Compressed sensing with regularization parameter
A method is provided for generating a signal-to-noise improved magnetic resonance (MR) image of an object under examination in an MR system using a compressed sensing technology. The method includes determining a first MR signal data set of the object under examination in which a corresponding k-space is randomly subsampled; determining a location dependent sensitivity map for each of at least one receiving coil used to detect MR signals of the first MR signal data set in the location where the object under examination is located; and determining the MR image using an optimization process of the compressed sensing technology in which a location dependent regularization parameter is used, wherein the location dependent regularization parameter is determined based on the location dependent sensitivity map.
1. A method for generating a signal-to-noise improved magnetic resonance (MR) image of an object under examination in an MR system using a compressed sensing technology, the method comprising:
determining a first MR signal data set of the object under examination in which a corresponding k-space is randomly subsampled;
determining a location dependent sensitivity map for each receiving coil of at least one receiving coil used to detect MR signals of the first MR signal data set in a location of the object under examination; and
generating the MR image using an optimization process of the compressed sensing technology in which a location dependent regularization parameter is used,
wherein the location dependent regularization parameter is determined based on the location dependent sensitivity map.
2. The method of claim 1 , further comprising:
determining noise information in the location of the object under examination,
wherein the location dependent regularization parameter is determined based on the location dependent sensitivity map and the determined noise information.
3. The method of claim 2 , wherein the location dependent regularization parameter is a function depending on the determined noise information and the location dependent sensitivity map as variables.
4. The method of claim 3 , wherein the location dependent regularization parameter is determined as follows:
λ f =af ( E,R )−λ 0
wherein:
l 0 is a constant predefined offset,
f is a function,
E is the location dependent sensitivity map,
R is the noise information, and
a is a scaling factor.
5. The method of claim 4 , wherein the function is as follows:
f
(
E
,
R
)
=
exp
(
-
b
E
R
2
)
.
6. The method of claim 4 , wherein the function is as follows:
f
(
E
,
R
)
=
{
λ
max
R
/
E
R
min
>
R
>
R
max
0
.
7. The method of claim 3 , wherein the function is proportional to the determined noise information and inversely proportional to the location dependent sensitivity map.
8. The method of claim 1 , wherein the location dependent sensitivity map fully covers a predefined region of interest within a maximum possible field of view of the MR system,
wherein the predefined region of interest is fully covered and does not comprise holes, and
wherein the location dependent regularization parameter is determined for the predefined region of interest.
9. The method of claim 1 , wherein the location dependent regularization parameter is averaged for a plurality of different locations to a region dependent regularization parameter,
wherein a single value of the region dependent regularization parameter is used within each location of the plurality of different locations, and
wherein the MR image is generated based on the region dependent regularization parameter.
10. The method of claim 9 , wherein the location dependent regularization parameter is determined as follows:
λ f =af ( E,R )−λ 0
wherein:
l 0 is a constant predefined offset,
f is a function,
E is the location dependent sensitivity map,
R is the noise information, and
a is a scaling factor.
11. The method of claim 10 , wherein the function is as follows:
f
(
E
,
R
)
=
exp
(
-
b
E
R
2
)
.
12. The method of claim 10 , wherein the function is as follows:
f
(
E
,
R
)
=
{
λ
max
R
/
E
R
min
>
R
>
R
max
0
.
13. A magnetic resonance (MR) system configured to generate a signal-to-noise improved MR image of an object under examination in an MR system using a compressed sensing technology, the MR system comprising:
a control unit configured to:
determine a first MR signal data set of the object under examination in which a corresponding k-space is randomly subsampled;
determine a location dependent sensitivity map for each receiving coil of at least one receiving coil used to detect MR signals of the first MR signal data set in a location of object under examination; and
generate the MR image using an optimization process of the compressed sensing technology in which a location dependent regularization parameter is used,
wherein the location dependent regularization parameter is determined based on the location dependent sensitivity map.
14. The MR system of claim 13 , wherein the control unit is further configured to:
determine noise information in the location of the object under examination,
wherein the location dependent regularization parameter is determined based on the location dependent sensitivity map and the determined noise information.
15. A non-transitory computer readable storage medium comprising a computer program having program code, wherein the computer program, when executed by a control unit of a magnetic resonance (MR) system, is configured to cause the MR system to:
determine a first MR signal data set of an object under examination in which a corresponding k-space is randomly subsampled;
determine a location dependent sensitivity map for each receiving coil of at least one receiving coil used to detect MR signals of the first MR signal data set in a location of object under examination; and
generate a MR image using an optimization process of a compressed sensing technology in which a location dependent regularization parameter is used,
wherein the location dependent regularization parameter is determined based on the location dependent sensitivity map.