Denoising AMP for MRI reconstruction: BM3D-AMP-MRI

There is a recurrent idea being promoted in the recent literature on iterative solvers for imaging problems, the idea being the use of an actual denoising step in each iteration. We give a brief review of some algorithms from the literature which utilize this idea, and we broadly label these algorithms as Iterative Denoising Regularization (IDR) algorithms. We extend the Denoising Approximate Message Passing (D-AMP) algorithm from this list to the magnetic resonance imaging (MRI) reconstruction problem. We utilize Block Matching 3D (BM3D) as the denoiser of choice for the introduced MRI reconstruction algorithm. The application of the denoiser for complex-valued data necessitates a special handling of the denoiser. The use of the adaptive and image-dependent BM3D image model prior together with D-AMP results in highly competitive MRI reconstruction performance.