WO2016097981A1 - Penalized maximum likelihood material decomposition - Google Patents

Penalized maximum likelihood material decomposition Download PDF

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Publication number
WO2016097981A1
WO2016097981A1 PCT/IB2015/059602 IB2015059602W WO2016097981A1 WO 2016097981 A1 WO2016097981 A1 WO 2016097981A1 IB 2015059602 W IB2015059602 W IB 2015059602W WO 2016097981 A1 WO2016097981 A1 WO 2016097981A1
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Prior art keywords
line integrals
decomposition
sets
noising
integrals
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PCT/IB2015/059602
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French (fr)
Inventor
Bernhard Johannes Brendel
Thomas Koehler
Frank Bergner
Roland Proksa
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Koninklijke Philips N.V.
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Publication of WO2016097981A1 publication Critical patent/WO2016097981A1/en

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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/002D [Two Dimensional] image generation
    • G06T11/003Reconstruction from projections, e.g. tomography
    • G06T11/005Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00Image generation
    • G06T2211/40Computed tomography
    • G06T2211/408Dual energy
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00Image generation
    • G06T2211/40Computed tomography
    • G06T2211/424Iterative

Definitions

  • a method generates a plurality of sets of de-noised decomposed line integrals with a material decomposition algorithm that concurrently decomposes and de- noises line integrals during a material decomposition of a plurality of sets of measured line integrals.
  • the method includes receiving projection data generated with data produced by an imaging system, wherein the projection data includes the plurality of sets of measured line integrals, wherein each of the sets of measured line integrals corresponds to a different X-ray spectrum.
  • the method further includes receiving a material decomposition with integrated de-noising algorithm which includes the algorithm that concurrently decomposes and de- noises the line integrals during the material decomposition of the plurality of sets of measured line integrals.
  • the method further includes concurrently de-noising and
  • an imaging system 100 such as a computed tomography (CT) scanner, is illustrated.
  • the imaging system 100 includes a stationary gantry 102 and a rotating gantry 104, which is rotatably supported by the stationary gantry 102 and rotates around an examination region 106 about a z-axis.
  • a subject support 107 such as a couch supports a subject or object in the examination region 106.
  • the subject support 107 is movable in coordination with scanning so as to guide the subject or object with respect to the examination region 106 for scan of the subject or object.
  • the reconstructor 130 can also combine the material line integrals and reconstruct a non-spectral (or conventional) volumetric image data set over the entire energy spectrum.
  • the one or more material volumetric image data sets are combined to produce a non-spectral (or conventional) volumetric image data set.
  • the material line integrals and/or material volumetric image data sets can also be used to generate virtual monochromatic images, iodine concentration maps, virtual non-contrast images, etc.
  • T v J represents a data term, which includes a noise model and compares the measured line integrals to calculations of the measured line integrals determined from the inverse functions.
  • the regularization term R(m l , m 2 ) controls a smoothness of the material line integrals.
  • Other cost functions are contemplated herein.

Abstract

A method includes receiving projection data generated with data produced by an imaging system (100), wherein the projection data includes the plurality of sets of measured line integrals, wherein each of the sets of measured line integrals corresponds to a different X-ray spectrum. The method further includes receiving a material decomposition with integrated de-noising algorithm (212) which includes the algorithm that concurrently decomposes and de-noises the line integrals during the material decomposition of the plurality of sets of measured line integrals. The method further includes concurrently de- noising and decomposing the corresponding plurality of sets of the measured line integrals with the material decomposition with the integrated de-noising algorithm. The method further includes generating a signal indicative of a result of the concurrent decomposing and de-noising, wherein the results include the de-noised decomposed line integrals.

