Wavelet-based compressed sensing of the system matrix for magnetic particle imaging

Magnetic particle imaging (MPI) is a trending tracer imaging technique relatively newly proposed. In MPI, a time-consuming system matrix (SM) calibration scan is required to reconstruct the spatial distribution of superparamagnetic nanoparticles. Compressed sensing (CS) techniques are widely utilized to reduce the time required for SM calibration, with Discrete Cosine Transform (DCT) being the state-of-the-art sparsifying transform. This paper proposes a wavelet-based CS method for SM reconstruction. To the best of our knowledge, this is the first work to employ wavelets as the sparsifying transform for SM recovery in MPI. To this goal, we employ biorthogonal wavelet transform to sparsify the SM rows. We propose a variant of the iterative shrinkage/thresholding-based algorithm for SM reconstruction with the help of bivariate shrinkage to take advantage of the multiscale nature of wavelets and the dependency between wavelet subband coefficients. The performance of the proposed method is assessed by phantom image reconstructions using the state-of-the-art Kaczmarz algorithm. Experimental results using the DCT and the proposed wavelet-based methods confirm that the proposed method outperforms the state-of-the-art DCT-based compression based on the comparisons of (i) the sparsity levels of several SM frequencies, (ii) the reconstruction error of SM frequencies, where the average error for channels 1 and 2 decreased by approximately 10% when using DWT instead of DCT, and (iii) the visual quality of reconstructed phantom images at different sparsity levels, as no ground truth is available for metric-based comparisons.