# US 10,482,634 B2 · Systems and methods for imaging with anisotropic voxels

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- Number: US 10,482,634 B2
- Document ID: US10482634B2
- Status: Granted
- Kind: B2
- Application number: 15/792,363
- Filed: 2017-10-24
- Published: 2019-04-25
- Granted: 2019-11-19
- Earliest claimed: 2017-10-24
- Assignees: General Electric Company
- Applicants: General Electric Company
- Inventors: Nitin Jain; Sangtae Ahn; Steven Ross
- Web page: https://patentgrep.com/patent/US10482634B2

## CPC

- G06T 12/30: Image post-processing, e.g. metal artefact correction
- A61B 6/037: {Emission tomography}
- A61B 6/5205: {involving processing of raw data to produce diagnostic data}
- G06T 3/4007: based on interpolation, e.g. bilinear interpolation (image demosaicing G06T3/4015; edge-driven or edge-based scaling G06T3/403)
- G06T 12/20: Inverse problem, i.e. transformations from projection space into object space
- G06T 12/10: Image preprocessing, e.g. calibration, positioning of sources or scatter correction
- G06T 2207/10104: Positron emission tomography [PET]
- G06T 2211/424: Iterative
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- A61B: DIAGNOSIS; SURGERY; IDENTIFICATION (usefulness limited to only animals A61D)

## Abstract

An imaging system is provided that includes at least one detector configured to acquire imaging information, a processing unit, and a display unit. The processing unit is operably coupled to the at least one detector, and is configured to reconstruct an image using the imaging information. The image is organized into voxels having non-uniform dimensions. The processing unit is configured to perform a penalized likelihood (PL) image reconstruction using the imaging information. The PL image reconstruction includes a penalty function. Performing the penalty function includes interpolating a voxel size in at least one dimension from an original size to an interpolated size before determining a penalty function, determining the penalty function using the interpolated size to provide an initial penalty, interpolating the initial penalty to the original size to provide a modified penalty, and applying the modified penalty in the PL image reconstruction.

## Claims

### Claim 1

A system comprising:
at least one detector configured to acquire imaging information;
a microprocessor operably coupled to the at least one detector and configured to acquire the imaging information from the at least one detector, the microprocessor configured to reconstruct an image using the imaging information, wherein the imaging information is organized into voxels having non-uniform dimensions, the microprocessor configured to:
perform a penalized likelihood (PL) image reconstruction using the imaging information, the PL image reconstruction comprising a penalty function, wherein performing the penalty function comprises:
interpolating a voxel size in at least one dimension from an original size to an interpolated size before determining a penalty function;
determining the penalty function using the interpolated size to provide an initial penalty;
interpolating the initial penalty to the original size to provide a modified penalty; and
applying the modified penalty in the PL image reconstruction; and
a display unit configured to display the image generated using the PL image reconstruction.

### Claim 2 (depends on 1)

The system of claim 1, wherein processing unit is configured to interpolate the voxel size in an axial direction.

### Claim 3 (depends on 1)

The system of claim 1, wherein the processing unit is configured to linearly interpolate the voxel size in the at least one direction.

### Claim 4 (depends on 1)

The system of claim 1, wherein the processing unit is configured to interpolate the voxel size only for determining the penalty function, and to not interpolate the voxel size for a remainder of the PL image reconstruction.

### Claim 5 (depends on 1)

The system of claim 1, wherein the penalty function is expressed as:
Φ(x)=Σiyi log([Px]i+ri)−([Px]i+ri)−βR(x),
where x denotes a vector representing the image, yi are emission sinogram data, P represents a forward projection operator which includes attenuation, normalization and point spread function resolution modeling, ri are estimated back round contributions including scatter and randoms, R(x) is a penalty function and β is a penalty parameter.

### Claim 6 (depends on 1)

The system of claim 1, wherein the processing unit is configured to maximize the following objective function to perform the PL image reconstruction:
R
⁡
(
x
)
=
Σ
j
⁢
⁢
Σ
k
∈
N
j
⁢
⁢
w
jk
⁢
β
j
⁢
β
k
⁢
(
x
j
-
x
k
)
2
x
j
+
x
k
+
γ
⁢

x
j
-
x
k

,
where x denotes a vector representing the image, Nj is a set of voxels neighboring voxel j, wjk are weights, βj, βk are penalty modulation factors and γ is a parameter that controls the degree of edge-preservation.

### Claim 7 (depends on 1)

The system of claim 1, wherein the at least one detector comprises at least one positron emission tomography (PET) detector.

