MRI reconstruction through Compressed Sensing using Principle Component Analysis (PCA)

Compressed Sensing (CS) is a theory with potential to reconstruct sparse images from a small number of random samples in the frequency domain, and with the aim of increasing achievable acceleration factors along with improved SNR and fidelity. Therefore we minimize an objective function defined as weighted sum of non-zero elements, error and total variation (TV). The accuracy and speed of the reconstruction depends on how we choose and update the aforementioned weights and how to solve the minimization problem. In this study, we proposed the Principle Component Analysis (PCA) for weighting the sparsity in the CS formulation. Considering the dimension reduction property of PCA, it is suitable for weighting the sparse transform in the CS algorithm. In the proposed implementation the weight of sparsity is updated at each iteration using the norm L1 of PCA significant components, which quantifies the sparsity at that stage. Results were compared with the zero-filling (ZF) and low resolution (LR) techniques. Compared to CS without using the sparse weighted, the proposed method took 15% higher SNR and reached 10% higher correlation with the original image.