Computer-implemented method for the reconstruction of medical image data

Abstract

A computer-implemented method for reconstruction of medical image data includes receiving medical measuring data, and minimizing a cost value via gradient descent. Minimizing the cost value includes: reconstructing the medical image data by applying a reconstruction function to the received medical measuring data in accordance with reconstruction parameters; determining a cost value by applying a cost function to the reconstructed medical image data; determining a gradient of the cost function with respect to the reconstruction parameters; adjusting the reconstruction parameters based on the gradient of the cost function with respect to the reconstruction parameters and the previous reconstruction parameters; and providing the adjusted reconstruction parameters. The acts of the minimizing are repeated until a termination condition is met. The reconstructed medical image data is provided.

Claims

1. A computer-implemented method for reconstruction of medical image data, the computer-implemented method comprising: receiving medical measuring data; minimizing a cost value via gradient descent, the minimizing comprising: reconstructing the medical image data, which includes a number of image values, the reconstructing comprising applying a reconstruction function to the received medical measuring data in accordance with reconstruction parameters; determining a cost value, the determining of the cost value comprising applying a cost function to the reconstructed medical image data, wherein the cost function is based on an image quality metric; determining a gradient of the cost function with respect to the reconstruction parameters; adjusting the reconstruction parameters based on the gradient of the cost function with respect to the reconstruction parameters and the previous reconstruction parameters; providing the adjusted reconstruction parameters; and repeating the reconstructing, the determining of the cost value, the determining of the gradient, the adjusting, and the providing until a termination condition is met; and providing the reconstructed medical image data.

2. The computer-implemented method of claim 1, wherein the termination condition comprises a maximum number of repetitions, a threshold value with respect to the cost value, or the maximum number of repetitions and the threshold value.

3. The computer-implemented method of claim 1, wherein the cost function comprises a trained function, wherein applying the cost function to the reconstructed medical image data comprises applying the trained function to input data, wherein the input data is based on the reconstructed medical image data, which includes a number of image values, and wherein at least one parameter of the trained function is based on the image quality metric.

4. The computer-implemented method of claim 1, wherein minimizing the cost value via gradient descent further comprises: determining at least one consistency value, the determining of the at least one consistency value comprising applying a consistency function to the medical measuring data in accordance with the reconstruction parameters; and determining a gradient of the consistency function with respect to the reconstruction parameters, wherein adjusting the reconstruction parameters further comprises: adjusting the reconstruction parameters additionally based on the gradient of the consistency function with respect to the reconstruction parameters.

5. The computer-implemented method of claim 4, wherein the consistency function comprises a consistency metric.

6. The computer-implemented method of claim 1, wherein determining the gradient of the cost function with respect to the reconstructions parameters comprises: determining partial derivatives of the reconstruction function with respect to the reconstruction parameters; and determining partial derivatives of the cost function with respect to the image values of the reconstructed medical image data.

7. The computer-implemented method of claim 6, wherein the cost function comprises a trained function, wherein determining the partial derivatives of the cost function with respect to the image values of the reconstructed medical image data takes place using a back propagation of the trained function, and wherein input data of the back propagation is based on the cost value.

8. The computer-implemented method of claim 1, wherein reconstructing the medical image data further comprises: generating corrected reconstruction parameters, the generating of the corrected reconstruction parameters comprising applying a correction function to the reconstruction parameters; and providing the corrected reconstruction parameters as reconstruction parameters for the reconstruction function.

9. In a non-transitory computer-readable storage medium that stores instructions executable by one or more processors of a medical imaging device for reconstruction of medical image data, the instructions comprising: receiving medical measuring data; minimizing a cost value via gradient descent, the minimizing comprising: reconstructing the medical image data, which includes a number of image values, the reconstructing comprising applying a reconstruction function to the received medical measuring data in accordance with reconstruction parameters; determining a cost value, the determining of the cost value comprising applying a cost function to the reconstructed medical image data, wherein the cost function is based on an image quality metric; determining a gradient of the cost function with respect to the reconstruction parameters; adjusting the reconstruction parameters based on the gradient of the cost function with respect to the reconstruction parameters and the previous reconstruction parameters; providing the adjusted reconstruction parameters; and repeating the reconstructing, the determining of the cost value, the determining of the gradient, the adjusting, and the providing until a termination condition is met; and providing the reconstructed medical image data.

