Under-determined non-cartesian MR reconstruction with non-convex sparsity promoting analysis prior

Area of Science:

• Medical Imaging
• Signal Processing
• Computational Science

Background:

• Magnetic Resonance (MR) image reconstruction often involves solving under-determined and ill-posed inverse problems.
• Acquiring sufficient K-space samples for high-resolution MR images can be challenging, leading to undersampling.
• Sparsity in the wavelet domain is a common prior assumption for MR image reconstruction.

Purpose of the Study:

• To investigate and compare the effectiveness of synthesis and analysis prior formulations for MR image reconstruction using wavelet sparsity.
• To determine which prior formulation, when applied to a redundant wavelet transform, yields superior reconstruction results.

Main Methods:

• The study formulates the MR reconstruction problem as an inverse problem with sparsity priors in the wavelet domain.
• Both synthesis prior (solving for wavelet coefficients) and analysis prior (solving for the image directly) formulations were explored.
• A non-convex lp-norm was used as a sparsity metric for wavelet coefficients.
• The analysis prior formulation was applied to a redundant wavelet transform.

Main Results:

• The analysis prior formulation on a redundant wavelet transform demonstrated superior performance in MR image reconstruction.
• Results indicate that solving for the image directly (analysis prior) in the wavelet domain provides better outcomes than solving for the wavelet coefficients (synthesis prior).

Conclusions:

• The analysis prior formulation utilizing redundant wavelet transforms offers improved MR image reconstruction compared to traditional synthesis prior methods.
• This finding suggests a more effective approach for reconstructing high-quality MR images from limited K-space data.