Sparse signal recovery via reweighted shrinkage thresholding: applications in compressed sensing MRI

Compressed sensing (CS) is a powerful technique for rapid magnetic resonance imaging (MRI). The iterative shrinkage thresholding algorithm (ISTA) is widely used due to its computational efficiency, but conventional versions lack adaptive adjustment of regularisation parameters, which limits both accuracy and speed. We propose a novel algorithm that dynamically updates regularisation weights according to the convergence status of previous iterations. To mitigate staircase artefacts commonly produced by wavelet-based reconstructions, the method incorporates the contourlet transform, which more effectively captures edges and contours. The approach is designed for sensor-based MRI systems, where efficient data acquisition and processing are critical for real-time imaging. Experiments on MR images from multiple anatomical regions and sampling rates demonstrate that the method achieves faster convergence and superior reconstruction quality compared to traditional ISTA, highlighting its potential in real-time medical imaging applications, including wireless health monitoring and sensor-network-based MRI systems.