Detector Blur Research Articles

X-ray source motion blur modeling and deblurring with generative diffusion for digital breast tomosynthesis

Objective. Digital breast tomosynthesis (DBT) has significantly improved the diagnosis of breast cancer due to its high sensitivity and specificity in detecting breast lesions compared to two-dimensional mammography. However, one of the primary challenges in DBT is the image blur resulting from x-ray source motion, particularly in DBT systems with a source in continuous-motion mode. This motion-induced blur can degrade the spatial resolution of DBT images, potentially affecting the visibility of subtle lesions such as microcalcifications. Approach. We addressed this issue by deriving an analytical in-plane source blur kernel for DBT images based on imaging geometry and proposing a post-processing image deblurring method with a generative diffusion model as an image prior. Main results. We showed that the source blur could be approximated by a shift-invariant kernel over the DBT slice at a given height above the detector, and we validated the accuracy of our blur kernel modeling through simulation. We also demonstrated the ability of the diffusion model to generate realistic DBT images. The proposed deblurring method successfully enhanced spatial resolution when applied to DBT images reconstructed with detector blur and correlated noise modeling. Significance. Our study demonstrated the advantages of modeling the imaging system components such as source motion blur for improving DBT image quality.

Model-based deep CNN-regularized reconstruction for digital breast tomosynthesis with a task-based CNN image assessment approach

Objective. Digital breast tomosynthesis (DBT) is a quasi-three-dimensional breast imaging modality that improves breast cancer screening and diagnosis because it reduces fibroglandular tissue overlap compared with 2D mammography. However, DBT suffers from noise and blur problems that can lower the detectability of subtle signs of cancers such as microcalcifications (MCs). Our goal is to improve the image quality of DBT in terms of image noise and MC conspicuity. Approach. We proposed a model-based deep convolutional neural network (deep CNN or DCNN) regularized reconstruction (MDR) for DBT. It combined a model-based iterative reconstruction (MBIR) method that models the detector blur and correlated noise of the DBT system and the learning-based DCNN denoiser using the regularization-by-denoising framework. To facilitate the task-based image quality assessment, we also proposed two DCNN tools for image evaluation: a noise estimator (CNN-NE) trained to estimate the root-mean-square (RMS) noise of the images, and an MC classifier (CNN-MC) as a DCNN model observer to evaluate the detectability of clustered MCs in human subject DBTs. Main results. We demonstrated the efficacies of CNN-NE and CNN-MC on a set of physical phantom DBTs. The MDR method achieved low RMS noise and the highest detection area under the receiver operating characteristic curve (AUC) rankings evaluated by CNN-NE and CNN-MC among the reconstruction methods studied on an independent test set of human subject DBTs. Significance. The CNN-NE and CNN-MC may serve as a cost-effective surrogate for human observers to provide task-specific metrics for image quality comparisons. The proposed reconstruction method shows the promise of combining physics-based MBIR and learning-based DCNNs for DBT image reconstruction, which may potentially lead to lower dose and higher sensitivity and specificity for MC detection in breast cancer screening and diagnosis.

Exact gram filtering and efficient backprojection for iterative CT reconstruction.

Forward and backprojections are the basis of all model-based iterative reconstruction (MBIR) methods. However, computing these accurately is time-consuming. In this paper, we present a method for MBIR in parallel X-ray beam geometry that utilizes a Gram filter to efficiently implement forward andbackprojection. We propose using voxel-basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of backprojection. In the special case of parallel X-ray beam geometry, the forward and backprojection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel-basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of backprojection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realisticscenarios. The proposed method is tested on both phantom and real computed tomography (CT) images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state-of-the-art projection models in terms of speed and accuracy for both backprojection andreconstruction. We proposed a iterative reconstruction methodology for 3D parallel-beam X-ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state-of-the-art projection models on both backprojection and reconstruction resultssignificantly.

High-resolution model-based material decomposition in dual-layer flat-panel CBCT.

