Joint processing of spectral data to obtain contrast distribution in material basis maps

Abstract

A method for obtaining a contrast distribution includes acquiring pre-contrast spectral data before contrast is administered, acquiring post-contrast spectral data after the contrast is administered, and generating at least one material basis map for at least one material by joint processing the pre-contrast spectral data and the post-contrast spectral data to solve for a pre-selected number of unknowns corresponding to the at least one material associated with the at least one material basis map. The method also includes where the joint processing enables visualization of contrast distribution from contrast agent injection or drug delivery contrast agents, and where the at least one material basis map includes the contrast distribution.

Description

JOINT PROCESSING OF SPECTRAL DATA TO OBTAIN CONTRAST DISTRIBUTION IN MATERIAL BASIS MAPS GOVERNMENT LICENSE RIGHTS

[0001] This invention was made with government support under contract number R01EB030494 awarded by the National Institute of Biomedical Imaging and Bioengineering. The government has certain rights in the invention. CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to, and the benefit of, U.S. Provisional Patent Application Ser. No.63 / 513,651, filed July 14, 2023, the disclosure of which is incorporated herein by reference. FIELD

[0003] This disclosure relates generally to generating material basis maps based on spectral data, specifically to a joint processing strategy applied to pre-contrast spectral data and post-contrast spectral data. BACKGROUND

[0004] Digital subtraction angiography (DSA) guides endovascular interventions including stent placement, lesion localization, and embolization in a wide range of anatomical sites (e.g., brain, spine, kidney, lower extremity liver, prostate); it also provides the criteria for the diagnostic workup of cerebrovascular diseases.

[0005] DSA is a well-established modality for the visualization of contrast-enhanced vasculature and is an interventional procedure for a wide range of diseases and treatments. Currently, DSA is typically performed on angiography systems with flat-panel detectors (FPDs), which boast wide-area coverage (detection areas up to ~40x40 cm), high-spatial resolution (pixel sizes of ~100 μm or less, though spatial resolution is often limited by light spread in the scintillator), fast read-out (up to ~30 frames per second), and compactdesigns / packaging. Due to their high resolution and dynamic imaging capability, DSA is extensively used in interventional procedures for diagnostics, pre-operative planning, and intra-operative guidance.

[0006] The state-of-the-art technique for DSA is “temporal subtraction” – where a pre-contrast fluoroscopic image is subtracted from a series of images acquired post-contrast injection, leaving contrast-enhanced blood vessels while eliminating overlaying background anatomy that (without subtraction) would decrease conspicuity of the vessels of interest. Temporal subtraction DSA is challenged by misregistration artifacts due to patient motion and incomplete separation of iodine contrast agent from background soft tissue and bone. Although gross patient motion is less common, involuntary soft tissue motion still degrades the diagnostic values of DSA images. An alternative technique, energy subtraction, has been proposed to mitigate patient motion. Such method relies on rapid kV switching or energy- resolving detectors to acquire (nearly) simultaneous measurements at different x-ray energies, enabling material decomposition of soft tissue and bone basis images without relying on a pre-contrast image. While misregistration can be minimized using this method, isolating the contrast agent is challenging. The resulting DSA image is presented with both iodine and bone, or iodine and soft tissue (if using a linear combination method for material decomposition), which can reduce diagnostic capabilities due to overlapping anatomy. A hybrid subtraction method that utilizes spectral measurements acquired both pre- and post- injection is possible. Material decomposition of soft tissue and bone is performed at both time points. The pre-contrast “bone” image contains calcium signals while the post-contrast bone image contains both calcium and iodine. A subtraction of the “bone” basis image can therefore eliminate bone structures, under the assumption of minimal bone movement. Both the energy and hybrid subtraction methods can suffer from poor image quality due to the noise amplifying nature of material decomposition. Even with modern day improvements in detector performance (high detection efficiency and lower readout noise), the image quality from spectral DSA using decomposition methods (e.g., from post-contrast spectral measurements) is still lagging behind temporal DSA.

[0007] What is needed is a joint processing strategy using spectral measurements acquired both pre- and post-contrast injection. Such a strategy could improve the noise performance for material basis map estimates, could leverage both the temporal and spectral information, and could yield material basis maps that outperform temporal-only and spectral-only processing. Both 2D DSA and 3D DSA imaging can be accommodated by these strategies. In the case of 3D DSA imaging, cone-beam computed tomography (CBCT) acquisitions from pre- and post-contrast injection are subtracted from each other to isolate iodine distribution in the vasculature. The joint processing strategy can be applied in at least two different scenarios to achieve different advantages. A first scenario in which motion between the pre- and post-injection can be considered negligible, or a second scenario in which motion can be compensated using motion-compensation algorithms can jointly leverage temporal and spectral information to improve image quality beyond what is achievable by temporal or spectral methods alone. Other scenarios are envisioned by the present disclosure. Advantages of the joint processing strategy include (1) improved noise performance that can enable reduced exposure acquisition, (2) improved visualization of contrast within patients, for example, but not limited to, vessel, especially small vessel, visualization, and / or (3) reduced contrast agent concentrations, compared to what is currently available.

[0008] What are further needed are systems and methods that focus on spectral measurements using technology such as a photon counting detector (PCD) or multi-layer (e.g., dual layer) detector to form spectral measurements pre- and post-contrast injection (e.g., two spectral channels pre-contrast, and two spectral channels post-contrast). It is also possible to apply the method to measurements containing more than two spectral channels pre- and post-contrast. By applying this strategy using a spectral detector with lower image noise and higher spatial resolution compared to flat panel detectors (e.g., PCD), the resulting images could also have lower image noise and higher spatial resolution that can improve the visualization of small, low contrast targets like small vessels and other small tissues. What are needed are processing techniques such as modified lookup table, model-based material estimation, and / or deep learning-based material decomposition techniques.

[0009] What is still further needed is a strategy that can mitigate motion artifact as occurs in DSA when applied to imaging scenarios where one tissue type is stationary pre- and post-contrast, while another tissue type moves freely, e.g., in the abdomen where the spine is stationary but soft tissue moves due to breathing, or in the thorax where, when imaging at high frame rate, the bone signal can be assumed to have minimal motion but the soft tissue moves rapidly from cardiac motion. What is also needed is an approach that allows multiple- material decomposition using a dual-layer flat panel detector in the presence of soft tissuemotion. This strategy could also be generalized from the joint processing of pre- and post- contrast images, to joint processing, possibly using an iterative estimation approach, of any two or more images acquired consecutively in time. SUMMARY

[0010] The system and method in accordance with embodiments of the present disclosure provide visualization of contrast enhancement within patients through the use of improved energy resolving detectors (for example, but not limited to, PCDs), and joint processing pre- and post-contrast acquisitions using spectral DSA. In an aspect, embodiments in accordance with the present disclosure overcome limitations of currently available techniques that study and diagnose vascular disease through imaging of blood vessels by combining the benefits of spectral imaging and energy resolving detectors. A process in accordance with the present disclosure enables three-material decomposition using a dual-layer flat panel detector. In an aspect, bone motion is assumed to be minimal between the pre- and post-contrast measurements and soft tissues move freely. A process in accordance with the present disclosure performs material decomposition for the pre- and post-measurements by jointly estimating four material bases – soft tissue pre-contrast, bone, soft tissue post-contrast, and iodine – using all four measurements. Such formulation allows three-material decomposition to be performed with a dual-layer detector and offers image quality advantages compared to a hybrid subtraction method. The process is applicable to other choices of materials, the number of material maps being based upon the number of spectral channels, and any number of consecutive images. The joint processing of the present disclosure allows three-material decomposition using two spectral / energy channels.