Description

PENALIZED MAXIMUM LIKELIHOOD MATERIAL DECOMPOSITION
FIELD OF THE INVENTION
The following generally relates to spectral imaging and more particularly to a material decomposition with integrated de-noising, and is described with particular application to computed tomography (CT).
BACKGROUND OF THE INVENTION
In spectral (multi-energy) CT, multiple projection data sets are acquired at multiple different X-ray spectra and represent the attenuation properties of a scanned subject or object for the different X-ray spectra. There are several approaches for acquiring such attenuation values, including using multiple x-ray tubes, kVp switching, multi-layer detectors, and photon counting detectors. Based on these data sets, physical properties can be determined locally. Examples of such properties include photoelectric effect, Compton scattering, and material content such as water content, bone content, iodine content, etc. The determination of these properties from the multiple projection data sets has been referred to as material decomposition.
A material decomposition can be performed in the image domain and/or in the projection domain. For the image domain, the projection data is reconstructed to generate volumetric image data. The material decomposition is performed on the volumetric image data and converts the reconstructed voxel values for one image location into material values. For the projection domain, the measured line integrals are decomposed into material line integrals. The material line integrals are reconstructed to generate material volumetric image data. The material volumetric image data can be used to generate virtual monochromatic images, iodine concentration maps, virtual non-contrast images, non-spectral images and/or other images.
The material decomposition is an ill-posed non-linear process. As a consequence, the noise of the measured line integrals is strongly magnified, and material volumetric image data directly reconstructed from the material line integrals tends to be noisy. Unfortunately, this noise may degrade diagnostic image quality, reducing the clinical value of the material volumetric image data. Furthermore, a mean of the material line integrals will not be equal to the decomposition of a mean of the measured line integrals. Instead, the material line integrals will include a noise induced bias, or a shift in the mean value. This noise induced bias varies within the sinogram and propagates to the material volumetric image data. Unfortunately, this may lead to quantitatively incorrect voxel values in the material volumetric image data such as inaccurate iodine concentration estimations, visible image artifacts in virtual monochromatic images, etc.
De-noising algorithms can be used to reduce the noise. Such algorithms have included de-noising the measured line integrals, de-noising the material line integrals, and/or de-noising the material volumetric image data. De-noising the measured line integrals (projection domain de-noising) may also reduce the noise induced bias introduced by the material decomposition. Unfortunately, executing de-noising algorithms consumes processing cycles and memory and increases the overall time it takes to produce the material volumetric image data, which can reduce overall computation and/or computer efficiency. Furthermore, the noise induced bias is not entirely removed. As such, there is an unresolved need for other approaches for mitigating noise and/or noise induced bias resulting from the material decomposition.
SUMMARY OF THE INVENTION
Aspects described herein address the above-referenced problems and others. The following describes an approach that reduces noise during decomposition. As described herein, this can be done in a statistical framework by searching for a set of de- noised material projections that most likely belong to the measured projections, e.g., through a maximum-likelihood based decomposition with a regularization enforcing smoothness on the material projections.
In one aspect, a method generates a plurality of sets of de-noised decomposed line integrals with a material decomposition algorithm that concurrently decomposes and de- noises line integrals during a material decomposition of a plurality of sets of measured line integrals. The method includes receiving projection data generated with data produced by an imaging system, wherein the projection data includes the plurality of sets of measured line integrals, wherein each of the sets of measured line integrals corresponds to a different X-ray spectrum. The method further includes receiving a material decomposition with integrated de-noising algorithm which includes the algorithm that concurrently decomposes and de- noises the line integrals during the material decomposition of the plurality of sets of measured line integrals. The method further includes concurrently de-noising and
