ALTERNATING DIRECTION OF MULTIPLIERS METHOD FOR PARALLEL MRI RECONSTRUCTION

• Main Authors: LIU JUN, NADAR MARIAPPAN, LEFEBVRE ALBAN
• Format: Patent
• Language: English
• Published: 03.10.2013
• Subjects: CALCULATING; COMPUTING; COUNTING; IMAGE DATA PROCESSING OR GENERATION, IN GENERAL; PHYSICS

A method for reconstructing parallel magnetic resonance images includes providing a set of acquired k-space MR image data y, and finding a target MR image x that minimizes ½ Fv-y 22+lambda z 1 where v=Sx and z=Wx where S is a diagonal matrix containing sensitivity maps of coil elements in an MR receiver array, F is an FFT matrix, W is a redundant Haar wavelet matrix, and lambda>=0 is a regularization parameter, by updating x k + 1 = ( mu 1  I + mu 3  S H  S ) - 1  [ mu 1  W H  ( z k - b z k ) + mu 3  S H  ( v k - b v k ) ] ,  z k + 1 = soft  ( Wx k + 1  b z k , 1 mu 1 )   where soft  ( x , T ) = { x + T if   x <= - T , 0 if    x  <= T , x - T if   x >= T ,   and   v k + 1 = ( F H  F + mu 3  I ) - 1  [ F H  y + mu 3  ( Sx k + 1 + b v k ) ] , where k is an iteration counter, mu1 and mu3 are parameters of an augmented Lagrangian function, and bz and bv are dual variables of the augmented Lagrangian.