[0011] A system of one or more computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination of them installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions. One general aspect includes a method for obtaining a contrast distribution. The method includes acquiring pre-contrast spectral data before contrast is administered; acquiring post-contrast spectral data after the contrast isadministered; and generating at least one material basis map for at least one material by joint processing the pre-contrast spectral data and the post-contrast spectral data to solve for a pre- selected number of unknowns corresponding to the at least one material associated with the at least one material basis map. The method also includes where the joint processing enables visualization of contrast distribution from contrast agent injection or drug delivery contrast agents. The method also includes where the at least one material basis map includes the contrast distribution. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

[0012] Implementations may include one or more of the following features. The method where the joint processing may include a model-based approach. The model-based approach may include creating a forward model by relating the at least one material basis map to the pre-contrast spectral data, the post-contrast spectral data, and temporal data associated with the pre-contrast spectral data and the post-contrast spectral data; estimating the at least one material basis map based on the forward model; and minimizing a difference between the estimated at least one material basis map and an actual at least one material map. The joint processing may include a deep learning-based approach. The deep learning-based approach may include training a deep learning model with spectral data identified as collected before and after the contrast is administered, temporal data associated with the spectral data, and the at least one material basis map; providing the pre-contrast spectral data, the post-contrast spectral data, and temporal data associated with the pre-contrast spectral data and the post-contrast spectral data to the trained deep learning model; and receiving the at least one material basis map from the trained deep learning model. The pre-contrast spectral data and the post-contrast spectral data may include image data. The pre-contrast spectral data and the post-contrast spectral data may include multi-layer detector data. The method as may include joint processing consecutive images from the pre-contrast spectral data and the post-contrast spectral data to achieve the at least one material basis map, and performing registration between the consecutive images to achieve motion compensation between the consecutive images. The method may include acquiring the pre-contrast spectral data using an energy-resolving detector (ERD). The ERD may include a photon counting detector (PCD). The method as may include estimating energy-dependent scatter by performing measurements at different energy thresholds of the PCD. The joint processingmay include an iterative estimation approach. The iterative estimation approach may include a paraboloidal surrogate approach. The method may include regularizing of the iterative estimation approach using quadratic penalties. The method may include regularizing of the iterative estimation approach using edge-preserving non-quadratic penalties. The method may include regularizing of the iterative estimation approach using cross basis penalties. The method may include applying a scatter correction factor to remove scatter bias from the at least one material basis map. The method may include post-processing the at least one material basis map using edge enhancement. The method may include post-processing the at least one material basis map using temporal frame averaging. The visualization may include providing a color overlay of soft tissue. The visualization may include providing a color overlay of boney landmarks. The joint processing is applied for two-dimensional or three- dimensional digital subtraction angiography (DSA). The joint processing may include performing decomposition into the at least one material basis map using a lookup table that relates the pre- and post- contrast spectral data to a number of the at least one material basis map. The joint processing may include estimating images of the at least one material basis map simultaneously using an optimization. The optimization method may include a roughness penalty having a penalty strength for the at least one material basis map. The roughness penalty may include a quadratic penalty acting over a pre-selected number of nearest neighbors within the images. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

[0013] One general aspect includes a system for obtaining a contrast distribution that may include a controller; a sensor configured to receive pre-contrast spectral data and post-contrast spectral data; where the controller is configured to execute instructions that perform operations including acquiring the pre-contrast spectral data before contrast is administered; acquiring the post-contrast spectral data after the contrast is administered; and generating at least one material basis map for at least one material by joint processing the pre- contrast spectral data and the post-contrast spectral data to solve for a pre-selected number of unknowns corresponding to the at least one material associated with the at least one material basis map, where the joint processing enables visualization of contrast distribution from contrast agent injection or drug delivery contrast agents, and where the at least one material basis map includes the contrast distribution. Other embodiments of this aspect includecorresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The above and / or other aspects and advantages will become more apparent and more readily appreciated from the following detailed description of examples, taken in conjunction with the accompanying drawings, in which:

[0015] FIG.1A is a pictorial representation of a DSA temporal subtraction;

[0016] FIG.1B is a pictorial representation of the use of energy subtraction leveraging spectral imaging acquisition where acquisitions of multiple energies are used;

[0017] FIG.1C is a pictorial representation of the use of hybrid subtraction to using both temporal and spectral information;

[0018] FIG.1D is a pictorial representation of the joint processing method in accordance with embodiments of the present disclosure;

[0019] FIG.2 are photographic and graphical comparisons of temporal DSA, joint processing in accordance with embodiments of the present disclosure, and spectral only;

[0020] FIG.3A is a photographic illustration of an image domain decomposition using FBP reconstructions and a dual-layer detector;

[0021] FIG.3B is a photographic illustration of a model-based approach using an idealized joint processing and a dual-layer detector;

[0022] FIG.3C is a photographic illustration of a one-step model-based decomposition for cone-beam computed tomography (CBCT) using a high-fidelity joint processing method that outperforms the methods of FIGs.3A and 3B;

[0023] FIG.4 is a pictorial illustration of a spectral DSA workflow that increases robustness against patient motion;

[0024] FIG.5A is a pictorial illustration of a model architecture of deep learning three material decomposition;

[0025] FIG.5B is a photographic illustration of decomposition results of ground truth versus estimated for soft tissue, bone, and iodine;

[0026] FIG.5C is a photographic illustration of the effect of gradient-based estimation bias and improving spatial resolution;

[0027] FIG.6 is a pictorial illustration of a clinical C-arm system for PCD integration;

[0028] FIG.7A is a pictorial illustration of a high resolution phantom depicting stenosis;

[0029] FIG.7B is a pictorial illustration of a small vessel tree using an SLA printer;

[0030] FIG.7C is a pictorial illustration of a commercial vessel model;

[0031] FIG.7D is a pictorial illustration of a customized pelvis phantom with bone inserts;

[0032] FIG.8 is a pictorial illustration of a digital phantom;

[0033] FIG.9 is a graphical illustration of noise-resolution characterization in iodine basis images;

[0034] FIGs.10A-10F are photographic illustrations of the resolution achieved by various techniques and devices;

[0035] FIGs.11A and 11B are photographic representations of four material decompositions using the lookup table method and the model-based method;

[0036] FIG.12 is a pictorial comparison of DSA methods and the method in accordance with embodiments of the present disclosure; and

[0037] FIG.13 is a flowchart of a method for obtaining a contrast distribution in accordance with embodiments of the present disclosure. DETAILED DESCRIPTION

[0038] Embodiments as described herein are described in sufficient detail to enable those skilled in the art to practice the described disclosure and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the disclosure. The present description is, therefore, merely exemplary.

[0039] The system and method of the present disclosure enable reduced exposure acquisition by decreasing noise, improve sub-millimeter visualization of contrast enhancement within patients, for example, but not limited to, vessel visualization, and enable the reduction of contrast agent concentrations. The system according to embodiments of the present disclosure includes spectral imaging equipment, one or more processors for receivingthe spectral data and applying the processing techniques described herein, and one or more data output mechanisms. The method according to embodiments of the present disclosure includes receiving spectral data, applying the processing techniques described herein, and providing the resulting data for storage, further processing, and / or visualizing contrast enhancement within patients.

[0040] Referring now to FIGs.1A-1D, various DSA subtraction schemes 100 and 101 are shown. In FIG.1A, temporal subtraction is shown. In FIG.1B, “energy subtraction” leverages spectral imaging acquisition where acquisitions at multiple energies are used to estimate material-specific images and to isolate iodine from bone via “hybrid subtraction” using pre- and post-injection images. In FIG.1C, “hybrid subtraction” uses both temporal and spectral information and has been used to mitigate the effects of patient motion via post- injection “energy subtraction”, but in a manner that results in significant noise amplification. In FIG.1D, the method in accordance with embodiments of the present disclosure and its improved results are shown. The system and method in accordance with embodiments of the present disclosure provide advantages over both temporal DSA as shown in FIG.1A, and spectral imaging as shown in FIGs.1B and 1C. A method in accordance with embodiments of the present disclosure includes joint processing data from both the pre- and post-contrast acquisitions as shown in FIG.1D. In some configurations, the method allows three-material decomposition using a dual-layer detector. Assuming that bone motion is minimal between the pre- and post-contrast measurements, but soft tissues can move freely, four material bases are jointly estimated – soft tissue pre-contrast, bone, soft tissue post-contrast, and iodine – and all four measurements are used. Such a formulation offers image quality advantages compared to the hybrid subtraction method. In an aspect, this method leads to a noise advantage compared to currently available techniques performed under the same conditions. Compared to DSA (FIG.1A), an improved energy resolving detector provides spectral information that enables improved data processing. Compared to spectral imaging (FIGs.1B and 1C), the pre-contrast image contains prior information on the material distribution of water and bone, which can be leveraged to reduce the uncertainty in the material estimation process.

