Efficient redundant haar minimization for parallel MRI reconstruction

• Main Authors: Liu Jun, Nadar Mariappan S, Rapin Jeremy, Lefebvre Alban, Chang Ti-chiun
• Format: Patent
• Language: English
• Published: 25.04.2017
• Subjects: CALCULATING; COMPUTING; COUNTING; HANDLING RECORD CARRIERS; IMAGE DATA PROCESSING OR GENERATION, IN GENERAL; MEASURING; MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES; PHYSICS; PRESENTATION OF DATA; RECOGNITION OF DATA; RECORD CARRIERS; TESTING

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 WTW=I, wherein I is an identity matrix, a regularization parameter lambda>=0, and a counter limit k, initializing a variable z0=Wv, and intermediate quantities p0=q0=0, calculating yi=arg minz 1/2 z-(pi+zi) 22+lambda z 1 for 0@i@k, wherein z denotes values of an MR image sought to be reconstructed, updating pi+1=(pi+zi)-yi, updating zi+1=arg minz 1/2 z-(qi+zi) 22+g(z), wherein g  ( z ) = { 0 , z = WW T  z , + ∞ , otherwise ; and updating qi+1=(qi+yi)-zi-1, wherein x=WTz is a solution of min x  1 2   Wx - Wv  2 2 + lambda   Wx  1 that specifies a reconstruction of the MR image.