decomposing the corresponding plurality of sets of the measured line integrals with the material decomposition with the integrated de-noising algorithm. The method further includes generating a signal indicative of a result of the concurrent decomposing and de- noising, wherein the results include the de-noised decomposed line integrals.
In another aspect, a computing system includes a memory device configured to store instructions. The computing system further includes a processor that executes the instructions, which causes the processor to concurrently decompose and de-noise line integrals during a material decomposition, and a material basis decomposition processor that executes the instructions to concurrently decompose and de-noise measured line integrals to produce de-noised decomposed line integrals.
In another aspect, a computer readable storage medium is encoded with computer readable instructions. The computer readable instructions, when executed by a processer, cause the processor to: concurrently de-noise and decompose a set of material line integrals from a plurality of sets of the measured line integrals based on a material decomposition with the integrated de-noising algorithm, generate a signal indicative of a result of the concurrent decomposing and de-noising, wherein the results includes the de- noised decomposed line integrals, generate a plurality of sets of material line integrals from signal, and reconstruct at least one of the plurality of sets of material line integrals to generate at least one material volumetric image data set.
The invention may take form in various components and arrangements of components, and in various steps and arrangements of steps. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention.
BRIEF DESCRIPTION OF THE DRAWINGS FIGURE 1 schematically illustrates an example imaging system including a console with a material basis decomposition processor ("decomposer").
FIGURE 2 schematically illustrates an example of the material basis decomposition processor ("decomposer").
FIGURE 3 illustrates an example method for concurrently reducing noise and decomposing material line integrals.
DETAILED DESCRIPTION OF EMBODIMENTS
The following describes an approach for mitigating noise and/or noise induced bias, which results from a material decomposition, without processing the projection data and/or the image data with a de-noising algorithm(s). The approach, general, simultaneously de-noises and decomposes the measured line integrals in the decomposition domain.
As used herein, data with respect to the projection domain is data that is not reconstructed, i.e., the data represents line integrals of object properties. The opposite of projection domain is the image domain, where the spatial distribution of the object properties is represented directly. The term measured line integrals refers to either the measured x-ray intensities at the detector pixels or values representing line integrals of the x-ray attenuation of the object that can be calculated from the measured intensities for each projection data set individually. The term material line integrals refers to line integrals of object properties, which can be real materials (e.g., water, soft tissue, calcium, bone, iodine,...) or physical effects leading to x-ray attenuation (e.g., photoelectric effect, Compton scattering,...).
Initially referring to FIGURE 1 , an imaging system 100, such as a computed tomography (CT) scanner, is illustrated. The imaging system 100 includes a stationary gantry 102 and a rotating gantry 104, which is rotatably supported by the stationary gantry 102 and rotates around an examination region 106 about a z-axis. A subject support 107 such as a couch supports a subject or object in the examination region 106. The subject support 107 is movable in coordination with scanning so as to guide the subject or object with respect to the examination region 106 for scan of the subject or object.
A radiation source 108, such as an x-ray tube, is rotatably supported by the rotating gantry 104, rotates with the rotating gantry 104, and emits radiation that traverses the examination region 106. A detector array 1 12 subtends an angular arc opposite the examination region 106 relative to the radiation source 108. The detector array 1 12 detects radiation that traverses the examination region 106 and generates projection data indicative thereof. The illustrated detector array 1 12 is configured to generate synchronously acquired projection data for the same rays for different X-ray spectra. Such a detector array may include an energy-resolving detector (e.g., multi-layered, photon counting, etc.) that produces spectral projection data and/or other detector array.
