Efficient redundant haar minimization for parallel MRI reconstruction

Patent metadata

Field	Value
Publication number	US-9632156-B2
Application number	US-201213717842-A
Country	US
Kind code	B2
Filing date	Dec 18, 2012
Priority date	Jun 1, 2012
Publication date	Apr 25, 2017
Grant date	Apr 25, 2017

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 W T W=I, wherein I is an identity matrix, a regularization parameter λ≧0, and a counter limit k, initializing a variable z 0 =Wv, and intermediate quantities p 0 =q 0 =0, calculating y i =arg min z ½∥z−(p i +z i )∥ 2 2 +λ∥z∥ 1 for 0≦i≦k, wherein z denotes values of an MR image sought to be reconstructed, updating p i+1 =(p i +z i )−y i , updating z i+1 =arg min z ½∥z−(q i +z i )∥ 2 2 +g(z), wherein
g ⁡ ( z ) = { 0 , z = WW T ⁢ z , + ∞ , otherwise ;
and updating q i+1 =(q i +y i )−z i−l , wherein x=W T z is a solution of

min x ⁢ 1 2 ⁢  Wx - Wv  2 2 + λ ⁢  Wx  1
that specifies a reconstruction of the MR image.

First claim

What is claimed is:

1. A method for parallel magnetic resonance imaging (MRI) reconstruction of digital images, comprising:
providing a set of acquired raw k-space MR image data v, a redundant Haar wavelet matrix W satisfying W T W=I, wherein I is an identity matrix, a regularization parameter λ≧0, and a counter limit k;
obtaining a proximal operator, the proximal operator obtained by the steps of:
initializing a variable z 0 =Wv, and intermediate quantities p 0 =q 0 =0;
calculating y i =arg min z ½∥z−(p i +z i )∥ 2 2 +λ∥z∥ 1 for 0≦i≦k, wherein z denotes values of an MR image sought to be reconstructed;
updating p i+1 =(p i +z i )−y i ;
updating z i+1 =arg min z ½∥z−(q i +z i )∥ 2 2 +g(z), wherein

g
⁡

(
z
)

=

{

0
,

z
=

WW
T

⁢
z

,

+
∞

,

otherwise
;

updating q i+1 =(q i +y i )−z i+1 ,
wherein x=W T z is a solution of

min
x

⁢

1
2

⁢



Wx
-
Wv



2
2

+

λ
⁢


Wx


1

that specifies a reconstruction of the MR image; and
reconstructing a digital MR image by applying the proximal operator to the acquired raw k-space MR image data, the digital MR image displayable on a computer system display.

2. The method of claim 1 , wherein

argmin
z

⁢

1
2

⁢



z
-

(

p
i

+

z
i

)



2
2

+

λ
⁢


z


1

=

{

(

p
i

+

z
i

)

-
λ

,

(

p
i

+

z
i

)

>
λ

,

(

p
i

+

z
i

)

+
λ

,

(

p
i

+

z
i

)

-
λ

,

Assignees

• Liu Jun
• Rapin Jeremy
• Lefebvre Alban
• Nadar Mariappan S
• Chang Ti-Chiun
• Siemens Healthcare Gmbh

Inventors

• Liu Jun
• Rapin Jeremy
• Lefebvre Alban
• Nadar Mariappan S
• Chang Ti-Chiun

Classifications

• G01R33/4818 Primary

  MR characterised by data acquisition along a specific k-space trajectory or by the temporal order of k-space coverage, e.g. centric or segmented coverage of k-space · CPC title

• G01R33/5611 Primary

  Parallel magnetic resonance imaging, e.g. sensitivity encoding [SENSE], simultaneous acquisition of spatial harmonics [SMASH], unaliasing by Fourier encoding of the overlaps using the temporal dimension [UNFOLD], k-t-broad-use linear acquisition speed-up technique [k-t-BLAST], k-t-SENSE (structural details of arrays of sub-coils G01R33/3415) · CPC title

• G06T7/0012

  Biomedical image inspection · CPC title

• G06T2207/10088

  Magnetic resonance imaging [MRI] · CPC title