Abstract:
A method for parallel magnetic resonance imaging (MRI) reconstruction of digital images includes providing a set of acquired k-space MR image data v, a redundant Haar wavelet matrix W satisfying WW=I, wherein I is an identity matrix, a regularization parameter λ≧0, and a counter limit k, initializing a variable z=Wv, and intermediate quantities p=q=0, calculating y=arg min1/2∥z−(p+z)∥+λ∥z∥for 0≦i≦k, wherein z denotes values of an MR image sought to be reconstructed, updating p=(p+z)−y, updating z=arg min1/2∥z−(q+z)∥+g(z), whereinand updating q=(q+y)−z, wherein x=Wz is a solution ofthat specifies a reconstruction of the MR image.