Low‐rank plus sparse compressed sensing for accelerated proton resonance frequency shift MR temperature imaging

Abstract

Purpose To improve multichannel compressed sensing (CS) reconstruction for MR proton resonance frequency (PRF) shift thermography, with application to MRI‐induced RF heating evaluation and MR guided high intensity focused ultrasound (MRgFUS) temperature monitoring. Methods A new compressed sensing reconstruction is proposed that enforces joint low rank and sparsity of complex difference domain PRF data between post heating and baseline images. Validations were performed on 4 retrospectively undersampled dynamic data sets in PRF applications, by comparing the proposed method to a previously described L1 and total variation‐ (TV‐) based CS approach that also operates on complex difference domain data, and to a conventional low rank plus sparse (L+S) separation‐based CS reconstruction applied to the original domain data. Results In all 4 retrospective validations, the proposed reconstruction method outperformed the conventional L+S and L1+TV CS reconstruction methods with a 3.6× acceleration ratio in terms of temperature accuracy with respect to fully sampled data. For RF heating evaluation, the proposed method achieved RMS error of 12%, compared to 19% for the L+S method and 17% for the L1+TV method. For in vivo MRgFUS thalamotomy, the peak temperature reconstruction errors were 19%, 31%, and 35%, respectively. Conclusion The complex difference‐based low rank and sparse model enhances compressibility for dynamic PRF temperature imaging applications. The proposed multichannel CS reconstruction method enables high acceleration factors for PRF applications including RF heating evaluation and MRgFUS sonication.

Systematic review of reconstruction techniques for accelerated quantitative MRI

“…Alternative ways to exploit the low‐rank nature of the signal . The low‐rank nature and sparsity of the signal evolution can be exploited by assuming it can be decomposed into its low‐rank component and sparse component , that is, 60,174‐178 . This results in the reconstruction problem: …”

“…Different transform operators 𝜙 and priors have been proposed to find a sparse representation of the images. This includes the wavelet transform, 27,[47][48][49][50][51][52] the total variation transform, 26,50,[52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] group sparsity where images are divided into multiple sparse regions, 69 weighted quadratic prior that aims to suppress the noise and reconstruction artifacts based on the intensity differences between neighboring voxels, 56 gradient across the contrast dimension, 53,[70][71][72][73][74] second-order discrete derivative in the contrast dimension, 75,76 principal component analysis-based transform, 75,[77][78][79][80] image ratio constraints, where the ratio between a low-resolution image and the reconstructed image is used as a constraint, 50 and learned sparsifying transform 𝜙 from the measurements. 81 Apart from these, alternative ways to use regularizers and transform domains have been proposed.…”