10. The non-transitory computer-readable storage medium of claim 9, wherein the termination condition comprises a maximum number of repetitions, a threshold value with respect to the cost value, or the maximum number of repetitions and the threshold value.

11. The non-transitory computer-readable storage medium of claim 9, wherein the cost function comprises a trained function, wherein applying the cost function to the reconstructed medical image data comprises applying the trained function to input data, wherein the input data is based on the reconstructed medical image data, which includes a number of image values, and wherein at least one parameter of the trained function is based on the image quality metric.

12. The non-transitory computer-readable storage medium of claim 9, wherein minimizing the cost value via gradient descent further comprises: determining at least one consistency value, the determining of the at least one consistency value comprising applying a consistency function to the medical measuring data in accordance with the reconstruction parameters; and determining a gradient of the consistency function with respect to the reconstruction parameters, wherein adjusting the reconstruction parameters further comprises: adjusting the reconstruction parameters additionally based on the gradient of the consistency function with respect to the reconstruction parameters.

13. The non-transitory computer-readable storage medium of claim 12, wherein the consistency function comprises a consistency metric.

14. The non-transitory computer-readable storage medium of claim 9, wherein determining the gradient of the cost function with respect to the reconstructions parameters comprises: determining partial derivatives of the reconstruction function with respect to the reconstruction parameters; and determining partial derivatives of the cost function with respect to the image values of the reconstructed medical image data.

15. The non-transitory computer-readable storage medium of claim 14, wherein the cost function comprises a trained function, wherein determining the partial derivatives of the cost function with respect to the image values of the reconstructed medical image data takes place using a back propagation of the trained function, and wherein input data of the back propagation is based on the cost value.

16. The non-transitory computer-readable storage medium of claim 9, wherein reconstructing the medical image data further comprises: generating corrected reconstruction parameters, the generating of the corrected reconstruction parameters comprising applying a correction function to the reconstruction parameters; and providing the corrected reconstruction parameters as reconstruction parameters for the reconstruction function.

17. A medical imaging device comprising: a processor configured to: receive medical measuring data; minimize a cost value via gradient descent, the minimization comprising: reconstruction of the medical image data, which includes a number of image values, the reconstruction comprising application of a reconstruction function to the received medical measuring data in accordance with reconstruction parameters; determination of a cost value, the determination of the cost value comprising application of a cost function to the reconstructed medical image data, wherein the cost function is based on an image quality metric; determination of a gradient of the cost function with respect to the reconstruction parameters; adjustment of the reconstruction parameters based on the gradient of the cost function with respect to the reconstruction parameters and the previous reconstruction parameters; provision of the adjusted reconstruction parameters; and repetition of the reconstruction, the determination of the cost value, the determination of the gradient, the adjustment, and the provision until a termination condition is met; and provide the reconstructed medical image data.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Exemplary embodiments of the invention are shown in the drawings and are described in more detail below. The same reference signs are used for the same features in different figures, in which:

(2) FIGS. 1 to 4 show schematic representations of exemplary embodiments of a computer-implemented method for reconstruction of medical image data;

(3) FIG. 5 shows a schematic flow diagram for providing a trained function;

(4) FIG. 6 shows an exemplary embodiment of a processing unit;

(5) FIG. 7 shows an exemplary embodiment of a training system; and

(6) FIG. 8 shows a schematic representation of one embodiment of a C-arm x-ray device.

DETAILED DESCRIPTION

(7) FIG. 1 shows a schematic representation of an embodiment of a computer-implemented method for reconstruction of medical image data. In a first act, medical measuring data {right arrow over (w)} may be received. In this regard, the medical measuring data {right arrow over (w)} may be recorded by a medical imaging device and/or received by a medical imaging device and/or a processing unit (e.g., including one or more processors). The medical measuring data may be provided by the processing unit (e.g., the medical imaging device).

