Wavelet-Based Compressed Sensing of the System Matrix for Magnetic Particle Imaging

Abstract Magnetic particle imaging (MPI) is a trending tracer imaging technique relatively newly proposed. In MPI, a time-consuming system matrix 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 system matrix calibration, with Discrete Cosine Transform (DCT) being the state-of-the-art sparsifying transform. This paper proposes a wavelet-based CS method for system matrix reconstruction. To the best of our knowledge, this is the first work to employ wavelets as the sparsifying transform for system matrix recovery in MPI. To this goal, we employ biorthogonal wavelet transform to sparsify the system matrix rows. We propose a variant of the iterative shrinkage/thresholding-based algorithm for system matrix 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 comparing the DCT and the proposed wavelet-based methods for the sparsity levels of several system matrix frequencies and the obtained reconstructions of system matrix and phantom images for different sparsity levels confirm that the proposed method outperforms the state-of-the-art DCT-based compression.