A computing system ("console") 116 serves an operator console and includes at least one processor 1 18 (e.g., a microprocessor, a central processing unit, etc.) that executes at least one computer readable instruction stored in computer readable storage medium or memory device ("memory") 120, which excludes transitory medium and includes physical memory and/or other non-transitory medium. The at least one processor 1 18 may also execute one or more computer readable instructions carried by a carrier wave, a signal or other transitory medium. The computing system 1 16 further includes an output device(s) 122 such as a display monitor, a filmer, etc., and an input device(s) 124 such as a mouse, keyboard, etc.
In the illustrated example, the at least one computer readable instruction implements a material basis decomposition processor ("decomposer") 126, which
decomposes measured line integrals into material line integrals based on a decomposition algorithm(s) 128. In one instance, the decomposer 126 concurrently de-noises and decomposes the measured line integrals. As described in greater detail below, this includes, for example, employing a decomposition algorithm with integrated de-noising such as a statistical approach that searches for a set of de-noised material projections that most likely belong to the measured projections, e.g., through a penalized maximum-likelihood based decomposition with a regularization enforcing smoothness on the material projections and/or otherwise.
Such an approach, in one instance, mitigates or reduces noise and/or noise induced bias resulting from the material decomposition without additional de-noising of the measured line integrals and/or the material line integrals in the projection domain. As such, in one instance, the approach described herein renders the overall decomposition process more efficient, for example, relative to a configuration in which this approach is omitted and one or more additional de-noising algorithms are employed in the projection domain. In a variation, the decomposer 126 is located in a computing apparatus separate and distinct from the console 1 16.
The illustrated decomposer 126 processes multi-energy projection data obtained from the imaging system 100. In a variation, such projection data is obtained from a different imaging system, a data repository such as a picture archiving and communication system (PACS), a radiology information system (RIS), a hospital information system (HIS), an electronic medical record (EMR), a database, a server, an imaging system, a computer, etc., a and/or other source. The projection data can be transferred via Digital Imaging and Communications in Medicine (DICOM), Health Level 7 (HL7), and/or other protocols. The decomposed material line integrals can be stored in the data repository, conveyed to another device, etc.
A reconstructor 130 reconstructs the material line integrals. In one instance, the reconstructor 130 generates one or more material volumetric image data sets
corresponding to one or more different energies. The reconstructor 130 can also combine the material line integrals and reconstruct a non-spectral (or conventional) volumetric image data set over the entire energy spectrum. In yet another instance, the one or more material volumetric image data sets are combined to produce a non-spectral (or conventional) volumetric image data set. The material line integrals and/or material volumetric image data sets can also be used to generate virtual monochromatic images, iodine concentration maps, virtual non-contrast images, etc.
FIGURE 2 schematically illustrates an example of the material basis decomposition processor ("decomposer") 126.
For sake of brevity and explanatory purposes, this example is described for two (2) different X-ray spectra. The decomposer 126 receives, as input, measured line integrals from the imaging system 100, a data repository, and/or another device. The measured line integrals for this example include a first set of measured line integrals lu and a second set of measured line integrals In, where i represents an acquisition ray index.
A map 202 provides a mapping 204 between the measured line integrals lu and In and two sets of material line integrals mu and mn. Functions 206 include inverse decomposition functions ku(mu,mn) and kn(mu,mn), which calculate the measured line integrals lu and In from the material line integrals mu and mu. Variances 208 include variances var(/i,) and var(/2,) for the measured line integrals In and In.
