Multiscale wavelet-based regularized reconstruction algorithm for three-dimensional compressed sensing magnetic resonance imaging

Nowadays, the most dynamic and safe imaging technique used in hospitals to diagnose is magnetic resonance imaging (MRI). In clinical applications, such as follow-up of patients with planning surgery, radiation therapy, therapy response in bone metastases assessment and treatment for brain disorders, repeated MRI scans are performed. Unfortunately, the slow acquisitions of MRI drive cost high by limiting patient throughput as well as limiting the potential indications for use. A mathematical framework called compressed sensing (CS) to accelerate MRI acquisition is used for generating undersampled measurements. Then, the iterative nonlinear numerical method is required for perfect reconstruction from highly undersampled measurements. In this work, the multiscale wavelet domain regularization prior-based iterative reconstruction algorithm is developed to address the above-mentioned reconstruction problem, in which multiscale wavelet domain generalized Gaussian mixture model is utilized for the regularization prior. The regularization-based algorithm is applied to generate three-dimensional (3D) high-quality MRI volume from multichannel k-space measurements in a compressed sensing framework. Several experiments using one synthetic and one real 3D CS multichannel k-space data were used to evaluate and validate the performance of the proposed algorithm. The total variation (TV)-based and soft-thresholding (ST) based-reconstruction methods were implemented to compare with the proposed algorithm. Extensive experimental results demonstrated that the proposed method has improved results in terms of visual quality and quantitative measurements compared to the existing methods.