(8) In a further act a), the medical image data {right arrow over (r)}, which includes a number of image values r.sub.i, may be reconstructed by applying a reconstruction function g to the received medical measuring data {right arrow over (w)} in accordance with reconstruction parameters {right arrow over (p)}. The reconstruction function g may, for example, include a mapping between the received medical measuring data {right arrow over (w)} onto the medical image data {right arrow over (r)}:
{right arrow over (r)}=g({right arrow over (w)},{right arrow over (p)}),g:.sup.u+v.fwdarw..sup.q  (1),
where {right arrow over (w)}∈.sup.u and {right arrow over (p)}∈.sup.v.

(9) In act b), a cost value ϵ may be determined by applying a cost function f=f({right arrow over (r)}) to the reconstructed medical image data {right arrow over (r)}. The cost function f may map the reconstructed medical image data r onto a scalar ϵ:
ϵ=ƒ({right arrow over (r)}),ƒ:.sup.q.fwdarw..sub.0,+  (2).

(10) Assuming that the cost function f may be differentiated (e.g., continuously) in accordance with the reconstruction parameters {right arrow over (p)}, in act c), a gradient {right arrow over (∇)}ƒ of the cost function f may be determined with respect to the reconstruction parameters {right arrow over (p)}. In act d), the reconstruction parameters {right arrow over (p)} may be adjusted both based on the gradient of the cost function ∇ƒ with respect to the reconstruction parameters {right arrow over (p)} and also the previous reconstruction parameters {right arrow over (p)}. In act e), the adjusted reconstruction parameters {right arrow over (p)}′ may be provided 2 as reconstruction parameters for act a). Further, acts a) to e) may be repeated until a termination condition A is met.

(11) The termination condition A may check, for example, according to act b) whether the determined cost value ϵ does not reach a predetermined threshold value. A maximum number of repetitions of acts a) to e) may be fixed by the termination condition. The termination condition A may bring about a check to determine whether the specific cost value ϵ is below a predetermined threshold value and/or the maximum number of repetitions has been reached and/or exceeded. If the termination condition A is met, the medical image data r reconstructed (e.g., finally) in step a) may be provided 3. The termination condition A may be checked according to act b).

(12) A minimization of the cost value ϵ may be achieved via gradient descent by repeatedly implementing acts a) to e). In this regard, the reconstruction parameters {right arrow over (p)} may be determined such that
{circumflex over ({right arrow over (p)})}=argmin.sub.{right arrow over (p)}½ϵ.sup.2=argmin.sub.{right arrow over (p)}½ƒ(g({right arrow over (p)})).sup.2  (3)
where {circumflex over ({right arrow over (p)})} refers to the optimum of the reconstruction parameters {circumflex over ({right arrow over (p)})} for minimizing the cost value ϵ. Further, the received measuring data {right arrow over (w)} is assumed to be unchangeable (e.g., during the minimization of the cost value ϵ).

(13) The determination of the gradient of the cost function {right arrow over (∇)}ƒ with respect to the reconstruction parameters {right arrow over (p)} may take place by determining the partial derivatives:

(14) $\begin{array}{cc}\stackrel{.fwdarw.}{\nabla }f=\frac{\partial f}{\partial \stackrel{.fwdarw.}{p}}.& \left(4\right)\end{array}$

(15) The partial derivatives of the cost function f are, for example, required with respect to each of the reconstruction parameters p.sub.1, . . . , p.sub.v∈{right arrow over (p)},

(16) $\begin{array}{cc}\stackrel{.fwdarw.}{\nabla }f=\frac{\partial f}{\partial \stackrel{.fwdarw.}{p}}=\left(\frac{\partial f}{\partial p_1},.Math.,\frac{\partial f}{\partial p_v}\right).& \left(5\right)\end{array}$

(17) The cost function f may be based on an image quality metric. The image quality metric may include, for example, a regression of a back projection error (e.g., with a movement correction).

(18) The image quality metric may be embodied to evaluate the image quality with respect to an x-ray beam hardening and/or a signal-to-noise ratio and/or a characteristic of image artifacts (e.g., metal artifacts).

