Local error detection in sparse magnetic resonance imaging

Due to the physical and the physiological constraints, the sparse magnetic resonance imaging (MRI) techniques operate in a regime where the theoretical guarantees of compressed sensing for recovery with high fidelity are improbable. Thus, the effective signal encoding in sparse MRI techniques is lossy, even at low acceleration factors. For widespread clinical use of sparse MRI, following two problems are proposed: 1) detection of errors in sparse recovered images and, 2) localized and highly fast acquisition of lossless image information in regions with high errors. This paper focuses on the former problem of detecting erroneously recovered image regions and proposes a solution based on joint statistics of wavelet coefficients across multiple subbands. The proposed technique uses multivariate generalized Gaussian distributions to jointly model the wavelet coefficients for all local regions conforming to a unique boundary signature in the image. Detection of local errors is formulated as measuring the degree of variation in the joint statistical model for boundary signatures between the recovered image and a training image. The training image can be a single Nyquist sampled image acquired prior to or during the sparse MRI volumetric scan. The preliminary experimental results show good conformance of the proposed method in detecting local error regions. The high error regions are detected with an accuracy of (91.8±1.6)% at (29.2±4.7)% false detection rate for acceleration factors up to 4.