtain a modulated light stream, wherein the light sensing device is configured to capture a temporal sequence of samples of intensity of the modulated light stream, wherein each of the spatial patterns corresponds to a respective row of the matrix H, wherein the vector s includes the intensity samples.