Compressed sensing MRI exploiting complementary dual decomposition

• We model an image as a union of complementary dual components.
• We employ feature-optimized alternating reconstruction of complementary dual images.
• We use TV and wavelet regularization for a baseline image and complementary details.
• The proposed method is evaluated using numerical phantom and in vivo data sets.
• The proposed method preserves image details well at high reduction factors.

Compressed sensing (CS) MRI exploits the sparsity of an image in a transform domain to reconstruct the image from incoherently under-sampled k-space data. However, it has been shown that CS suffers particularly from loss of low-contrast image features with increasing reduction factors. To retain image details in such degraded experimental conditions, in this work we introduce a novel CS reconstruction method exploiting feature-based complementary dual decomposition with joint estimation of local scale mixture (LSM) model and images. Images are decomposed into dual block sparse components: total variation for piecewise smooth parts and wavelets for residuals. The LSM model parameters of residuals in the wavelet domain are estimated and then employed as a regional constraint in spatially adaptive reconstruction of high frequency subbands to restore image details missing in piecewise smooth parts. Alternating minimization of the dual image components subject to data consistency is performed to extract image details from residuals and add them back to their complementary counterparts while the LSM model parameters and images are jointly estimated in a sequential fashion. Simulations and experiments demonstrate the superior performance of the proposed method in preserving low-contrast image features even at high reduction factors.

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