[0041] The “subtraction” scheme of joint processing the spectral information in both the pre- and post-contrast images provides improved noise management over temporal DSA. Another advantage of the joint processing strategy is that iodine decomposition can beachieved using two spectral channels, thus reducing the total signal-to-noise ratio and, hence, improving the quality of the resulting images. Furthermore, decomposition of iodine and bone is sensitive to noise because of the similar attenuation properties of iodine and calcium. Moreover, decomposition processes applied in such scenarios are susceptible to convergence issues, for example, getting stuck in local optima, etc. Such estimation errors can manifest as bias where calcium is misestimated as iodine and vice versa. The joint processing strategy of the present disclosure enables spectral differentiation of materials and incorporates temporal information that further enables improved differentiation.

[0042] While there exists a plethora of denoising processes that can be applied to improve signal-to-noise ratio, the system and method in accordance with embodiments of the present disclosure result in image quality improvement even in the absence of such processes due to more efficient acquisition and processing of information. Additional postprocessing processes can be applied to increase the advantage even further compared to currently available approaches. Compared to temporal DSA, the system and method in accordance with embodiments of the present disclosure (1) reduce image noise without increasing dose due to the joint processing strategy, high spectral separability and low readout noise of devices such as PCDs; (2) maintain and / or improve contrast resolution due to the ability to isolate iodine signals without overlaying background anatomy; (3) improve spatial resolution via smaller pixel size and direct detection / reduced detector blur of devices such as PCDs; and (4) maintain dynamic imaging capabilities with real-time processing and display through deep learning accelerated decomposition combined with the fast readout time of devices such as PCDs. Thus, a system and method in accordance with embodiments of the present disclosure provide visualization of contrast enhancement within patients, for example, but not limited to, visualization of sub-millimeter vessels. Although specific applications of the system and method are described herein, such as a spine angiogram, the system and method can be applied to other interventional applications where sub-millimeter visualization of contrast enhancement within patients is challenging.

[0043] Referring now to FIG.2, a PCD can be used to demonstrate performance of the joint processing strategy compared to currently available techniques. For example, a comparison 200 is shown of temporal DSA using a 650µm CsI energy integrating detector (EID), joint processing using a 750µm CdTd PCD with energy separation at 40keV, and a spectral only method using PCD with three spectral channels separated at 30 and 50keV.Shown is a phantom simulated with iodine enhanced vessels (30 mg / ml) from 1mm to 125µm diameter, varying amounts of calcium, and 16cm of water (not shown). In the simulation results shown in FIG.2, both joint processing and spectral only were estimated using a maximum likelihood estimator without regularization. Detector blur was not simulated in order to demonstrate noise only performance. In the simulation, the joint processing strategy has ~28.6% variance reduction compared to temporal DSA, while the “spectral only” has amplified noise (average 3.3e-10 mg2 / ml2, not shown). Source spectra and fluence are the same for all three cases.

[0044] Continuing to refer to FIG.2, the joint processing technique includes a simulated PCD with two spectral channels with a threshold at 40 keV. The ~28.6% improvement in voxel variance in the iodine image is compared to the noise level in temporal DSA normalized to the same iodine signal. Spectral decomposition using a single post- contrast acquisition with three spectral channels results in noise amplification of ~22 times compared to temporal DSA in the iodine image. Improved image quality with the joint processing method is shown in the simulation, without increasing the total dose to the patient. The noise advantage of the joint processing technique enables improved low contrast visualization of contrast enhancement within patients, for example, but not limited to, visualization of vessels, including high-resolution vessels. The joint processing technique in this example yields three material maps – soft tissue, bone, and iodine. The availability of projection-domain soft tissue and bone images is useful for clinical applications. For example, the bone image may provide detection of calcified plaques, stenosis, etc. Display strategies such as color overlay of soft tissue or boney landmarks can be used for visualization of contrast enhancement within patients. To enable dynamic imaging capabilities, fast material decomposition and post-processing can be performed on graphics processing units (GPUs) as well as low latency display directly from GPU memory at an acquisition speed of 7.5 frames per second (fps). Neural network processing and deep learning enable real-time processing of the incoming data.

[0045] In a use of the system and method of the present disclosure, water, calcium, and iodine are the materials for which basis material maps are generated. Other choices of material bases can be used. The number of material maps is based on the number of spectral channels. Assuming the same material density maps of water and calcium in both the pre- and post-contrast images, a joint processing method can solve three unknowns (water,calcium, and iodine) from four measurements (two spectral channels from pre- / post- acquisition) using a model-based approach. A baseline maximum likelihood process can be used to achieve relatively low noise and relatively low bias iodine decomposition compared to temporal DSA and spectral decomposition. The joint processing method applies to pre- and post-contrast images, in accordance with embodiments of the present disclosure: ^^^^̅pre= B ^^^^1exp(− ^^^^^^^^2 ^^^^^^^^^^^^2 ^^^^− ^^^^^^^^ ^^^^^^^^^^^^ ^^^^) ^^^^̅pre= BS2exp(− ^^^^^^^^2 ^^^^^^^^^^^^2 ^^^^– ^^^^^^^^ ^^^^^^^^^^^^ ^^^^) (1) ^^^^̅post= B ^^^^1exp(− ^^^^^^^^2 ^^^^^^^^^^^^2 ^^^^− ^^^^^^^^ ^^^^^^^^^^^^ ^^^^– ^^^^^^^^^^^^^^^^) ^^^^̅post= BS2exp(− ^^^^^^^^2 ^^^^^^^^^^^^2 ^^^^– ^^^^^^^^ ^^^^^^^^^^^^ ^^^^– ^^^^^^^^^^^^^^^^) (2) In a joint processing method, three material density line integrals, ^^^^H2O, ^^^^Ca, ^^^^I, are solved with four measurements. B stands for system blur, for example, detector blur from charge sharing, focal spot blur, etc., and S stands for spectral sensitivity dependent on the spectral channel. Q is the mass attenuation coefficient that scales the line integrals of material density, l. The line integrals can be modified to accommodate four unknowns – water ( ^^^^H2O), calcium ( ^^^^Ca), iodine ( ^^^^I), and the change in iodine (Δ ^^^^I).^^^^̅post= B ^^^^1exp(− ^^^^^^^^2 ^^^^^^^^^^^^2 ^^^^− ^^^^^^^^ ^^^^^^^^^^^^ ^^^^– ^^^^^^^^( ^^^^^^^^+ Δ ^^^^I)) ^^^^̅post= BS2exp(− ^^^^^^^^2 ^^^^^^^^^^^^2 ^^^^– ^^^^^^^^ ^^^^^^^^^^^^ ^^^^– ^^^^^^^^( ^^^^^^^^+ Δ ^^^^I)) (4) The aggregate of iodine estimates ( ^^^^I+ Δ ^^^^I) forms the iodine map for the latest acquisition. A high-fidelity joint processing method can include effects like charge sharing and pulse pileup. Both effects can introduce bias in the estimated material maps – spectral distortion through pulse pileup and increased detector blur through charge sharing. A model-based compensation process can enable joint processing for DSA to manage these effects. For example, a paraboloidal surrogate approach can be used to implement an iterative estimate approach to the joint processing of the present disclosure. To manage scatter, if the scattered signal is energy-dependent, it can be estimated separately for spectral channels. An angiography application can have a large air gap that reduces both the amount and the heterogeneity of scatter. A separate scalar scatter correction factor for each bin can be applied. Scatter management can include performing measurements at different energy thresholds of the PCD to arrive at an energy-dependent scatter estimation.

[0046] Options for regularizing include quadratic regularization and edge-preserving non-quadratic penalties. Other options are cross-basis penalties, which are penalties jointlyapplied to multiple material maps. Cross-basis penalties enable customization of image quality in specific material images. Cross-basis penalties can be designed to, for example, optimize an iodine-only image if other types of images such as water and calcium, are of less importance clinically. Post-processing processes can include edge enhancement (e.g., unsharp masking) and temporal frame averaging, among others.