(19) FIG. 2 shows a schematic representation of a further embodiment of the proposed computer-implemented method for the reconstruction of medical image data {right arrow over (r)}. In act b2, at least one consistency value K may be determined by applying a consistency function h to the measuring data {right arrow over (w)} according to reconstruction parameters {right arrow over (p)}.

(20) In a further act c2), a gradient of the consistency function {right arrow over (∇)}h may be determined {right arrow over (p)} with respect to the reconstruction parameters. The consistency function h may include a mapping of the received medical measuring data and the reconstruction parameters {right arrow over (p)} onto a scalar k.
k=h({right arrow over (w)},{right arrow over (p)}),h:.sup.u+v.fwdarw..sub.0,+  (6).

(21) It may be assumed that the consistency function h may be differentiated (e.g., continuously) in accordance with the reconstruction parameters {right arrow over (p)}. The determination of the gradient {right arrow over (∇)}h of the consistency function with respect to the reconstruction parameters {right arrow over (p)} may take place similarly to the determination of the gradient of the cost function {right arrow over (∇)}ƒ with respect to the reconstruction parameters {right arrow over (p)}. In one embodiment, all partial derivatives of the consistency function h may be determined with respect to each of the reconstruction parameters p.sub.1, . . . , p.sub.v∈{right arrow over (p)}:

(22) $\begin{array}{cc}\stackrel{.fwdarw.}{\nabla }h=\frac{\partial h}{\partial \stackrel{.fwdarw.}{p}}=\left(\frac{\partial h}{\partial p_1},.Math.,\frac{\partial h}{\partial p_v}\right).& \left(7\right)\end{array}$

(23) The adjustment of the reconstruction parameters {circumflex over ({right arrow over (p)})} in act d) may take place additionally based on the gradient of the consistency function {right arrow over (∇)}h with respect to the reconstruction parameters. The optimization problem described in equation (3) may be expressed as follows:
{circumflex over ({right arrow over (p)})}=argmin.sub.{right arrow over (p)}½ϵ.sup.2+λk=argmin.sub.{right arrow over (p)}½ƒ(g({circumflex over ({right arrow over (p)})})).sup.2+λh({right arrow over (w)},{right arrow over (p)})  (8),
where λ refers to a scalar for scaling the consistency value k of the consistency function h.

(24) The consistency function h may include a consistency metric. For example, the consistency metric may be based on the Grangeat theorem and/or the Nyquist theorem.

(25) The consistency metric may be embodied to evaluate the consistency between reconstruction parameters and medical measuring data with respect to an epipolar consistency condition and/or a sampling consistency condition and/or a symmetry consistency condition.

(26) FIG. 3 shows a schematic representation of a further embodiment of the proposed computer-implemented method for the reconstruction of medical image data {right arrow over (r)}. Act c) may also include a determination of partial derivatives of the reconstruction function g

(27) with respect to the reconstruction parameters {right arrow over (p)},

(28) $\frac{\partial g}{\partial p_j}\forall j=1,.Math.,v.$
In act c), the partial derivatives of the cost function f may also be determined with respect to the image values r.sub.i of the reconstructed medical image data {right arrow over (r)},

(29) $\frac{\partial f}{\partial r_i}\forall i=1,.Math.,q.$
The gradient of the cost function {right arrow over (∇)}ƒ with respect to the reconstruction parameters {right arrow over (p)} may be determined (e.g., analytically) in accordance with the chain rule for multidimensional derivatives of the differential computation.

(30) $\begin{array}{cc}\frac{\partial f}{\partial p_j}=\frac{\partial f\left(g\left(\stackrel{.fwdarw.}{p}\right)\right)}{\partial p_j}=\underset{i=1}{\overset{q}{.Math.}}\frac{\partial f}{\partial r_i}\frac{\partial g}{\partial p_j}.& \left(9\right)\end{array}$
thus applies to the partial derivatives of the cost function f in accordance with each of the reconstruction parameters p.sub.1, p.sub.v∈{circumflex over ({right arrow over (p)})} in equation (5).