Spectral CT uses energy-dependent measurements that enable material discrimination in addition to reconstruction of structural information. Flat-panel detectors (FPDs) have been widely used in dedicated and interventional systems to deliver high spatial resolution, volumetric cone-beam CT (CBCT) in compact and OR-friendly designs. In this work, we derive a model-based method that facilitates high-resolution material decomposition in a spectral CBCT system equipped with a prototype dual-layer FPD. Through high-fidelity modeling of multilayer detector, we seek to avoid resolution loss that is present in more traditional processing and decomposition approaches. A physical model for spectral measurements in dual-layer flat-panel CBCT is developed including layer-dependent differences in system geometry, spectral sensitivities, and detector blur (e.g., due to varied scintillator thicknesses). This forward model is integrated into a model-based material decomposition (MBMD) method based on minimization of a penalized weighted least-squared (PWLS) objective function. The noise and resolution performance of this approach was compared with traditional projection-domain decomposition (PDD) and image-domain decomposition (IDD) approaches as well as one-step MBMD with lower-fidelity models that use approximated geometry, projection interpolation, or an idealized system geometry without system blur model. Physical studies using high-resolution three-dimensional (3D)-printed water-iodine phantoms were conducted to demonstrate the high-resolution imaging performance of the compared decomposition methods in iodine basis images and synthetic monoenergetic images. Physical experiments demonstrate that the MBMD methods incorporating an accurate geometry model can yield higher spatial resolution iodine basis images and synthetic monoenergetic images than PDD and IDD results at the same noise level. MBMD with blur modeling can further improve the spatial-resolution compared with the decomposition results obtained with IDD, PDD, and MBMD methods with lower-fidelity models. Using the MBMD without or with blur model can increase the absolute modulation at 1.75 lp/mm by 10% and 22% compared with IDD at the same noise level. The proposed model-based material decomposition method for a dual-layer flat-panel CBCT system has demonstrated an ability to extend high-resolution performance through sophisticated detector modeling including the layer-dependent blur. The proposed work has the potential to not only facilitate high-resolution spectral CT in interventional and dedicated CBCT systems, but may also provide the opportunity to evaluate different flat-panel design trade-offs including multilayer FPDs with mismatched geometries, scintillator thicknesses, and spectral sensitivities.

Measurement of the x-ray effective focal spot size with edge response analysis using digital detectors.

Purpose: For the focal spot measurement of x-ray tubes, we propose a practical method in which only a metal edge and a digital detector are used, together with a process of removing detector blur inherently associated. Approach: The evaluation was made through the optical transfer function (OTF) measurements using the edge response of a 1-mm-thick tungsten plate. First, we made the acquisition of a geometrically magnified edge response, which consists of focal spot penumbra and detector blur, followed by the acquisition of nonmagnified edge response, which includes only detector blur. Then the detector blur was removed by taking the ratio of the two OTFs. Finally, the focal spot profile was obtained by the inverse Fourier transform of this ratio. Results: Resultant full widths at the half-maximum of a small focus profile were for the proposed method and for the conventional slit method with film, indicating excellent agreement between both methods. Comparing between results obtained using two flat panel detectors with different pixel pitches (0.143 and 0.175mm) confirmed no differences with these variations. Conclusion: Through the whole study, the accuracy and the practicality of the proposed method were demonstrated, indicating a possibility of the method to be widely used to evaluate the effective focal spot size and profile of x-ray systems.

Forward model with space-variant of source size for reconstruction on X-ray radiographic image

The Forward Imaging Technique is a method to solve the inverse problem of density reconstruction in radiographic imaging. In this paper, we introduce the forward projection equation (IFP model) for the radiographic system with areal source blur and detector blur. Our forward projection equation, based on X-ray tracing, is combined with the Constrained Conjugate Gradient method to form a new method for density reconstruction. We demonstrate the effectiveness of the new technique by reconstructing density distributions from simulated and experimental images. We show that for radiographic systems with source sizes larger than the pixel size, the effect of blur on the density reconstruction is reduced through our method and can be controlled within one or two pixels. The method is also suitable for reconstruction of non-homogeneousobjects.

