Adaptive Regularization in Compressed Sensing Using the Discrepancy Principle

Kevin F. King¹, Luca Marinelli², Christopher J. Hardy²

Compressed sensing images are usually reconstructed by finding the minimum of an objective function with two terms: one that measures the difference between the k-space data of the reconstructed image and the measured k-space data (discrepancy term), and a term that measures the L1-norm of the image in a sparsifying transform domain. A weighting factor (regularization parameter) that must be properly chosen for good image quality, balances the contribution of the two terms. A method called the discrepancy principle automatically chooses the regularization parameter based on the size of the discrepancy term and the measured noise in the k-space data.