Referenced compressed sensing for accurate and fast spatio-temporal signal reconstruction

We address two challenges of applying compressed sensing in a practical application, namely, its poor reconstruction quality and its high computational complexity. Since most signals are not fully sparse in practice, the reconstructed signals from conventional reconstruction methods often suffer from reconstruction artifacts due to the distortion of small coefficients. To improve the reconstruction quality, we introduce referenced compressed sensing (RefCS), a reconstruction method that exploits the spatial and/or temporal redundancy between a pair of signals. We show that using a correlated reference—an arbitrary signal close to the compressed signal—there exists the bound of reconstruction error that depends on the distance between the reference and the signal. By exploiting the correlated reference, RefCS can improve the reconstruction quality by up to 90% in terms of peak signal-to-noise ratio. Moreover, it is possible to reduce the computational complexity of the proposed RefCS using the least squares method. The least squares reconstruction results can be obtained with quality comparable to that of iterative algorithms by employing the correlated reference. Using the least squares method improves the reconstruction time by a factor in the range of 9 to 5.4  ×  10^4 according to our experiments.