RECONSTRUCTION OF AN IMAGE DATA SET FROM MEASUREMENT DATA OF AN IMAGE CAPTURING DEVICE

Abstract

A method for reconstructing an image data set from magnetic resonance data is provided. First measurement data is captured using an image capturing device. The first measurement data is captured using temporal and/or spatial subsampling and is used for reconstructing the image data set with a compressed sensing algorithm in which a boundary condition that provided agreement with the measurement data and a target function that is used in an iterative optimization. The compressed sensing algorithm evaluates candidate data sets for the image data set are used. In the reconstruction using the compressed sensing algorithm, in addition to the first measurement data, second measurement data that is captured by a second imaging modality that is different from the first imaging modality of the first measurement data but by the same image capturing device. The second measurement data is registered to the first measurement data, by a modification of the boundary condition and/or target function.

Claims

1. A method for reconstructing an image data set, the method comprising: capturing first measurement data with an image capturing device with a first modality using temporal, spatial, or temporal and spatial subsampling; capturing second measurement data with the image capturing device with a second imaging modality that is different than the first image modality; registering the second measurement data to the first measurement data using a boundary condition, a target function, or a boundary condition and target function; and reconstructing the image data set using a compressed sensing algorithm including the boundary condition and the target function, wherein the boundary condition provides agreement with the first and second measurement data and the target function is used in an iterative optimization and evaluates one or more candidate data sets for the image data set.

2. The method of claim 1, wherein the compressed sensing algorithm comprises a l.sub.1 norm of a reconstructed candidate data set that has been sparsified by applying a sparsifying operator as at least part of the target function that is to be iteratively minimized, wherein the boundary condition includes producing the first measurement data by applying to the candidate data set a measurement operator that maps measurement of the first measurement data.

3. The method of claim 1, wherein, for incorporation into the reconstruction, virtual measurement data of the first imaging modality is determined from the second measurement data, virtual measurement data of the second imaging modality is determined from the current candidate data set, and a virtual comparison data set of the first imaging modality, that is associated with the current candidate data set is determined from the second measurement data.

4. The method of claim 1, wherein the second measurement data is X-ray data.

5. The method of claim 4, wherein the boundary condition includes a Radon transform applied to a three-dimensional X-ray attenuation value set that has been derived from a current candidate data set of the iterative optimization, and virtual projections that are obtained are compared with the X-ray data.

6. The method of claim 5, wherein the boundary condition is a function of the sum of deviations of the magnetic resonance data from comparison data that results from applying a measurement operator that maps the measurement of the first image data and includes a Fourier transform onto the candidate data set, and the X-ray data of the virtual projections, lies within a tolerance range, the tolerance range selected as a function of the noise properties of the magnetic resonance data and the X-ray data.

7. The method of claim 1, wherein for the target function, either a comparison data set for the candidate data set is determined by reconstructing a three-dimensional intermediate data set from the second measurement data and mapping the attenuation values of the intermediate data set onto magnetic resonance values, or virtual projections are determined by applying a Radon transform to the three-dimensional X-ray attenuation value set that is derived from the current candidate data set of the iterative optimization procedure.

8. The method of claim 6, wherein the target function is defined as a weighted sum of a l.sub.1 norm of a difference either between the candidate data set and the comparison data set or between the virtual projections and the second measurement data, to which difference a first sparsifying operator was applied, and a l.sub.1 norm of the candidate data set, to which a second sparsifying operator was applied.

9. An image capturing device comprising: a magnetic resonance device configured to acquire first measurement data using temporal, spatial, or temporal and spatial subsampling; an X-ray device configured to acquire second measurement data; and a controller configured to register the second measurement data to the first measurement data using a boundary condition, a target function, or a boundary condition and target function and reconstruct an image data set using a compressed sensing algorithm including the boundary condition and the target function, wherein the boundary condition provides agreement with the first and second measurement data and the target function is used in an iterative optimization and evaluates one or more candidate data sets for the image data set.

10. The device of claim 9, wherein the compressed sensing algorithm comprises a l.sub.1 norm of a reconstructed candidate data set that has been sparsified by applying a sparsifying operator as at least part of the target function that is to be iteratively minimized, wherein the boundary condition includes producing the first measurement data by applying to the candidate data set a measurement operator that maps measurement of the first measurement data.

11. The device of claim 9, wherein, for incorporation into the reconstruction, virtual measurement data of the first imaging modality is determined from the second measurement data, virtual measurement data of the second imaging modality is determined from the current candidate data set, and a virtual comparison data set of the first imaging modality, that is associated with the current candidate data set is determined from the second measurement data.