[0047] Referring now to FIGs.3A-3C, the relative performance 300 of a high- fidelity joint processing method of PCD data is shown. Specifically, in an experiment using a spectral cone-beam computed tomography (CBCT) with a dual-layer detector, FIG.3C shows a comparison between a one-step model-based decomposition for CBCT using a high-fidelity joint processing method and (1) the image domain decomposition using filtered back projection (FBP) reconstructions shown in FIG.3A and (2) the model-based approach using an idealized joint processing method shown in FIG.3B.

[0048] Referring now to FIG.4, the joint processing technique assumes there is no motion between the pre- and post-acquisitions. To generalize the process to manage patient motion, a registration / motion compensation step can be included between the image pairs. To manage registration interpolation blurs, a modified DSA workflow, such as, for example, but not limited to, the flow 400 can be used in which consecutive post-contrast images are joint processed to enable three material estimation. As these images are acquired in rapid succession, there is minimal motion in neuro interventions.

[0049] Referring now to FIGs.5A-5C, in an aspect, real-time processes can be based on deep learning methods. Deep learning methods can speed up computations and incorporate generalized prior information. Deep learning methods for general material decomposition and denoising of spectral results, charge sharing and pulse pileup management for PCD, motion management in DSA, and various segmentation and automatic lesion detection processes based on DSA are relevant to network formulation for deep learning. FIGs.5A-5C illustrate a deep learning network capable of three material decomposition 500 and 501 in the projection domain using data from a triple layer detector. A U-Net architecture (FIG.5A) with three measurements from each layer as input yields estimates of soft tissue, bone, and iodine material maps. FIG.5B illustrates decomposition results of ground truth versus estimated values for soft tissue, bone, and iodine. Low estimation bias is shown in FIG.5B in all three materials with preservation of small vessels in the iodine map. A gradient-based loss term in addition to the mean squared error (MSE) loss can reduceestimation bias ( ^^^^ ^^^^ ^^^^ ^^^^ =∑�(^^^^ − ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^) ^^^^+ FIG. 5C illustratesthe effect of the gradient-based loss term in reducing estimation bias and improving spatial resolution. FIG.5C illustrates a comparison between the ground truth and network outputs following two different loss functions: ^^^^ = 0 (MSE without gradient loss), and ^^^^ = 100 (MSE with gradient loss).

[0050] Network efficiency and inference speed can be improved by a two-input “butterfly” network enabling differentiation between the pre- and post-contrast inputs, varying the number of residual blocks and structure within the block, and reducing the number of outputs. A data consistency loss term can reduce estimation bias and increase generalizability of the deep learning model.

[0051] For spectral acquisitions, protocols with fixed contrast and density of images (e.g., disabling automatic exposure controls) can be defined. The combination of kV, filtration, and energy thresholds of PCD can be optimized to maximize spectral separability based on a separability index metric. Optimization for high dimensional space can be accomplished by a search at discretized steps of the parameters of interest. The mA can be determined by matching the dose (entrance skin dose via air kerma measurements) to standard clinical protocols for each anatomical site (spine and head) using anthropomorphic phantoms of different sizes.

[0052] Referring now to FIG.6, a clinical spectral angiography system can include, but is not limited to including, a C-arm, a PCD, a mechanical mount to hold the PCD in place, a display monitor, and a workstation that connects and controls the components. In an aspect, the PCD can include a tileable PCD configured with 36 (6x6, ~12cm x 12cm total area) detector modules. In an aspect, a cadmium telluride (CdTe) detector includes at least two spectral channels, configured to include additional thresholds, 100 μm pixels, and a 100% fill factor. In an aspect, the gaps between modules are limited to approximately 1 pixel. In an aspect, the mechanical mount for the PCD is modular, allowing the PCD to be installed and removed from both a characterization system (not shown) and the clinical system. In an aspect of a characterization system, a PCD is mounted on two perpendicular linear stages to enable translation in two dimensions. Such a geometry enables characterization and experimentation to be performed with a relatively small area PCD. In the clinical system, on the C-arm gantry, the PCD mount can operate under either of twoconfigurations: 1) an imaging mode where the PCD is placed over a central area of a flat panel detector; or 2) an off-mode that moves the PCD out of the field of view to allow operation of the C-arm under fluoroscopy mode. The off mode can be used during navigation as well as during comparison studies where spectra acquisition using an energy resolving detector (ERD) such as, for example, but not limited to, a flat panel detector is performed. In an aspect, the characterization system includes a pulsed rad / fluoro x-ray tube and generator, along with associated mounts, cabling, collimation, etc. In an aspect, the characterization system includes a flat panel detector that can be removed and replaced with a PCD and mount. Controlling parameters for the characterization system can include, but are not limited to including, contrast and density of the image, pulse length, and pulse rate. In an aspect, the clinical system includes an x-ray source and built-in collimation configured to align with the PCD. In an aspect, the workstation receives data from the PCD. In an aspect, hardware synchronization in the pulsed X-ray clinical system includes either or both of synchronous or asynchronous control. With respect to synchronous control, the workstation is connected directly to the control computer. A trigger associated with each X-ray pulse is transmitted to the workstation and the PCD to synchronize each X-ray exposure with detector signal integration. With respect to asynchronous control, X-ray exposures are controlled by the clinical computer, and the PCD and workstation operate in free-running mode. This mode is enabled by the readout time of the PCDs. Since there is no readout noise with a PCD, individual exposures can be integrated from high-framerate data without a noise penalty. Protocols with fixed contrast and image density can be defined for spectral characterization and the joint-processing material decompositions. In an aspect, exposures are initiated with foot controls.

[0053] In an aspect, the system is configured to acquire data and process and display the data in real-time. In an aspect, the workstation is configured with GPUs and is connected to the PCD. In an aspect, the workstation includes a 60” display monitor. In an aspect, the workstation is configured to be positioned according to clinician preference. In an aspect, the system is configured to be moved from one location to another. The system can be configured to acquire data synchronously or asynchronously. For synchronous mode, in an aspect, a data acquisition card is used to control hardware signaling between the X-ray generator and the PCD. For asynchronous mode, individual exposure intervals are detected for example, but not limited to, using data thresholds, and data are summed into singleframes. In an aspect, PCD data are routed to GPU memory, through transfer operations or memory mapping, to enable real-time processing. In an aspect, the GPU performs data processing to minimize latency between X-ray exposure and display. In an aspect, processes are implemented in CUDA or OpenCL. In an aspect, the decomposition processes are parallelizable and configured to be implemented on a GPU. In an aspect, the neural network structures are implemented using currently available products such as, for example, but not limited to, Pytorch, using GPU operations. In an aspect, image outputs are stored in GPU memory and transmitted to the display monitor using on-GPU memory transfers and / or mappings. In an aspect, recursive filtering and gap filling enable continuous display at a given pulse rate. In an aspect, the display interface of the characterization system mimics the layout of the clinical system, ensuring a smooth transition between the clinical system and the characterization system. In an aspect, post-processing processes, for example, but not limited to, temporal frame averaging, edge enhancement, and last image hold, are configured as options that can be enabled and disabled depending on a clinician’s preference. In an aspect, the system includes tools for the workstation that implement features for image viewing, including the ability to change window / level settings, add annotations to images, digital magnification, and on-screen measurement, for example, but not limited to, digital calipers.

