Comparative Evaluation of L1 Vs Lp Minimization Techniques for Compressed Sensing MRI

Juan Carlos Ramirez Giraldo¹, Joshua D. Trzasko¹, Armando Manduca¹

Compressed sensing(CS) can provide accurate reconstructions from highly undersampled data for certain types of MR scans, allowing faster acquisition times. Standard CS is based on l₁-norm minimization, which offers mathematical guarantees of global convergence. It is known that fewer samples are required for CS based on minimization of an l₀-norm, but this is mathematically more difficult and no convergence guarantees exist. We compare standard l₁-norm CS with two algorithms that approximate the l₀-norm with the l_p-norm (p between 0 and 1), with different sampling pattern densities and parameterizations. Despite the lack of theoretical guarantees, both l_p-norm algorithms always outperformed standard l₁-norm CS.