12. The device of claim 9, wherein the boundary condition includes a Radon transform applied to a three-dimensional X-ray attenuation value set that has been derived from a current candidate data set of the iterative optimization, and virtual projections that are obtained are compared with the second measurement data from the X-ray device.

13. The device of claim 9, wherein the boundary condition is a function of the sum of deviations of the magnetic resonance data from comparison data that results from applying a measurement operator that maps the measurement of the first image data and includes a Fourier transform onto the candidate data set, and the second measurement data of the virtual projections, lies within a tolerance range, the tolerance range selected as a function of the noise properties of the magnetic resonance data and the first measurement data.

14. The device of claim 9, wherein for the target function, either a comparison data set for the candidate data set is determined by reconstructing a three-dimensional intermediate data set from the second measurement data and mapping the attenuation values of the intermediate data set onto magnetic resonance values, or virtual projections are determined by applying a Radon transform to the three-dimensional X-ray attenuation value set that is derived from the current candidate data set of the iterative optimization procedure.

15. The device of claim 14, wherein the target function is defined as a weighted sum of a l.sub.1 norm of a difference either between the candidate data set and the comparison data set or between the virtual projections and the second measurement data, to which difference a first sparsifying operator was applied, and a l.sub.1 norm of the candidate data set, to which a second sparsifying operator was applied.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0030] FIG. 1 depicts a flowchart of an embodiment.

[0031] FIG. 2 depicts a flowchart of an embodiment of the method according to the invention, and

[0032] FIG. 3 depicts an image capturing device according to an embodiment.

DETAILED DESCRIPTION

[0033] In an embodiment, the first measurement data is magnetic resonance data and the second measurement data is X-ray data, with all of the measurement data captured by the same image capturing device. A further acceleration of the magnetic resonance imaging is provided by further subsampling. Disadvantages that arise in magnetic resonance imaging are compensated by the X-ray imaging that is carried out simultaneously. The X-ray data is additionally incorporated into the compressed sensing algorithm that is extended.

[0034] FIG. 1 depicts relationships and procedures in an embodiment of the method where the X-ray data is taken into account in a boundary condition of the compressed sensing algorithm.

[0035] The starting point is the magnetic resonance data 1 and the X-ray data 2. Candidate data sets 3 only from the magnetic resonance data 1 are used in the context of the iterative reconstruction that is indicated by the arrow 4, to minimize the target function. The optimization method for determining the image data set x may be formulated as follows:

[00001]$\begin{array}{cc}x=\underset{z}{\mathrm{argmin}}\left({.Math.\psi .Math..Math.z^{\mathrm{MR}}.Math.}_1\right),& \left(1\right)\end{array}$

[0036] where z.sup.MR represents the candidate data sets, e.g. magnetic resonance images in the position space, and ψ represents the sparsifying operator used, for example a wavelet transform.

[0037] Modified in relation to a currently available compressed sensing algorithm, the boundary condition is:

s.t.∥F{z.sup.MR}−y.sub.MR∥.sub.2+∥R{z.sub.virtual x-ray.sup.MR}−y.sub.x-ray∥.sub.2≦ε,  (2)

[0038] into which the X-ray data 2 is also incorporated, as in formula (2) and FIG. 1. In formula (2), y.sub.MR represents the first measurement data, e.g. the magnetic resonance data 1, as k space samples. Y.sub.x-ray represents the second measurement data, e.g. the X-ray data 2, in the projection space. F represents a Fourier transform and R a Radon transform, and ε represents a specific threshold value that defines a tolerance range within which the current candidate data set z.sup.MR must agree with the measurement data.

[0039] As depicted in FIG. 1, for the boundary condition to be evaluated, a transform 5 is applied to the candidate data set 3 to obtain a virtual X-ray attenuation value set, that is designated z.sup.MR.sub.virtualx-ray in the formula. A database may store attenuation values that are associated with magnetic resonance values. The X-ray attenuation value set undergoes a Radon transform 6 in respect of the projection directions in which there is X-ray data 2. Virtual projections are produced that may be compared with the X-ray data 2 in the boundary condition by subtraction 7. In an analogous manner, by applying a Fourier transform 8 as the measurement operator to the candidate data set 3, comparison data may be determined that may be compared with the magnetic resonance data 1, similarly by subtraction 9. The threshold value E, that defines the tolerance range in which deviations in the two comparisons may be present, is selected as a function of the noise level of the magnetic resonance data 1, the X-ray data 2 and the transforms 5, 6.