[0054] Referring now to FIGs.7A-7D, vessel model sub-millimeter vessels 700 are shown. These vessel phantoms are used to evaluate the process of the present disclosure. Realistic vessel tree structures segmented from 3D DSA of patients are shown as created using flexible materials to permit deformation of the vessel trees with patient motion. For each anatomical site of interest, for example, but not limited to, the spine and the brain, spine data obtained from patients who are being evaluated or treated for spinal arteriovenous fistula, and brain data obtained from patients undergoing evaluation for cerebral aneurysms, arteriovenous malformations, and arteriovenous fistulas are shown. As shown in FIG.7A, the major spinal vessels show a high-resolution phantom depicting stenosis. As shown in FIG. 7B, a small vessel tree is printed using a stereolithographic (SLA) printer. In FIG.7C, a commercially available vessel model is shown. In FIG.7D, a customized pelvis phantom with bone inserts is shown. A phantom filled with organ-shaped shells can be filled with low impedance (e.g.150-600 ohms) solutions to mimic different soft tissue, for example, but not limited to, radicular, radiculomedullary, radiculopial, anterior spinal, and posterior spinal arteries, as well as cerebral vessels such as first and second order branches of the Circle ofWillis, to generate different realizations of vessel phantoms. Organ shaped shells are filled with low atomic number solutions of different concentrations to mimic soft tissues of different densities. For contrast not clearly visualized within patients due to resolution and / or noise limits, data augmentation strategies can be used to generate 3D models of these tissues. For example, vessel tree models, down to a minimum vessel diameter of 100 µm, can be created. The vessel models can be modified, for example, but not limited to, produce a mirror image to permit continuous flow of liquid. The 3D models of the vessels can be printed on a 3D printer capable of high resolution (~10 micron) printing of flexible filament, for example, but not limited to, thermoplastic elastomer or thermoplastic polyurethane. The printed vessel trees can be scanned using high resolution cone-beam CT or microCT to establish the ground truth vessel tree distribution. In an aspect, the printed vessels can be stored in anthropomorphic shells with custom-fitted bones as shown in, for example, FIG.7D.

[0055] With respect to both 2D and 3D spectral data, both temporal and energy information can be leveraged for image quality improvement. A method in accordance with embodiments of the present disclosure includes acquiring projection data using a spectral imaging system at multiple times, for example, but not limited to, before and after contrast injection. The method further includes obtaining measurements in multiple spectral channels for each acquisition. Under the assumption of minimal patient motion (valid for intubated patients in anatomical sites without involuntary motion like cardiac and breathing), the method relates, for example, but not limited to, a three-material object (water, bone / calcium, iodine) to four (two pre- and two post-contrast) measurements as follows:where { ^^^^̅1, ^^^^̅2} denotes the pre-contrast mean measurements containing water and bone / calcium, { ^^^^3̅, ^^^^̅4} denotes the post-contrast mean measurements containing water, calcium, and iodine, ^^^^1and ^^^^2model the spectral sensitivities of each spectral channel, and ^^^^ contains the mass attenuation coefficients for each basis material, and where A denotes the system matrix, and ^^^^ represents material densities.

[0056] In general, the method of the present disclosure relates an arbitrary number of spectral channels to an arbitrary number of material basis as shown in Equation (5a). Such a general relationship is solvable if the number of material basis is less than or equal to the total number of measurements pre- and post-contrast. ^�^^^t1 ^^^^ ^^^�…t1 ^t1�=� …� exp�−^�^^^tn^^^^tn^^^^tnwhere ^�^^^t1through ^�^^^tnis a matrix of measurements taken at time points t1through tnrespectively, ^^^^t1through ^^^^tnis a matrix of spectral sensitivity at time points t1through tnrespectively, ^^^^ represents material basis line integrals, It1through Itnis a matrix that selects which material basis is present in which measurement, at time points t1through tnrespectively, and Q is a mass attenuation matrix.

[0057] In Equation (5), a masking matrix composed of identity matrices and zeros selectively zero out the pre-contrast measurements associated with iodine. This form of joint processing method (linear-exponential-linear) can be solved by an optimization process using a separable paraboloidal surrogate approach. Assuming the measurements follow a multivariate Gaussian distribution, ^^^^~ ^^^^( ^̅^^^, ^^^^), the material density, ^^^^, can be solved using a nonlinear weighted least squares objective: ^^^^̂=arg^^^^min Φ( ^^^^, ^^^^) (6)

[0058] In an aspect, a quadratic penalty, ^^^^, is used. In an aspect, the densities of, for example, water, calcium, and iodine are initialized with zeros and iteratively solved using a pre-selected number of iterations, for example, 600, of the separable quadratic surrogate process with another pre-selected number, for example 10, of ordered subsets and Nesterov’s acceleration.

[0059] Alternatively, another process involves performing a projection-domain decomposition followed by an analytic or model-based reconstruction. In an aspect an estimate of the material density line integral, ^^^^= ^^^^ ^^^^ replaces the physical density ^^^^ in the joint processing method of Equation (5):^^^^ ^^^^ ^^^^

[0060] An objective function as shown in Equation (7) based on ^^^^ is as follows:^^^^̂=arglmin Φ( ^^^^, ^^^^) (10)

[0061] In an aspect, no additional regularization is included in this objective function. Smoothing in the volumetric reconstruction relies on apodization filter in FDK or regularization in model-based iterative reconstruction. In an aspect, a modified Newton’s method is used to solve this objective function, where a proximal regularization term is added to the diagonal of the Hessian to improve conditioning of the inversion process. In an aspect, zero initialization and a pre-selected number of iterations such as, for example, 50, of an optimizer are used. In an aspect, volumetric reconstruction of the estimated material density line integrals is performed using either analytical or iterative processes. In an aspect, filtered back-projection (FBP) with a Hann apodization filter with various cutoff frequencies are used.

[0062] Referring now to FIG.8, in an aspect, a digital phantom can enable data generation. The digital phantom 800 includes a 1000 mg / mL water background, a 4.0 mm- thick 200 mg / mL calcium ring, and 10 mg / mL iodine-enhanced vessels of diameter ranging from 0.3 mm to 4.0 mm. The phantom can be used to evaluate high-resolution imaging of small targets such as intracranial vessels. In some evaluations, pre-contrast imaging involves a water background and a calcium ring, while post-contrast imaging includes the enhanced vessels.

[0063] Referring now to FIGs.9 and 10A-10F, four 3D spectral techniques are compared. (1) Pre- and post-contrast measurements generated using an EID with a 600-μm CsI scintillator. In this simulation, these measurements emulate data from DSA using temporal subtraction and what might be used in a 3D-DSA interventional imaging system (e.g., C-arm). (2) Pre- and post-contrast measurements generated using a single spectral channel (10–150 keV) from a photon counting detector (PCD) with 750-μm CdTe. In this simulation, the dataset is used to evaluate performance of temporal subtraction with a PCD.(3) Post-contrast measurements using a PCD. In this simulation, two energy thresholds are applied (40 keV and 60 keV) to obtain data from three spectral channels. The PCD is modeled with pre-selected energy resolution. These data provide an example of spectral imaging in 3D, where energy information is leveraged for material decomposition. This technique is evaluated at both 1x and 2x the total dose for a comparison to techniques using both the pre- and post- measurements. (4) Pre- and post-contrast measurements from the PCD with two spectral channels. This dataset contains both temporal and energy information and is used to evaluate the joint processing strategy of the present disclosure. The energy threshold is set to 50 keV.

[0064] In the simulation, projection data for 3D imaging (1080 × 5 pixels, 0.154 mm pixel pitch, 360 views uniformly distributed over 360°) are generated for a system geometry with a source-to-axis distance of 800 mm and a source-to-detector distance of 1100 mm. The x-ray spectrum is generated at 100 kVp with 0.25 mm aluminum as intrinsic filtration. The nominal tube current-time product is 1.0 mAs per projection. Poisson noise is added to the measurements, and detector blur measured from a physical EID is applied to data from the EID. In the simulation, blur is assumed to be negligible for the PCD, and volumetric images are reconstructed at 0.1 mm isotropic voxel size.

[0065] In temporal subtraction, in the simulation, the iodine distribution is obtained by subtracting two single energy reconstructions. The scale and units are therefore mismatched from physical density obtained from spectral decomposition. To enable direct quantitative comparisons, an “oracle” scaling factor computed from noiseless measurements is applied to convert attenuation coefficient differences to iodine density. In spectral imaging, the density line integrals are estimated via model-based projection domain decomposition considering three energy sensitive channels and post-contrast measurements. For quantitative comparison of methods in the simulation, the noise-resolution trade-off in the iodine basis image is evaluated by varying the cutoff frequency of the Hann filter. In the simulation, resolution is characterized by the full width at half maximum (FWHM) of the 0.3 mm diameter vessel measured in a noiseless reconstruction. Noise is measured within a 21 × 21 × 1 region of interest at the center of the 4.0 mm diameter vessel over 10 repeated reconstructions with different noise realizations.