### Claim 8

A method comprising:
acquiring, with at least one detector, imaging information;
reconstructing an image using the imaging information, wherein the imaging information is organized into voxels having non-uniform dimensions, wherein reconstructing the image comprises:
performing a penalized likelihood (PL) image reconstruction using the imaging information, the PL image reconstruction comprising a penalty function, wherein performing the penalty function comprises:
interpolating a voxel size in at least one dimension from an original size to an interpolated size before determining a penalty function;
determining the penalty function using the interpolated size to provide an initial penalty;
interpolating the initial penalty to the original size to provide a modified penalty; and
applying the modified penalty in the PL image reconstruction; and
displaying the image generated using the PL image reconstruction.

### Claim 9 (depends on 8)

The method of claim 8, further comprising interpolating the voxel size in an axial direction.

### Claim 10 (depends on 8)

The method of claim 8, further comprising linearly interpolating the voxel size in the at least one direction.

### Claim 11 (depends on 8)

The method of claim 8, further comprising interpolating the voxel size only for determining the penalty function, and to not interpolating the voxel size for a remainder of the PL image reconstruction.

### Claim 12 (depends on 8)

The method of claim 8, wherein the penalty function is expressed as:
Φ(x)=Σiyi log([Px]i+ri)−([Px]i+ri)−βR(x),
where x denotes a vector representing the image, yi are emission sinogram data, P represents a forward projection operator which includes attenuation, normalization and point spread function resolution modeling, ri are estimated background contributions including scatter and randoms, R(x) is a penalty function and β is a penalty parameter.

### Claim 13 (depends on 8)

The method of claim 8, wherein the processing unit is configured to maximize the following objective function to perform the PL image reconstruction:
R
⁡
(
x
)
=
Σ
j
⁢
⁢
Σ
k
∈
N
j
⁢
⁢
w
jk
⁢
β
j
⁢
β
k
⁢
(
x
j
-
x
k
)
2
x
j
+
x
k
+
γ
⁢

x
j
-
x
k

,
where x denotes a vector representing the image, Nj is a set of voxels neighboring voxel j, wjk are weights, βj, βk are penalty modulation factors and γ is a parameter that controls the degree of edge-preservation.

### Claim 14 (depends on 8)

The method of claim 8, wherein acquiring the imaging information comprises acquiring positron emission tomography (PET) imaging information with a PET detector.

### Claim 15

A tangible and non-transitory computer-readable medium having instructions stored thereon, the instructions, when executed by a computer, causing the computer to:
acquire, with at least one detector, imaging information;
reconstruct an image using the imaging information, wherein the imaging information is organized into voxels having non-uniform dimensions, wherein reconstructing the image comprises:
performing a penalized likelihood (PL) image reconstruction using the imaging information, the PL image reconstruction comprising a penalty function, wherein performing the penalty function comprises:
interpolating a voxel size in at least one dimension from an original size to an interpolated size before determining a penalty function;
determining the penalty function using the interpolated size to provide an initial penalty,
interpolating the initial penalty to the original size to provide a modified penalty; and
applying the modified penalty in the PL image reconstruction; and
display the image generated using the PL image reconstruction.

### Claim 16 (depends on 15)

The computer-readable medium of claim 15, wherein performing the PL image reconstruction further comprises interpolating the voxel size in an axial direction.

### Claim 17 (depends on 15)

The computer-readable medium of claim 15, wherein performing the PL image reconstruction further comprises linearly interpolating the voxel size in the at least one direction.

### Claim 18 (depends on 15)

The computer-readable medium of claim 15, wherein performing the PL image reconstruction further comprises interpolating the voxel size only for determining the penalty function, and to not interpolating the voxel size for a remainder of the PL image reconstruction.

### Claim 19 (depends on 15)

The computer-readable medium of claim 15, wherein the penalty function is expressed as:
Φ(x)=Σiyi log([Px]i+ri)−([Px]i+ri)−βR(x),
where x denotes a vector representing the image, yi are emission sinogram data, P represents a forward projection operator which includes attenuation, normalization and point spread function resolution modeling, ri are estimated background contributions including scatter and randoms, R(x) is a penalty function and β is a penalty parameter.

### Claim 20 (depends on 15)

The computer-readable medium of claim 15, wherein performing the PL image reconstruction further comprises maximizing the following objective function to perform the PL image reconstruction:
R
⁡
(
x
)
=
Σ
j
⁢
⁢
Σ
k
∈
N
j
⁢
⁢
w
jk
⁢
β
j
⁢
β
k
⁢
(
x
j
-
x
k
)
2
x
j
+
x
k
+
γ
⁢

x
j
-
x
k

,
where x denotes a vector representing the image, Nj is a set of voxels neighboring voxel j, wjk are weights, βj, βk are penalty modulation factors and γ is a parameter that controls the degree of edge-preservation.