(31) FIG. 4 shows a schematic representation of a further embodiment of the computer-implemented method. Act a) may further include a generation of corrected reconstruction parameters {tilde over ({right arrow over (p)})} by applying a correction function 1 to the reconstruction parameters {right arrow over (p)}. The correction function 1 may map the reconstruction parameters {right arrow over (p)} onto the corrected reconstruction parameters {tilde over ({right arrow over (p)})}:
{tilde over ({right arrow over (p)})}=l({right arrow over (p)}),l:.sup.v.fwdarw..sup.v  (10).

(32) The corrected reconstruction parameters p may be provided as reconstruction parameters {right arrow over (p)} for the reconstruction function in act a).
{right arrow over (r)}=g({right arrow over (w)},{tilde over ({right arrow over (p)})})=g({right arrow over (w)},l({right arrow over (p)}))  (11)
results from equations (1) and (10).

(33) $\begin{array}{cc}\frac{\partial g}{\partial p_j}=\frac{\partial g}{\partial {\tilde{p}}_i}\frac{\partial l}{\partial p_j}& \left(12\right)\end{array}$
therefore applies in order to determine the gradient of the partial derivatives of the reconstruction function g according to each of the reconstruction parameters {right arrow over (p)} in equation (9).

(34) Outlined below by way of example is a three-dimensional movement correction during the reconstruction of medical image data from two-dimensional projection x-ray images as medical measuring data w of an examination object. The correction function 1 may be embodied, for example, in order to correct a rigid movement of the examination object. A rigid three-dimensional movement may be described by a homogenous movement matrix M({right arrow over (p)})∈.sup.4×4, where {right arrow over (p)}∈.sup.6. In this regard, the correction function 1 may include the homogenous movement matrix M.

(35) Recording parameters (e.g., an acquisition geometry) of the received medical measuring data {right arrow over (w)} may be described by a projection matrix D∈.sup.3×4. The reconstruction function g may include the projection matrix D. First, the received medical measuring data may be interpolated:
s(φ,ρ):.sup.2.fwdarw.  (13),
where s refers to a continuous function along the two spatial directions φ and ρ.

(36) A movement-compensated image value r.sub.i of the medical image data {right arrow over (r)} (with r.sub.i∈{right arrow over (r)}) may be determined according to:
r.sub.i=r.sub.i.sup.0+s(φ,ρ)  (14)
where φ=[DMx.sub.i].sub.1/[DMx.sub.i].sub.3  (15)
and ρ=[DMx.sub.i].sub.2/[DMx.sub.i].sub.3  (16),
where [⋅].sub.z extracts the row z from the respective matrix, r.sub.i.sup.0 refers to the sealing value of an x-ray slice image reconstructed without projection s, and x.sub.i∈.sup.4 describes spatial positions of the image values r.sub.i (e.g., of the voxels) in homogenous coordinates.

(37) $\begin{array}{cc}\frac{\partial r_i}{\partial \stackrel{.fwdarw.}{p}}=\frac{\partial r_i}{\partial \phi }\frac{\partial \phi }{\partial \stackrel{.fwdarw.}{p}}+\frac{\partial r_i}{\partial \rho }\frac{\partial \rho }{\partial \stackrel{.fwdarw.}{p}}& \left(17\right)\end{array}$
results from the equations (14) to (16) (and similarly to equation (12)).

(38) In equation (17),

(39) $\frac{\partial r_i}{\partial \phi }\mathrm{and}\frac{\partial r_i}{\partial \rho }$
correspond to the numerical derivatives of the projection x-ray image along the rows and columns. Further,

(40) 0$\frac{\partial \phi }{\partial \stackrel{.fwdarw.}{p}}\mathrm{and}\frac{\partial \rho }{\partial \stackrel{.fwdarw.}{p}}$
are determined analytically.

(41) FIG. 5 shows a schematic flow diagram of one embodiment of a method for providing a trained function TF. The cost function f may include a trained function TF. For example, the trained function TF may be applied to the reconstructed medical image data {right arrow over (r)} as a cost function f in act b) for determining the cost value ϵ.

(42) The cost value ϵ may be determined by applying the trained function TF to the input data, where the input data may be based on the reconstructed medical image data {right arrow over (r)} including a number of image values r.sub.i. Further, at least one parameter of the trained function TF may be based on the image quality metric.

