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.