Abstract
This work addresses the problem of recovering multi-echo T1 or T2 weighted images from their partial K-space scans. Recent studies have shown that the best results are obtained when all the multi-echo images are reconstructed by simultaneously exploiting their intra-image spatial redundancy and inter-echo correlation. The aforesaid studies either stack the vectorised images (formed by row or columns concatenation) as columns of a Multiple Measurement Vector (MMV) matrix or concatenate them as a long vector. Owing to the inter-image correlation, the thus formed MMV matrix or the long concatenated vector is row-sparse or group-sparse respectively in a transform domain (wavelets). Consequently the reconstruction problem was formulated as a row-sparse MMV recovery or a group-sparse vector recovery. In this work we show that when the multi-echo images are arranged in the MMV form, the thus formed matrix is low-rank. We show that better reconstruction accuracy can be obtained when the information about rank-deficiency is incorporated into the row/group sparse recovery problem. Mathematically, this leads to a constrained optimization problem where the objective function promotes the signal's groups-sparsity as well as its rank-deficiency; the objective function is minimized subject to data fidelity constraints. The experiments were carried out on ex vivo and in vivo T2 weighted images of a rat's spinal cord. Results show that this method yields considerably superior results than state-of-the-art reconstruction techniques.
Highlights
In multi-echo imaging, different images of the same cross-section are acquired by changing certain scan parameters, e.g., the echo times for T2 weighted images or the repetition times for T1 weighted images
Owing to limitations in space, we only show the results for 64 lines
In this work we address the problem of multi-echo MRI reconstruction form under-sampled
Summary
In multi-echo imaging, different images of the same cross-section are acquired by changing certain scan parameters, e.g., the echo times for T2 weighted images or the repetition times for T1 weighted images. The objective is to obtain images (of the same cross-section) with varying tissue contrasts. We address the reconstruction of the images from their partial K-space samples. The K-space was obtained using full sampling on a uniform Cartesian grid. Full sampling of the K-space is time consuming. Recent advances in Compressed Sensing (CS) allowed MRI researchers to reconstruct the MR images, almost perfectly, using partial, i.e., not fully sampled, K-space scans [2,3]. Partial sampling of the K-space has the advantage of reducing the acquisition time. When the K-space is not fully sampled, the reconstruction problem becomes under-determined and prior information about the solution is needed for reconstructing the images
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