On Tikhonov regularization for image reconstruction in parallel MRI

Parallel imaging using multiple receiver coils has emerged as an effective tool to reduce imaging time in various MRI applications. When a large number of receiver channels are used to achieve large acceleration factors, the image reconstruction problem can become very ill conditioned. This problem can be alleviated by optimizing the geometry of the coils or by mathematical regularization. Among the regularization methods, the Tikhonov scheme is most popular because of rough Gaussianity of the data noise, the easiness to incorporate prior information, as well as the existence of a closed-form solution. A central issue in implementing the Tikhonov scheme is the choice of the regularization parameter and the regularization image, which is addressed systematically in this paper. A new algorithm is also proposed for generating the regularization image and selecting the regularization parameter. Experimental results will be shown to demonstrate the performance of the algorithm.