A processing engine 210 is configured to concurrently de-noise and decompose the measured line integrals In and In to produce the material line integrals mu and mn, which have reduced noise and/or noise induced bias. In one instance, the processing engine 210 concurrently de-noises and decomposes line integrals based on a decomposition with an integrated de-noising algorithm 212, which can be obtained from the decomposition algorithms 128 and/or other source and/or device.
An example of the decomposition with integrated de-noising algorithm 212 includes a penalized maximum-likelihood decomposition. A cost function for a maximum- likelihood decomposition can be derived assuming Gaussian noise distributions and is shown in EQUATION 1 :
EQUATION 1 :
1
L = ∑∑ rn - kfi (mi" m l ))2 + *(m1 , m2 )
where i and j represents indices, R( ) represents a regularization term, and mi and m2 are vectors containing all elements mu and mn- The term— V V—— h .. - k (ml , mr ))2
2 T v J represents a data term, which includes a noise model and compares the measured line integrals to calculations of the measured line integrals determined from the inverse functions. The regularization term R(ml , m2 ) , controls a smoothness of the material line integrals. Other cost functions are contemplated herein.
A non-limiting example of the regularization term R(ml , m2 ) is a gradient- based Huber regularization, such as the one shown in EQUATION 2:
EQUATION 2: i keN, ; keN, where Ni is a spatial neighborhood of the ray with index i, wuk and wuk are weights to modify the regularization strength and weight the influence of rays within one neighborhood, and ψ( ) is a Huber potential function. Other smoothing priors are also contemplated herein.
The processing engine 210 decomposes the line integrals while simultaneously de-noising the line integrals through an iterative process which minimizes EQUATION 1 for the given measured line integrals In and In and variances var(/i,) and var(/2;) to determine the set of material line integrals mu and mn. An optimization can be performed with known and/or other approaches.
This approach, in one instance, can achieve a same amount of de-noising as 1) de-noising the measured line integrals In and In, and 2) de-noising the material line integrals mu and mn, while mitigating noise induced bias that is present after 1) and/or 2). The approach described herein can also be used together with 1) and/or 2), and/or other de- noising approaches.
FIGURE 2 describes an example for two (2) different X-ray spectra.
However, it is to be understood that the approached described herein can be used for N materials and M measured projection data sets, wherein N and M are positive integers and N < M. This is shown in EQUATION 3 :
EQUATION 3 :
L : ∑∑ m fa - k fi (mw-> mNi )y + ^(m1 ,..., m w ).
2 i ) Furthermore, one of ordinary skill in the art will understand, without undue experimentation that it is straightforward to extend the data term to also consider covariances between measured line integral data sets.
FIGURE 3 illustrates an example method for reducing spectral projection data noise in photoelectric and Compton scatter components.
It is to be appreciated that the ordering of the acts is not limiting. As such, other orderings are contemplated herein. In addition, one or more acts may be omitted and/or one or more additional acts may be included.
At 302, a plurality of measured projection data sets, each with a set of measured line integrals corresponding to different X-ray spectra, are obtained. As described herein, this includes retrieving and/or receiving the projection data sets from an imaging system a data repository, etc.
At 304, the sets of measured line integrals are concurrently decomposed and de-noised using a maximum likelihood material decomposition that concurrently decomposes and de-noises material line integrals, as described herein and/or otherwise.
At 306, one or more sets of material line integrals are generated via the material decomposition.
At 308, the one or more sets of material line integrals are reconstructed to generate one or more material volumetric image data sets.
The method herein may be implemented by way of computer readable instructions, encoded or embedded on computer readable storage medium, which, when executed by a computer processor(s), cause the processor(s) to carry out the described acts. Additionally or alternatively, at least one of the computer readable instructions is carried by a signal, carrier wave or other transitory medium.
The invention has been described with reference to the preferred embodiments. Modifications and alterations may occur to others upon reading and understanding the preceding detailed description. It is intended that the invention be constructed as including all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.

