Automatic hard thresholding for sparse signal reconstruction from NDE measurements

We propose an automatic hard thresholding (AHT) method for sparse-signal reconstruction. The measurements follow an underdetermined linear model, where the regression-coefficient vector is modeled as a superposition of an unknown deterministic sparse-signal component and a zero-mean white Gaussian component with unknown variance. Our method demands no prior knowledge about signal sparsity. Our AHT scheme approximately maximizes a generalized maximum likelihood (GML) criterion, providing an approximate GML estimate of the signal sparsity level and an empirical Bayesian estimate of the regression coefficients. We apply the proposed method to reconstruct images from sparse computerized tomography projections and compare it with existing approaches.