(43) In order to provide the trained function TF, in a first act, reconstructed medical training image data {right arrow over (Tr)} may be received, for example, by a training interface TIF and/or a training computing unit TCU. The reconstructed medical training image data {right arrow over (T)}r may be reconstructed, for example, by applying the reconstruction function g to medical training measuring data in accordance with training reconstruction parameters.

(44) A further act may include the determination of a training cost value Tϵ by applying the trained function TF to input data (e.g., using the training computing unit TCU). The input data may, for example, be based on the reconstructed medical training image data. In this regard, the trained function TF may be a neural network (e.g., a convolutional neural network or a network including a convolutional layer).

(45) A comparison cost value Vϵ that corresponds to the respective reconstructed medical training image data {right arrow over (Tr)} may be determined. The comparison cost value Vϵ may be determined by applying the image quality metric BQM to the reconstructed medical training image data {right arrow over (Tr)} (e.g., using the training computing unit TCU).

(46) In a further act ADJ-TF, at least one parameter of the trained function TF may be adjusted (e.g., using the training computing unit TCU) based on a comparison of the comparison cost value Vϵ and the training cost value Tϵ. In this exemplary embodiment, the trained function TF may include an artificial neural network. The adjustment of the artificial neural network may include the adjustment of at least one edge weight of the artificial neural network. Further, the adjustment may be based on a back propagation algorithm.

(47) In act PROV-TF, the trained function TF may be provided, for example, by the training interface TIF and/or the training computing unit TCU. In the exemplary embodiment shown, the trained function TF may be stored. Alternatively, the trained function TF (or one or more of its parameters) may also be indicated or transmitted for further processing.

(48) Further, the partial derivatives of the cost function f may be determined with respect to the image values r.sub.i of the reconstructed medical image data {right arrow over (r)} in equation (9) using a back propagation of the trained function TF. The input data of the back propagation may be based on the cost value ϵ.

(49) FIG. 6 shows one embodiment of a processing unit 22, and FIG. 7 shows one embodiment of a training system TRS. The processing unit 22 shown may be embodied to carry out one embodiment of a computer-implemented method for the reconstruction of medical image data {right arrow over (r)}. The training system TRS shown may be embodied to implement a method for providing a trained function TF. The processing unit 22 may include an interface IF, a computing unit CU, and a memory unit MU. The training system TRS may include a training interface TIF, a training computing unit TCU, and a training memory unit TMU.

(50) The processing unit 22 and/or the training system TRS may be, for example, a computer, a microcontroller, or an integrated switching circuit. Alternatively, the processing unit 22 and/or the training system TRS may be a real group of computers (e.g., a cluster) or a virtual group of computers (e.g., a “cloud”). The processing unit 22 and/or the training system TRS may also be embodied as a virtual system that is executed on a real computer or a real (e.g., cluster) or virtual (e.g., cloud) group of computers (e.g., virtualization).

(51) An interface IF and/or a training interface TIF may be a hardware or software interface (e.g., PCI bus, USB, or Firewire). A computing unit CU and/or a training computing unit TCU may have hardware elements or software elements (e.g., a microprocessor or a field programmable gate array (FPGA)). A memory unit MU and/or a training memory unit TMU may be realized as a random access memory (RAM) or as a permanent mass memory (e.g., hard disk, USB stick, SD card, solid state disk).

(52) The interface IF and/or the training interface TIF may, for example, include a number of sub interfaces that implement different acts of the respective method. In other words, the interface IF and/or the training interface TIF may also be a plurality of interfaces IF or a plurality of training interfaces TIF. The computing unit CU and/or the training computing unit TCU may, for example, include a number of sub computing units that implement different acts of the respective method. In other words, the computing unit CU and/or the training computing unit TCU may also be a plurality of computing units CU or a plurality of training computing units TCU.