[0066] Referring again to FIG.9, the noise-resolution curves 900 for the simulation for spectral imaging, temporal subtraction, and joint processing with model-based projectiondomain decomposition are shown. Temporal subtraction using the PCD improves resolution, as well as ~25% reduction in noise at matched resolution. Joint processing with MB-PDD exhibited a ~12% noise reduction compared to temporal subtraction using the same PCD.

[0067] Referring again to FIGs.10A-10E, example decomposed iodine images 1000 of the 0.46 mm diameter vessel at a matched resolution as indicated by the black dashed vertical line in FIG.9 are shown. An elevated level of noise is present in FIGs.10A and 10B, obscuring the small vessel target. By contrast, the vessel can be easily differentiated from background noise in FIGs.10C-10E, while the magnitude of noise is noticeably lower in FIGs.10D and 10E.

[0068] Referring again to FIG.10F, a preliminary model-based one-step decomposition result, which exhibits higher resolution (~0.3 mm) and markedly reduced noise compared to other methods is shown. FIG.10F shows noise-resolution characterization in iodine basis images estimated through joint processing with varying cutoff frequencies for FBP reconstruction.

[0069] Alternatively, detector blur can be factored in. In an aspect, a pre-contrast injection projection image followed by a post-contrast injection projection image are generated. Both exposures use a dual-layer flat-panel detector, yielding a total of four images. The joint processing method for the four pre- and post-contrast measurements, y, can thus be written as: ^^^^̅1( ^^^^) = Bt^^^^texp(− ^^^^^^^^2 ^^^^^^^^1^^^^2 ^^^^− ^^^^^^^^ ^^^^^^^^^^^^ ^^^^) (11) ^^^^̅2( ^^^^) = Bb^^^^bexp(− ^^^^^^^^2 ^^^^^^^^1^^^^2 ^^^^− ^^^^^^^^ ^^^^^^^^^^^^ ^^^^) (12) ^^^^̅3( ^^^^) = Bt^^^^texp(− ^^^^^^^^2 ^^^^^^^^2^^^^2 ^^^^− ^^^^^^^^ ^^^^^^^^^^^^ ^^^^− ^^^^^^^^^^^^^^^^) (13)where the operator B denotes detector blur, S is the spectral response (including effects of both x-ray source spectrum and spectral sensitivity of the detector), and Q is the mass attenuation coefficient that scales the line integrals of material density, l. The superscripts denote the materials, and the subscripts t and b denote spectral channels. The measurements {y1, y2} are pre-contrast injection, {y3, y4} are post-contrast injection, and the water distribution in the pre- and post-contrast measurements are ^^^^1^^^^2 ^^^^and ^^^^2^^^^2 ^^^^, respectively. Material decomposition involves processing the four measurements in Equations (11)-(14) to obtain the material path lengths { ^^^^1^^^^2 ^^^^, ^^^^2^^^^2 ^^^^, ^^^^^^^^ ^^^^, ^^^^^^^^}. The process in accordance withembodiments of the present disclosure presumes there is minimal motion of bone between the pre-contrast and post-contrast acquisitions, or that bone motion can be compensated via registration. The calcium distribution in the pre- and post-contrast images can therefore be assumed to be unchanged.

[0070] In an aspect, material decomposition includes staged decomposition methods where a projection-domain decomposition for the pre- and post-contrast measurements are conducted sequentially using two lookup tables: { ^^^^1^^^^2 ^^^^, ^^^^^^^^ ^^^^} = LH20,Ca(log y1, log y2) { ^^^^2^^^^2 ^^^^, ^^^^^^^^ ^^^^} = LH20,I(log y3, log y4; ^^^^^^^^ ^^^^) (15)

[0071] In the look-up table method, pre-contrast measurements are decomposed into water and calcium basis images using a lookup table that relates different density line integrals of water and calcium { ^^^^1^^^^2 ^^^^, ^^^^^^^^ ^^^^} to the logarithm of the intensity measurements from the spectral channelsThe post-contrast decomposition is performed using a three material lookup table that maps different density line integrals of water and iodine { ^^^^1^^^^2 ^^^^, ^^^^^^^^} indexed at a fixed amount of calcium { ^^^^^^^^ ^^^^} from the spectral channel measurements { ^^^^̅3,^^^^̅4}.

[0072] In an aspect, embodiments of the present disclosure include a model-based projection domain decomposition process where the density line integrals are estimated directly from the measurements. This embodiment is similar to a model-based reconstruction process for dual energy computed tomography (CT) material decomposition that models the (potentially mismatched) geometry and scintillator blurs in the top and bottom layers. The process includes estimating four material images, l = { ^^^^1^^^^2 ^^^^, ^^^^2^^^^2 ^^^^, ^^^^^^^^ ^^^^, ^^^^^^^^}, simultaneously using a penalized likelihood objective function assuming that measurements, y = {y1, y2, y3, y4}, in each spectral channel follow a multivariate Gaussian distribution with covariance K:^^^^ = arg minlΦ(l, y) where Φ(l, y) = ½ (y − y¯ )T ^^^^−^^^^1(y − y¯ ) + R(l)(16)

[0073] In the model-based process, the roughness penalty, R(l) is chosen to be a quadratic penalty acting over the four nearest neighbors within each material image, and the penalty strength for each material image is set to, for example, but not limited to, 105, 106, 105, and 108. Other configurations are possible.

[0074] To simulate the look-up table and model-based projection domain decomposition processes, ground truth phantoms can be generated using currently available techniques such as, for example, the XCAT phantom simulation package. In an aspect, the phantoms are generated in 3D and include ground truth density distributions of water, calcium, and iodine. In an aspect, a perfect breath-hold is simulated where the diaphragm movement and anterior-posterior (AP) expansion parameters are set to 0. In an aspect, a male thorax phantom is simulated at 20 time points through the default cardiac cycle. In the simulation, the 1st point without iodine is used as the pre-contrast imaging, and the 15th time point with iodine enhanced vasculature is used as the post-contrast image. In the simulation, measurements were simulated using the joint processing method in Equations (11)-(14). The source spectrum and spectral sensitivity of the detector can be, for example, determined by commercially-available products such as, for example, LABSPHERE® products. In an aspect, detector blurs for each layer are based on techniques known to those skilled in the art. In the simulation, independent Poisson noise is added to the measurements prior to the application of detector blur.

[0075] Referring now to FIGs.11A and 11B, illustrations of the four material decompositions 1100 and 1101 using both the lookup table and model-based approaches are shown. Material maps for water (pre- and post-injection), calcium, and iodine are shown, along with the ground truth and difference from truth images. The model-based method effectively mitigates noise and produces material images with low bias compared to the ground truth as seen from the difference images.

[0076] Referring now to FIG.12, iodine images 1200 containing vessels in the left lung and comparisons between the performance of traditional spectral methods (temporal and hybrid subtraction) with the look-up table and model-based methods are shown. A zoomed region is shown where there is a significant change in the cardiac soft tissue that yields subtraction artifacts in temporal spectral data. Temporal subtraction has marked motion artifact due to cardiac motion. In comparison, major vessels around the heart are visible in the model-based material images. The structure similarity index measure (SSIM) and mean square error (MSE) were computed within the region of interest (ROI). From left to right, the SSIM to the ground truth is: 0.67, 0.77, 0.20, 0.19; the MSE to the ground truth is: 7.7e-9, 6.2e-10, 1.9e-8, 1.7e-8. Beyond the application presented herein, the joint processing strategy can be modified for other imaging scenarios as well. For example, two post-contrastacquisitions at consecutive time points can be processed together (assuming no soft tissue or bone motion) to solve for the change in contrast agent distribution. If motion can be assumed negligible (e.g., in neurovascular interventions where patients are under anesthesia), the joint processing strategy can also be used to solve for three material maps using the same four measurements. This processing strategy can lower image noise in the iodine material maps and mitigate noise amplification due to material decomposition in spectral acquisition schemes.