Claims

1. A method for generating a plurality of sets of de-noised decomposed line integrals with a material decomposition algorithm that concurrently decomposes and de- noises line integrals during a material decomposition of a plurality of sets of measured line integrals, comprising:
receiving projection data generated with data produced by an imaging system (100), wherein the projection data includes the plurality of sets of measured line integrals, wherein each of the sets of measured line integrals corresponds to a different X-ray spectrum;
receiving a material decomposition with integrated de-noising algorithm (212) which includes the algorithm that concurrently decomposes and de-noises the line integrals during the material decomposition of the plurality of sets of measured line integrals;
concurrently de-noising and decomposing the corresponding plurality of sets of the measured line integrals with the material decomposition with the integrated de-noising algorithm; and
generating a signal indicative of a result of the concurrent decomposing and de-noising, wherein the results include the de-noised decomposed line integrals.
2. The method of claim 1, further comprising:
generating a plurality of sets of material line integrals from the signal.
3. The method of claim 2, wherein one or more of the plurality of sets of material line integrals represents one of water, soft tissue, calcium, bone, or iodine.
4. The method of any of claims 2 to 3, wherein one or more of the plurality of sets of material line integrals represents one of a photoelectric effect or Compton scattering.
5. The method of any of claims 2 to 4, further comprising:
reconstructing at least one of the plurality of sets of material line integrals to generate at least one material volumetric image data set.
6. The method of any of claims 1 to 5, wherein the material decomposition with integrated de-noising algorithm includes an iterative maximum-likelihood decomposition that includes a data term with a noise model and a regularization term.
7. The method of claim 6, wherein data term compares measured line integrals for an acquisition ray with calculated measured line integrals for the same acquisition ray.
8. The method of claim 7, further comprising:
generating the calculated measured line integrals by performing an inverse decomposition on material line integrals for the same acquisition ray.
9. The method of any of claims 6 to 8, wherein regularization term performs a gradient based Huber regularization which smooths the material line integrals.
10. The method of any of claims 6 to 9, wherein the material decomposition with integrated de-noising algorithm includes a cost function, and further comprising:
minimizing the cost function to generate de-noised decomposed line integrals.
1 1. A computing system (1 16), comprising:
a memory device (120) configured to store instructions of that concurrently decompose and de-noise line integrals during a material decomposition; and
a material basis decomposition processor (126) configured to executes the instructions to concurrently decompose and de-noise measured line integrals to produce de- noised decomposed line integrals line integrals.
12. The computing system of claim 1 1, wherein the material basis decomposition processor generates a plurality of sets of material line integrals from the de-noised decomposed line integrals.
13. The computing system of claim 12, further comprising:
a reconstructor (130) configured to reconstruct at least one of the plurality of sets of material line integrals to generate at least one material volumetric image data set.
14. The computing system of any of claims 1 1 to 13, wherein the material basis decomposition processor is configured to concurrently decompose and de-noise the measured line integrals.
15. The computing system of any of claims 1 1 to 14, wherein the material basis decomposition processor is configured to decompose and de-noise the measured line integrals with a likelihood decomposition algorithm that includes a data term with a noise model and a regularization term.
16. The computing system of claim 15, wherein data term compares measured line integrals for an acquisition ray with calculated measured line integrals for the same acquisition ray.
17. The computing system of claim 16, wherein the material basis decomposition processor generates the calculated measured line integrals by performing an inverse decomposition on material line integrals for the same acquisition ray.
18. The computing system of any of claims 15 to 17, wherein the regularization term smooths the material line integrals.
19. The computing system of any of claims 15 to 18, wherein the material decomposition with integrated de-noising algorithm includes a cost function, and the material basis decomposition processor minimizes the cost function to generate de-noised
decomposed line integrals.
20. A computer readable storage medium encoded with computer readable instructions, which, when executed by a processer, causes the processor to:
concurrently de-noise and decompose a set of material line integrals from a plurality of sets of the measured line integrals based on a material decomposition with the integrated de-noising algorithm;
generate a signal indicative of a result of the concurrent decomposing and de- noising, wherein the results includes the de-noised decomposed line integrals;
generate a plurality of sets of material line integrals from signal; and reconstruct at least one of the plurality of sets of material line integrals to generate at least one material volumetric image data set.
PCT/IB2015/059602 2014-12-16 2015-12-14 Penalized maximum likelihood material decomposition WO2016097981A1 (en)

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Cited By (3)

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WO2018114964A1 (en) 2016-12-19 2018-06-28 Koninklijke Philips N.V. Detection and/or correction of residual iodine artifacts in spectral computed tomography (ct) imaging
WO2019141769A1 (en) 2018-01-19 2019-07-25 Koninklijke Philips N.V. Scan parameter adaption during a contrast enhanced scan
EP4047557A1 (en) 2021-02-19 2022-08-24 Koninklijke Philips N.V. Projection-domain material decomposition for spectral imaging

Non-Patent Citations (2)

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Title
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WONSEOK HUH ET AL: "Iterative image reconstruction for dual-energy X-ray CT using regularized material sinogram estimates", 2011 8TH IEEE INTERNATIONAL SYMPOSIUM ON BIOMEDICAL IMAGING: FROM NANO TO MACRO (ISBI 2011), IEEE, UNITED STATES, 30 March 2011 (2011-03-30), pages 1512 - 1515, XP031944818, ISBN: 978-1-4244-4127-3, DOI: 10.1109/ISBI.2011.5872688 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018114964A1 (en) 2016-12-19 2018-06-28 Koninklijke Philips N.V. Detection and/or correction of residual iodine artifacts in spectral computed tomography (ct) imaging
WO2019141769A1 (en) 2018-01-19 2019-07-25 Koninklijke Philips N.V. Scan parameter adaption during a contrast enhanced scan
EP4047557A1 (en) 2021-02-19 2022-08-24 Koninklijke Philips N.V. Projection-domain material decomposition for spectral imaging
WO2022175259A1 (en) 2021-02-19 2022-08-25 Koninklijke Philips N.V. Projection-domain material decomposition for spectral imaging

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