[0040] FIG. 2 depicts an embodiment in which the X-ray data 2 is directly included in the iterative reconstruction, symbolized by an arrow 4, when the target function is changed. Only the magnetic resonance data is used in the boundary condition. There are two different variants of how the X-ray data 2 may be incorporated in the target function. In the first variant, the optimization may be described by the following:

[00002]$\begin{array}{cc}x=\underset{z}{\mathrm{argmin}}\left(\alpha .Math.{.Math.{\psi }_1\left(z^{\mathrm{MR}}-z_{\mathrm{virtual}.Math..Math.\mathrm{MR}}^{x.Math.\text{-}.Math.\mathrm{ray}}\right).Math.}_1+\left(1-\alpha \right).Math.{.Math.{\psi }_2.Math.z^{\mathrm{MR}}.Math.}_1\right).Math..Math.s.t..Math.{.Math.F.Math.\left\{z^{\mathrm{MR}}\right\}-y_{\mathrm{MR}}.Math.}_2\le \mathrm{.Math.},& \left(3\right)\end{array}$

[0041] where z.sup.x-ray.sub.virtual MR represents a comparison data set derived from the X-ray data, α represents a weighting parameter, and ψ.sub.1 and ψ.sub.2 are sparsifying operators. The comparison data set is determined by a reconstruction of a three-dimensional intermediate data set from the X-ray data 2 and mapping of the attenuation values of the intermediate data set onto magnetic resonance values. An alternative variant that permits direct use of the X-ray data 2, may be expressed as:

[00003]$\begin{array}{cc}x=\underset{z}{\mathrm{argmin}}\left(\alpha .Math.{.Math.{\psi }_1\left(R.Math.\left\{z_{\mathrm{virtual}.Math..Math.x.Math.\text{-}.Math.\mathrm{ray}}^{\mathrm{MR}}\right\}-y^{x.Math.\text{-}.Math.\mathrm{ray}}\right).Math.}_1+\left(1-\alpha \right).Math.{.Math.{\psi }_2.Math.z^{\mathrm{MR}}.Math.}_1\right).Math..Math..Math.s.t..Math.{.Math.F.Math.\left\{z^{\mathrm{MR}}\right\}-y_{\mathrm{MR}}.Math.}_2\le \mathrm{.Math.},& \left(4\right)\end{array}$

[0042] where z.sup.MR.sub.virtualx-ray represents an X-ray attenuation value set derived from the candidate data set 3, as described above. The projection directions of the Radon transform correspond to the projection directions of the actual X-ray data. Virtual projections are determined, but are incorporated directly into the target function, in that—as in formula (4)—a weighted sum of two terms is formed, in a manner analogous to formula (3). The weighting factor α is selected in accordance with the result that is sought. For example, if the temporal resolution is given particular importance, α may be selected to be relatively small, but then if the spatial resolution becomes more important a may also be selected to be correspondingly larger, with the result that a greater proportion of the good spatial resolution from X-ray data 2 is incorporated into the iterative reconstruction.

[0043] The sparsifying operators ψ.sub.1 and ψ.sub.2 may also be selected differently in order to compensate for constraints in the modalities. The corresponding advantages of the imaging modalities, e.g. specifically temporal resolutions and spatial resolutions, are emphasized by focusing on them in the sparsifying.

[0044] FIG. 3 depicts an image capturing device 10, for example, a combined magnetic resonance and X-ray device 11. The image capturing device 10 includes as subsystems an X-ray system 12, e.g. a computer tomography system, and a magnetic resonance system 13 that provide the imaging of X-rays and magnetic resonance respectively. The coordinate systems are registered to one another. Additionally, the main magnet unit of the magnetic resonance system 13 may be divided into two in the center to provide space for a computer tomography gantry of the X-ray system 12.

[0045] Operation of the image capturing device 10 is controlled by a controller 14.

[0046] It is to be understood that the elements and features recited in the appended claims may be combined in different ways to produce new claims that likewise fall within the scope of the present invention. Thus, whereas the dependent claims appended below depend from only a single independent or dependent claim, it is to be understood that these dependent claims may, alternatively, be made to depend in the alternative from any preceding or following claim, whether independent or dependent, and that such new combinations are to be understood as forming a part of the present specification.

[0047] While the present invention has been described above by reference to various embodiments, it may be understood that many changes and modifications may be made to the described embodiments. It is therefore intended that the foregoing description be regarded as illustrative rather than limiting, and that it be understood that all equivalents and/or combinations of embodiments are intended to be included in this description.