[0077] Referring now to FIG.13, a method 1300 for obtaining a contrast distribution includes, but is not limited to including, acquiring 1302 pre-contrast spectral data before contrast is administered, acquiring 1304 post-contrast spectral data after the contrast is administered, and generating 1306 at least one material basis map for at least one material by joint processing the pre-contrast spectral data and the post-contrast spectral data to solve for a pre-selected number of unknowns corresponding to the at least one material associated with the at least one material basis map, wherein the joint processing enables visualization of contrast distribution from contrast agent injection or drug delivery contrast agents, and wherein the at least one material basis map includes the contrast distribution.

[0078] Certain embodiments can be performed using a computer program or set of programs executed by an electronic processor. The computer programs can exist in a variety of forms both active and inactive. For example, the computer programs can exist as software program(s) comprised of program instructions in source code, object code, executable code or other formats; firmware program(s), or hardware description language (HDL) files. Any of the above can be embodied on a transitory or non-transitory computer readable medium, which include storage devices and signals, in compressed or uncompressed form. Exemplary computer readable storage devices include conventional computer system RAM (random access memory), ROM (read-only memory), EPROM (erasable, programmable ROM), EEPROM (electrically erasable, programmable ROM), and magnetic or optical disks or tapes.

[0079] While the disclosure includes descriptions that refer to the exemplary embodiments thereof, those skilled in the art will be able to make various modifications to the described embodiments without departing from the true spirit and scope. The terms and descriptions used herein are set forth by way of illustration only and are not meant as limitations. In particular, although the method has been described by examples, the steps ofthe method can be performed in a different order than illustrated or simultaneously. Those skilled in the art will recognize that these and other variations are possible within the spirit and scope as defined in the following claims and their equivalents.

Claims

CLAIMS 1. A method for obtaining a contrast distribution comprising: acquiring pre-contrast spectral data before contrast is administered; acquiring post-contrast spectral data after the contrast is administered; and generating at least one material basis map for at least one material by joint processing the pre-contrast spectral data and the post-contrast spectral data to solve for a pre-selected number of unknowns corresponding to the at least one material associated with the at least one material basis map, wherein the joint processing enables visualization of contrast distribution from contrast agent injection or drug delivery contrast agents, and wherein the at least one material basis map includes the contrast distribution.

2. The method as in claim 1 wherein the joint processing comprises: a model-based approach.

3. The method as in claim 2 wherein the model-based approach comprises: creating a forward model by relating the at least one material basis map to the pre- contrast spectral data, the post-contrast spectral data, and temporal data associated with the pre-contrast spectral data and the post-contrast spectral data; estimating the at least one material basis map based on the forward model; and minimizing a difference between the estimated at least one material basis map and an actual at least one material map.

4. The method as in claim 1 wherein the joint processing comprises: a deep learning-based approach.

5. The method as in claim 4 wherein the deep learning-based approach comprises: training a deep learning model with historical spectral data identified as collected before and after the contrast is administered, historical temporal data associated with the spectral data, and at least one historical material basis map;providing the pre-contrast spectral data, the post-contrast spectral data, and temporal data associated with the pre-contrast spectral data and the post-contrast spectral data to the trained deep learning model; and receiving the at least one material basis map from the trained deep learning model.

6. The method as in claim 1 wherein the pre-contrast spectral data and the post-contrast spectral data comprise: image data.

7. The method as in claim 1 wherein the pre-contrast spectral data and the post-contrast spectral data comprise: multi-layer detector data.

8. The method as in claim 1 further comprising: joint processing consecutive images from the pre-contrast spectral data and the post- contrast spectral data to achieve the at least one material basis map; and performing registration between the consecutive images to achieve motion compensation between the consecutive images.

9. The method as in claim 1 further comprising: acquiring the pre-contrast spectral data using an energy-resolving detector (ERD).

10. The method as in claim 9 wherein the ERD comprises: a photon counting detector (PCD).

11. The method as in claim 10 further comprising: estimating energy-dependent scatter by performing measurements at different energy thresholds of the PCD.

12. The method as in claim 1 wherein the joint processing comprises: an iterative estimation approach.

13. The method as in claim 12 wherein the iterative estimation approach comprises: a paraboloidal surrogate approach.

14. The method as in claim 13 further comprising: regularizing of the iterative estimation approach using quadratic penalties.

15. The method as in claim 13 further comprising: regularizing of the iterative estimation approach using edge-preserving non-quadratic penalties.

16. The method as in claim 13 further comprising: regularizing of the iterative estimation approach using cross basis penalties.

17. The method as in claim 1 further comprising: applying a scatter correction factor to remove scatter bias from the at least one material basis map.

18. The method as in claim 1 further comprising: post-processing the at least one material basis map using edge enhancement.

19. The method as in claim 1 further comprising: post-processing the at least one material basis map using temporal frame averaging.

20. The method as in claim 1 wherein the visualization comprises: providing a color overlay of soft tissue.

21. The method as in claim 1 wherein the visualization comprises: providing a color overlay of boney landmarks.

22. The method as in claim 1 wherein the joint processing is applied for two-dimensional or three-dimensional digital subtraction angiography (DSA).

23. The method as in claim 1 wherein the joint processing comprises: ^^^^̅pre= B ^^^^1exp(− ^^^^A^^^^A− ^^^^B^^^^B) ^^^^̅pre= BS2exp(− ^^^^A^^^^A– ^^^^B^^^^B) ^^^^̅post= B ^^^^1exp(− ^^^^A^^^^A− ^^^^B^^^^B− ^^^^C^^^^C) ^^^^̅post= BS2exp(− ^^^^A^^^^A− ^^^^B^^^^B– ^^^^C^^^^C) wherein ^^^^̅preis a pre-contrast measurement, ^^^^̅postis a post-contrast measurement, B is system blur, S is spectral sensitivity dependent on a spectral channel, ^^^^Ais a mass attenuation coefficient that scales a line integral of material A density, ^^^^Bis the mass attenuation coefficient that scales the line integral of material B density, ^^^^Cis the mass attenuation coefficient that scales the line integral of material C density, ^^^^Ais a material density line integral for material A, ^^^^Bis a material density line integral for material B, and ^^^^Cis a material density line integral for material C.

24. The method as in claim 1 wherein the joint processing comprises:wherein ^^^^̅1 ,^̅^^^2are pre-contrast measurements, ^^^^3̅ ,^̅^^^4are post-contrast measurements, ^^^^1is spectral sensitivity dependent on a spectral channel for the pre-contrast measurements, ^^^^2is spectral sensitivity dependent on the spectral channel for the post-contrast measurements, ^^^^ is a mass attenuation coefficient, ^^^^H2Ois a material density line integral for water, ^^^^Cais a material density line integral for calcium, and ^^^^Iis a material density line integral for iodine.

25. The method as in claim 1 wherein the joint processing comprises:where^^^^̅1 ,^̅^^^2are pre-contrast measurements, ^^^^3̅ ,^̅^^^4are post-contrast measurements, ^^^^1is spectral sensitivity for spectral channel 1, ^^^^2is spectral sensitivity for spectral channel 2, ^^^^ is a mass attenuation coefficient,^^^^ H2O is a material density line integral for water,^^^^ Ca is a material density line integral for calcium,^^^^ I is a material density line integral for iodine, andA is a system matrix.

26. The method as in claim 1 wherein the joint processing comprises: performing decomposition into the at least one material basis map using a lookup table that relates the pre- and post- contrast spectral data to a number of the at least one material basis map.

27. The method as in claim 1 wherein the joint processing comprises: estimating images of the at least one material basis map simultaneously using an optimization method.

28. The method as in claim 27 wherein the optimization method comprises: including a roughness penalty having a penalty strength for the at least one material basis map.

29. The method as in claim 28 wherein the roughness penalty comprises: a quadratic penalty acting over a pre-selected number of nearest neighbors within the images.

30. A system for obtaining a contrast distribution comprising: a controller; a sensor configured to receive pre-contrast spectral data and post-contrast spectral data; wherein the controller is configured to execute instructions that perform operations including: acquiring the pre-contrast spectral data before contrast is administered; acquiring the post-contrast spectral data after the contrast is administered; and generating at least one material basis map for at least one material by joint processing the pre-contrast spectral data and the post-contrast spectral data to solve for a pre-selected number of unknowns corresponding to the at least one material associated with the at least one material basis map, wherein the joint processing enables visualization of contrast distribution from contrast agent injection or drug delivery contrast agents, and wherein the at least one material basis map includes the contrast distribution.

31. The system as in claim 30 wherein the operations further comprise: maintaining contrast resolution based on isolating signals from a pre-selected material without overlaying background anatomy.

32. The system as in claim 30 wherein the sensor comprises: a photon counting detector (PCD).

33. The system as in claim 32 wherein the operations further comprise: estimating energy-dependent scatter by performing measurements at different energy thresholds of the PCD.

34. The system as in claim 30 wherein the operations further comprise: managing effects that introduce bias into the at least one material basis map.

35. The system as in claim 34 wherein the effects comprise: charge sharing and pulse pileup.

36. The system as in claim 30 wherein the joint processing comprises: an iterative estimation approach.

37. The system as in claim 36 wherein the operations further comprise: regularizing of the iterative estimation approach using quadratic penalties.

38. The system as in claim 36 wherein the operations further comprise: regularizing of the iterative estimation approach using edge-preserving non-quadratic penalties.

39. The system as in claim 36 wherein the instructions further comprise: regularizing of the iterative estimation approach using cross basis penalties.

40. The system as in claim 36 wherein the iterative estimation approach comprises: a paraboloidal surrogate approach.

41. The system as in claim 30 wherein the operations further comprise: applying a scatter correction factor to remove scatter bias from the at least one material basis map.

42. The system as in claim 41 wherein the scatter correction factor comprises: an energy-dependent scalar.

43. The system as in claim 30 wherein the operations further comprise: dynamically estimating the at least one material basis map; and displaying the at least one material basis map using a graphics processing unit.

44. The system as in claim 30 wherein the operations further comprise: performing real-time processing of the pre- and post-contrast spectral data using machine learning.

45. The system as in claim 44 wherein the machine learning comprises: deep learning.

46. The system as in claim 30 wherein the operations further comprise: post-processing the at least one material basis map using edge enhancement.

47. The system as in claim 30 wherein the operations further comprise: post-processing the at least one material basis map using temporal frame averaging.

48. The system as in claim 30 wherein the operations further comprise: joint processing consecutive images from the pre- and post-contrast spectral data to achieve the at least one material basis map; and performing registration to achieve motion compensation between the consecutive images.

49. The system as in claim 30 wherein the visualization comprises: providing a color overlay of soft tissue.

50. The system as in claim 30 wherein the visualization comprises: providing a color overlay of boney landmarks.

51. The system as in claim 30 wherein the joint processing comprises: ^^^^̅pre= B ^^^^1exp(− ^^^^A^^^^A−BB^^^^B^^^^B) ^^^^̅pre= BS2exp(− ^^^^A^^^^A– ^^^^B^^^^B) ^^^^̅post= B ^^^^1exp(− ^^^^A^^^^A− ^^^^B^^^^B− ^^^^C^^^^C) ^^^^̅post= BS2exp(− ^^^^A^^^^A− ^^^^B^^^^B– ^^^^C^^^^C) wherein ^^^^̅preis a pre-contrast measurement, ^^^^̅postis a post-contrast measurement,B is system blur, S is spectral sensitivity dependent on a spectral channel, ^^^^Ais a mass attenuation coefficient that scales a line integral of material A density, ^^^^Bis the mass attenuation coefficient that scales the line integral of material B density, ^^^^Cis the mass attenuation coefficient that scales the line integral of material C density, ^^^^Ais a material density line integral for material A, ^^^^Bis a material density line integral for material B, and ^^^^Cis a material density line integral for material C.

52. The system as in claim 30 wherein the joint processing comprises:wherein ^^^^̅1 ,^̅^^^2are pre-contrast measurements, ^^^^3̅ ,^̅^^^4are post-contrast measurements, ^^^^1is spectral sensitivity dependent on a spectral channel for the pre-contrast measurements, ^^^^2is spectral sensitivity dependent on the spectral channel for the post-contrast measurements, ^^^^ is a mass attenuation coefficient, ^^^^H2Ois a material density line integral for water, ^^^^Cais a material density line integral for calcium, and ^^^^Iis a material density line integral for iodine.

53. The system as in claim 30 wherein the joint processing comprises:^^^^ ^^^^ ^^^^ ^�^^^1^^^^ ^^^^^^^^ é ^^^^ ^^^^ ^^^^ù ^�^^^ æ ê ú ^^^^ ^^^^ ^^^^ ^^^^^^^^2 ^^^^ö �2^�^^^3� =�^^^^^^^^^^^^� exp ^^^^ ^^^^^^^^çç −�^^^^^^^^ ^^^^^^^^�ê ^^^^ ^^^^ ^^^^ú� ^^^^ ^^ ^^^^^^^^ ^^^^� ê ^^^^ ^^^^ ^^^^ ^^ ^^^^ ú÷÷^�^^^4^^^^ ^^^^^^^^ê ^^^^ ^^^^ ^^^^ú ^^^^ ^^^^ ^^^^ ^^^^^^^^è ë ^^^^ ^^^^^^^^ûøwhere^^^^̅1 ,^̅^^^2are pre-contrast measurements, ^^^^3̅ ,^̅^^^4are post-contrast measurements, ^^^^1is spectral sensitivity for spectral channel 1, ^^^^2is spectral sensitivity for spectral channel 2, ^^^^ is a mass attenuation coefficient,^^^^ H2O is a material density line integral for water,^^^^ Ca is a material density line integral for calcium,^^^^ I is a material density line integral for iodine, andA is a system matrix.

54. The system as in claim 30 wherein the joint processing comprises: performing decomposition into the at least one material basis map using a lookup table that relates the pre- and post- contrast spectral data to a number of the at least one material basis map.

55. The system as in claim 30 wherein the joint processing comprises: estimating images of the at least one material basis map simultaneously using an optimization method.

56. The system as in claim 55 further comprising: a roughness penalty having a penalty strength for the at least one material basis map.

57. The system as in claim 56 wherein the roughness penalty comprises:a quadratic penalty acting over a pre-selected number of nearest neighbors within the images.

58. A computer program product for obtaining a contrast distribution, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computing device to cause the computing device to perform operations comprising: acquiring the pre-contrast spectral data before contrast is administered; acquiring the post-contrast spectral data after the contrast is administered; and generating at least one material basis map for at least one material by joint processing the pre-contrast spectral data and the post-contrast spectral data to solve for a pre-selected number of unknowns corresponding to the at least one material associated with the at least one material basis map, wherein the joint processing enables visualization of contrast distribution from contrast agent injection or drug delivery contrast agents, and wherein the at least one material basis map includes the contrast distribution.

59. The method as in claim 1 further comprising: obtaining the pre-contrast spectral data and the post-contract spectral data using kV switching.

60. The system as in claim 30 wherein the operations further comprise: obtaining the pre-contrast spectral data and the post-contract spectral data using kV switching.

61. The computer program product as in claim 58 wherein the operations further comprise: obtaining the pre-contrast spectral data and the post-contract spectral data using kV switching.

62. The method as in claim 1 further comprising: joint processing consecutive images from the the post-contrast spectral data to achieve the at least one material basis map; andperforming registration between the consecutive images to achieve motion compensation between the consecutive images.

63. The system as in claim 30 wherein the operations further comprise: joint processing consecutive images from the the post-contrast spectral data to achieve the at least one material basis map; and performing registration between the consecutive images to achieve motion compensation between the consecutive images.

64. The computer program product as in claim 58 wherein the operations further comprise: joint processing consecutive images from the the post-contrast spectral data to achieve the at least one material basis map; and performing registration between the consecutive images to achieve motion compensation between the consecutive images.

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