Sparsity Level Comparison of Different Wavelet Transforms for the System Matrix in Magnetic Particle Imaging

Magnetic particle imaging is a relatively new medical imaging technique to image superparamagnetic iron oxide nanoparticles. One of the methods to obtain images is the system matrix method, a time-consuming process repeated every time environmental factors change. Compressed sensing techniques are frequently used in the literature to scan a subsampled system matrix instead of the entire counterpart and perform reconstruction. Compressed sensing techniques are based on the assumption that images are sparse in a certain transform domain. In this work, we compare the sparsity level of the system matrix under different wavelet transforms and demonstrate that biorthogonal wavelet transform provides sparsity at a level comparable to the Discrete Cosine Transform, the state-of-the-art transform for system matrix reconstruction.