(53) The interface IF of the processing unit 22 may, for example, be embodied to receive the medical measuring data {right arrow over (w)}. The computing unit CU may be configured to reconstruct the medical image data {right arrow over (r)}, including a number of image values r.sub.i, by applying the reconstruction function g to the received medical measuring data {right arrow over (w)}. The computing unit CU may be embodied to determine the cost value ϵ with respect to the reconstruction parameters {right arrow over (p)}. The computing unit CU may be embodied to adjust the reconstruction parameters {right arrow over (p)} both based on the gradient of the cost function {right arrow over (∇)}ƒ with respect to the reconstruction parameters {right arrow over (p)} and also on the previous reconstruction parameters {right arrow over (p)}. The computing unit CU and/or the interface IF may be embodied to provide the adjusted reconstruction parameters {right arrow over (p)}′. The interface IF may be embodied to provide the reconstructed medical image data {right arrow over (r)}.

(54) The training interface TIF may be embodied to receive the reconstructed medical training image data {right arrow over (Tr)}. In addition, the training computing unit TCU may also be embodied to determine a comparison cost value Vϵ based on the reconstructed medical training image data {right arrow over (Tr)}. The training computing unit TCU may be embodied to determine a training cost value Tϵ by applying the trained function TF to input data, where the input data is based on the reconstructed medical training image data {right arrow over (TR)}. Further, the training computing unit TCU may be embodied to adjust ADJ-TF at least one parameter of the trained function TF based on a comparison of the comparison cost value Vϵ and the training cost value Tϵ. The training interface TIF may also be embodied to provide PROV-TF the trained function TF.

(55) FIG. 8 shows a schematic representation of one embodiment of a medical C-arm x-ray device 37 as an example of a medical imaging device. The medical C-arm X-ray device may be embodied to implement an embodiment of the computer-implemented method. In this regard, the medical C-arm x-ray device 37 includes a detector unit 34, an x-ray source 33, and a processing unit 22. In order to receive the medical measuring data {right arrow over (w)} (e.g., of projection x-ray images), the arm 38 of the C-arm x-ray device may be mounted movably about one or more axles. In this way, the medical measuring data {right arrow over (w)} may be recorded with, in each case, recording parameters (e.g., acquisition geometries) that differ in relation to one another. The medical C-arm x-ray device 37 also includes a movement device 39 that enables a movement of the C-arm x-ray device 37 in the space.

(56) In order to record the medical measuring data {right arrow over (w)} of a region to be mapped of an examination object arranged on a patient support device 32, the processing unit 22 may send a signal 24 to the x-ray source 33. Hereupon, the x-ray source 33 may send an x-ray beam bundle (e.g., a cone beam and/or fan beam). When the x-ray beam bundle strikes a surface of the detector unit 34 after interaction with the region of the examination object 31 to be mapped, the detector unit 34 may send a signal 21 to the processing unit 22. The processing unit 22 may receive the medical measuring data {right arrow over (w)} with the aid of the signal 21, for example. The processing unit 22 may then implement an embodiment of the computer-implemented method for the reconstruction of medical image data {right arrow over (r)}.

(57) The medical C-arm x-ray device 37 may include an input unit 41 (e.g., a keyboard) and/or a display unit 42 (e.g., a monitor and/or display). The input unit 41 may be integrated into the display unit 42 (e.g., with a capacitive input display). In this way, control of the method and/or the medical C-arm x-ray device 37 may be enabled by an operator inputting on the input unit 41. For example, a graphical display of the reconstructed medical image data {right arrow over (r)} and/or the cost value ϵ and/or the reconstruction parameters {right arrow over (p)} may be shown on the display unit 42.

(58) The schematic representations contained in the described figures do not show anything to scale or proportion.

(59) The methods described in detail above and the presented apparatuses are merely exemplary embodiments that may be modified by a person skilled in the art in many ways without departing from the scope of the invention. In addition, the use of the indefinite article “a” or “an” does not rule out the possibility of there also being more than one of the features concerned. Similarly, the expressions “unit” and “module” do not preclude the components in question from including a plurality of cooperating partial components that may also be spatially distributed.

(60) 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. Such new combinations are to be understood as forming a part of the present specification.

(61) While the present invention has been described above by reference to various embodiments, it should be understood that many changes and modifications can 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.