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 u min that at least approximates the solution to the problem given by: max  p  ≤ M ′ ⁢ min u ⁢ { p · ∇ u + μ 2 ⁢  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.