Apparatus and method of iterative image reconstruction using regularization-parameter control

Patent metadata

Field	Value
Publication number	US-9911208-B2
Application number	US-201615095951-A
Country	US
Kind code	B2
Filing date	Apr 11, 2016
Priority date	Apr 11, 2016
Publication date	Mar 6, 2018
Grant date	Mar 6, 2018

Abstract

A method and apparatus is provided to predict a regularization parameter for regularized iterative reconstruction of radiation detection data (e.g., computed tomography (CT) data or positron-emission tomography (PET) data) to generate a reconstructed image having specified statistical properties. The predicted regularization parameter is determined using a root-finding method performed on a transcendental objective function. The objective function is calculated using a three-dimensional Fourier transforms of an approximation to a shift invariant Hessian matrix and of matrix products between the forward-projection and back projection matrices of the system model and various (statistical) weight matrices. The specified statistical properties can include the standard deviation within a region of interest, a local spatial resolution, a low-contrast-detectability metric, etc. In addition to the specified statistical properties, the prediction of the regularization parameter accounts for the statistical properties of the radiation detection data, the display field of view, and the system model.

First claim

The invention claimed is:

1. An apparatus, comprising:
processing circuitry configured to
obtain radiation detection data representing an intensity of X-ray radiation detected at a plurality of detector elements,
predict a regularization parameter that multiplies a regularization function, the regularization parameter being predicted to generate a reconstructed image having predefined statistical properties within a region of interest, when the reconstructed image is reconstructed using the radiation detection data and a regularized iterative reconstruction process that includes the regularization function and the regularization parameter, and
iteratively reconstruct the reconstructed image based on the radiation detection data using the regularized iterative reconstruction process that includes the regularization function and the regularization parameter.

2. The apparatus according to claim 1 , wherein the processing circuitry is further configured to predict the regularization parameter using a system model that includes a forward-projection matrix and a back-projection matrix, a product of the forward-projection matrix and the back-projection matrix being a non-identity matrix.

3. The apparatus according to claim 2 , wherein the processing circuitry is further configured to predict the regularization parameter to generate the reconstructed image having the predefined statistical properties, the predefined statistical properties being one of a low-contrast-detectability-model parameter, a modulation-transfer-function parameter, a noise-power-spectrum parameter, a d-prime metric, and a standard deviation.

4. The apparatus according to claim 2 , wherein the processing circuitry is further configured to predict the regularization parameter using a calculation of a three-dimensional Fourier transform of a matrix product that includes the back-projection matrix and the forward-projection matrix.

5. The apparatus according to claim 2 , wherein the processing circuitry is further configured to predict the regularization parameter using a calculation of an approximation of a shift invariant Hessian matrix.

6. The apparatus according to claim 2 , wherein the processing circuitry is further configured to predict the regularization parameter to generate the reconstructed image having the predefined statistical properties within the region of interest, the region of interest including a plurality of pixels or pixels.

7. The apparatus according to claim 1 , wherein the processing circuitry is further configured to select the region of interest in the reconstructed image to be arranged within a region of uniform density within the reconstructed image.

8. The apparatus according to claim 1 , wherein the processing circuitry is further configured to iteratively reconstruct the reconstructed image using the regularization function, which is one or more of a quadratic regularization function, a non-quadratic regularization function, and Huber regularization function, and a total-variation minimization regularization function.

9. The apparatus according to claim 1 , wherein the processing circuitry is further configured to predict the regularization parameter using a root-finding method to find a root of a objective function, the root-finding method being one of a Newton's root-finding method, a secant root-finding method, a bisection root-finding method, an interpolation-based root-finding method, an inverse-interpolation-based root-finding method, a Brent's root-finding method, a Budan-Fourier-based root-finding method, and a Strum-chain-based root-finding method.

10. The apparatus according to claim 9 , wherein the processing circuitry is further configured to predict the regularization parameter using the bisection root finding method by
determining a parameter range for the regularization parameter, the parameter range spanning from a lower value to an upper value,
determining a mid-point value between the lower value and the upper value,
querying whether an objective function for predicting the regularization parameter when evaluated at the mid-point value has an absolute value less than a predefined threshold,
returning the mid-point value when the objective function evaluated using the mid-point value has the absolute value less than the predefined threshold,
setting the upper value to the mid-point value when the objective function evaluated using the mid-point value has the absolute value greater than the predefined threshold and a sign of the objective function evaluated using the mid-point value is equal to a sign of the objective function evaluated using the upper value, and
setting the lower value to the mid-point value when the objective function evaluated using the mid-point value has the absolute value greater than the predefined threshold and a sign of the objective function evaluated using the mid-point value is equal to a sign of the objective function evaluated using the lower value.

11. The apparatus according to claim 1 , wherein the processing circuitry is further configured to predict the regularization parameter using a weight matrix that includes diagonal values determined using a predefined cap value.

12. The apparatus according to claim 11 , wherein the diagonal values of the weight matrix include a ratio between a square of an inverse variance and a minimum between the inverse variance and the cap value.

13. The apparatus according to claim 1 , wherein the processing circuitry is further configured to predict the regularization parameter to account for
a size of a display field of view used in the iterative reconstruction of the reconstructed image,
a system model that includes a forward-projection matrix and a back-projection matrix used in the iterative reconstruction of the reconstructed image, and
a weighting matric representing statistical properties of the radiation detection data.

14. The apparatus according to claim 1 , wherein the processing circuitry is further configured to obtain the radiation detection data, which is one of computed-tomography projection data, and positron-emission tomography detection data.

15. The apparatus according to claim 1 , wherein the processing circuitry is further configured to predict the regularization parameter using three dimensional Fourier transformations of respective local response arrays of matrices representing
an approximation of a shift-invariant Hessian matrix,
a matrix product including a back-projection matrix, a diagonal weight matrix, a statistical weight matrix, and a forward-projection matrix, and
a matrix product including the back-projection matrix, the statistical weight matrix, a diagonal weight matrix for which a weight cap has been applied, and the forward-projection matrix.

16. The apparatus according to claim 1 , wherein the processing circuitry is further configured to estimate a standard deviation of the reconstructed image within a region of interest by solving an objective function based on a selected regularization parameter, a display field of view, a back-projection matrix, a forward-projection matrix.

17. An apparatus, comprising:
an X-ray source radiating X-rays;
a plurality of detector elements each configured to
detect a plurality of energy components of the X-rays that are radiated from the X-ray source,
generate projection data representing an intensity of X-ray radiation detected at a plurality of energy-resolving detector elements; and

processing circuitry configured to
predict a regularization parameter that multiplies a regularization function, the regularization

Assignees

• Toshiba Medical Sys Corp

Inventors

• Zhou Jian
• Wang Wenli
• Fan Yi
• Yu Zhou

Classifications

• G06T12/20 Primary

  Inverse problem, i.e. transformations from projection space into object space · CPC title

• G06T12/30 Primary

  Image post-processing, e.g. metal artefact correction · CPC title

• G06T11/008 Primary

  Physics · mapped topic

• G06T2207/10104

  Positron emission tomography [PET] · CPC title

• G06T2207/10081

  Computed x-ray tomography [CT] · CPC title