An Automatic Threshold OMP Algorithm Based on QR Decomposition for Magnetic Resonance Image Reconstruction

In magnetic resonance (MR) image reconstruction, the orthogonal matching pursuit (OMP) is widely recognized for its simplicity and competitive performance. However, OMP designs a termination condition based on some prior information such as sparsity and noise intensity. In practice, the unknown prior information of MR images cannot guarantee accurate reconstruction. To make OMP suitable for magnetic resonance imaging (MRI), we propose an automatic threshold OMP algorithm based on QR decomposition (ATOMP-QR). The termination condition of ATOMP-QR, which utilizes the mutual incoherence property of the sensing matrix, is related to whether the residual vector includes the orthogonal projection component of measurements. Then, to avoid the computation of pseudo-inverse and accelerate reconstruction speed, we perform QR decomposition on the measurement matrix. We conduct the MRI experiments to evaluate the superiority and effectiveness of ATOMP-QR in peak signal-to-noise ratio (PSNR), structure similarity index measure (SSIM), and running time. Specifically, for the T1-w image with a sparsity of 10, the PSNR was improved from 24 to 32 dB; the SSIM was increased from 0.87 to 0.99. The maximum time consumed decreased from 0.2276 to 0.0107 s.