Two-stage adaptive random Fourier sampling method for image reconstruction

Abstract

We propose a random Fourier sampling scheme to enhance the accuracy of the high frequency pattern estimation for image reconstruction. This method is designed to work in a constrained l(1) minimization based on the Fourier-Haar interplay revealing a column-wise maximum coherent structure that we provide. Essential in the scheme is to generate a data-driven density function by a small percentage of Fourier samples. The density function governs a random sampling procedure to acquire high frequency information, resulting in better reconstruction of the Haar wavelet coefficients. We also discuss a few examples of exact recovery of the Haar wavelet coefficients from which the proposed sampling scheme has emerged. Numerical experiments confirm superiority of the proposed sampling scheme to other conventional sampling schemes in the l(1) framework. (C) 2021 Elsevier Ltd. All rights reserved.