Iterative deblending with robust fourier thresholding

The present piece offers a generalized view of the classic Fourier thresholding, which could be derived in two ways. One of these corresponds to an 0 regularization subproblem with Fourier sensing matrices. In the case of non-Gaussian noise, such as blending noise, one can generalize it by adopting alternative robust misfit terms, and solve it using iterative hard thresholding algorithms. In this way, one imposes sparsity in the transform that describes the data and robustness on the data itself. In doing so, this paper also illustrates how iterative deblending can be optimized using robust projection operators. Such denoisers provide strong blending noise attenuation at the early stages of iterative deblending, thereby improving its convergence rates. The above could be illustrated using a numerically blended dataset.