Sparse Reconstruction of Breast MRI Using Homotopic $L_0$ Minimization in a Regional Sparsified Domain

The use of MRI for early breast examination and screening of asymptomatic women has become increasing popular, given its ability to provide detailed tissue characteristics that cannot be obtained using other imaging modalities such as mammography and ultrasound. Recent application-oriented developments in compressed sensing theory have shown that certain types of magnetic resonance images are inherently sparse in particular transform domains, and as such can be reconstructed with a high level of accuracy from highly undersampled k-space data below Nyquist sampling rates using homotopic L₀ minimization schemes, which holds great potential for significantly reducing acquisition time. An important consideration in the use of such homotopic L₀ minimization schemes is the choice of sparsifying transform. In this paper, a regional differential sparsifying transform is investigated for use within a homotopic L₀ minimization framework for reconstructing breast MRI. By taking local regional characteristics into account, the regional differential sparsifying transform can better account for signal variations and fine details that are characteristic of breast MRI than the popular finite differential transform, while still maintaining strong structure fidelity. Experimental results show that good breast MRI reconstruction accuracy can be achieved compared to existing methods.