A Hybrid L0-L1 Minimization Algorithm for Compressed Sensing MRI

INTRODUCTION Both L1 minimization [1] and homotopic L0 minimization [2] techniques have shown success in compressed-sensing MRI reconstruction using reduced k-space data. L1 minimization algorithm is known to usually shrink the magnitude of reconstructions especially for larger coefficients [1, 3] and non-convex penalty used in homotopic L0 minimization is advocated to replace L1 penalty [3]. However, homotopic L0 minimization only finds local minimum which may not be sufficiently robust when the signal is not strictly sparse but also has small elements after a sparsifying transform or the measurements are contaminated by noise [4]. Since practical MR images are never strictly sparse after a transform, it is desirable to estimate both large and small coefficients more accurately. In this abstract, we propose a homotopic L0-L1 hybrid minimization algorithm to combine the benefits of both L1 and homotopic L0 minimization algorithms for MRI. The proposed algorithm minimizes the L0 quasi-norm of large transform coefficients but the L1 norm of small transform coefficients for the image to be reconstructed. The experimental results show the proposed algorithm outperforms either homotopic L0 or L1 minimization when the same reduction factor is used.