Compressed Sensing Reconstruction in the Presence of a Reference Image

Introduction: Sparsity is an essential condition for compressed sensing (CS). Conventional CS-based MRI method relies on finding a good sparsifying transform in order to produce high quality CS-based reconstructions [1]. If sufficient sparsity cannot be achieved, CS-based reconstructions from reduced samples will typically contain artifacts. In this work, we aim at further improving signal sparsity using a reference image, which is available in various MRI applications, such as dynamic contrast-enhanced imaging and interventional imaging. One straightforward approach is subtracting the reference data from the acquired data to form a “new” data set and the corresponding difference image is reconstructed using a CS-based algorithm [2]. However, the presence of object motion, as is often the case in many applications such as interventional imaging, will degrade the improvement of sparsity. To address this issue, this work presents a compressed sensing reconstruction scheme with a novel motion compensation algorithm. Theory: The image model we used is: ( ) ( ( )) ( ) t r d I r I T r I r = + r r r , where ( ) t I r r is the