Fourier Domain Regularized Inversion (FDRI, DOI:10.1364/OE.26.020009) is a reconstruction method for compressive imaging based on the generalized inverse of the measurement matrix. The solution is regularized by minimizing norms of convolutions of the solution with a set of spatial filters. The method requires matrix inversion in order to obtain the regularized inverse matrix, but once the matrix is stored in the memory the reconstruction requires only single matrix by vector multiplication, which outperforms l1 minimization based methods in terms of reconstruction time. At the same time, it provides similar reconstruction quality.

From this web-page you can download a simple Matlab/Octave code which uses FDRI for image reconstruction from a DCT-based compressive measurement. The program is licensed under the GPL license. We also provide for download a Python3 translation of the code which has been sent to us by Gene Stoltz.

A word on the timing: the image reconstruction time calculated on a PC with a 4-core processor  with the sample program executed for a default 256x256 pixel image at the compression ratio of 3% should not exceed 0.1s (on an AMD FX-8150 with 64 bit Debian, the results are 0.03s - for Octave 4.0.3, and 0.08s for Matlab(TM) 2018a). This makes it possible to reconstruct the compressive measurement in real-time with a single-pixel camera. If you get longer times, you are probably not using any BLAS-like library in calculations.

SINCE APR 2019 THE FDRI CODE HAS BEEN MOVED TO https://github.com/KMCzajkowski/FDRI-single-pixel-imaging