Wavelet-based Compressed Sensing using Gaussian Scale Mixtures

Introduction: A novel theory, called Compressed Sensing (CS) [1, 2], has demonstrated that MR images can be successfully reconstructed from a small number of k-space measurements [3]. The practical impact and success of CS in imaging applications can be attributed to the fact that most signals of practical interest have sparse representations in a transform domain. While initial CS techniques assumed that the sparsity transform coefficients are independently distributed, recent results indicate that dependencies between transform coefficients can be exploited for improved performance [4]. In this paper, we propose the use of a Gaussian Scale Mixture (GSM) model for exploiting the dependencies between wavelet coefficients in CS MRI. Our results indicate that the proposed model can significantly reduce the reconstruction artifacts in wavelet-based CS MRI. Theory: The wavelet-based CS MRI can be represented as the following minimization problem: