Adaptive regularization in compressed sensing using the discrepancy principle

coil and the Fourier operator, Ψ is a transform that produces a compressible function when operating on the image m, and the constant λ is adjusted to balance data fidelity and artifact reduction (first and second terms in J). If λ is chosen too small, uncorrected aliasing remains in the image. If λ is chosen too large, the image appears blurry. Many methods have been developed to automatically determine the optimal λ (3). Most are problematic for MRI data because either the assumptions are inapplicable or the computational burden is too high. Here we focus on a simple method called the discrepancy principle that chooses λ based on the size of the first term in J, also called the discrepancy term. A version of this method has been used for GRAPPA regularization (4). Methods