Detector Blur and Correlated Noise Modeling for Digital Breast Tomosynthesis Reconstruction.

This paper describes a new image reconstruction method for digital breast tomosynthesis (DBT). The new method incorporates detector blur into the forward model. The detector blur in DBT causes correlation in the measurement noise. By making a few approximations that are reasonable for breast imaging, we formulated a regularized quadratic optimization problem with a data-fit term that incorporates models for detector blur and correlated noise (DBCN). We derived a computationally efficient separable quadratic surrogate (SQS) algorithm to solve the optimization problem that has a non-diagonal noise covariance matrix. We evaluated the SQS-DBCN method by reconstructing DBT scans of breast phantoms and human subjects. The contrast-to-noise ratio and sharpness of microcalcifications were analyzed and compared with those by the simultaneous algebraic reconstruction technique. The quality of soft tissue lesions and parenchymal patterns was examined. The results demonstrate the potential to improve the image quality of reconstructed DBT images by incorporating the system physics model. This paper is a first step toward model-based iterative reconstruction for DBT.

Model-based iterative reconstruction for flat-panel cone-beam CT with focal spot blur, detector blur, and correlated noise

While model-based reconstruction methods have been successfully applied to flat-panel cone-beam CT (FP-CBCT) systems, typical implementations ignore both spatial correlations in the projection data as well as system blurs due to the detector and focal spot in the x-ray source. In this work, we develop a forward model for flat-panel-based systems that includes blur and noise correlation associated with finite focal spot size and an indirect detector (e.g. scintillator). This forward model is used to develop a staged reconstruction framework where projection data are deconvolved and log-transformed, followed by a generalized least-squares reconstruction that utilizes a non-diagonal statistical weighting to account for the correlation that arises from the acquisition and data processing chain. We investigate the performance of this novel reconstruction approach in both simulated data and in CBCT test-bench data. In comparison to traditional filtered backprojection and model-based methods that ignore noise correlation, the proposed approach yields a superior noise-resolution tradeoff. For example, for a system with 0.34 mm FWHM scintillator blur and 0.70 FWHM focal spot blur, using the correlated noise model instead of an uncorrelated noise model increased resolution by 42% (with variance matched at 6.9 × 10−8 mm−2). While this advantage holds across a wide range of systems with differing blur characteristics, the improvements are greatest for systems where source blur is larger than detector blur.

Investigation of spatial resolution characteristics of an in vivo microcomputed tomography system

The spatial resolution characteristics of an in vivo microcomputed tomography (CT) system was investigated in the in-plane (x–y), cross plane (z) and projection imaging modes. The microCT system utilized in this study employs a flat panel detector with a 127µm pixel pitch, a microfocus x-ray tube with a focal spot size ranging from 5–30µm, and accommodates three geometric magnifications (M) of 1.72, 2.54 and 5.10. The in-plane modulation transfer function (MTF) curves were measured as a function of the number of projections, geometric magnification (M), detector binning and reconstruction magnification (MRecon). The in plane cutoff frequency (10% MTF) ranged from 2.31lp/mm (M=1.72, 2×2 binning) to 12.56lp/mm (M=5.10, 1×1 binning) and a bar pattern phantom validated those measurements. A slight degradation in the spatial resolution was observed when comparing the image reconstruction with 511 and 918 projections, whose effect was visible at the lower frequencies. Small value of MRecon has little or no impact on the in-plane spatial resolution owning to a stable system. Large value of MRecon has implications on the spatial resolution and it was evident when comparing the bar pattern images reconstructed with MRecon=1.25 and 2.5. The cross plane MTF curves showed that the spatial resolution increased as the slice thickness decreased. The cutoff frequencies in the projection imaging mode yielded slightly higher values as compared to the in-plane and cross plane modes at all the geometric magnifications (M). At M=5.10, the cutoff resolution of the projection and cross plane on an ultra-high contrast resolution bar chip phantom were 14.9lp/mm and 13–13.5lp/mm. Due to the finite focal spot size of the x-ray tube, the detector blur and the reconstruction kernel functions, the system׳s spatial resolution does not reach the limiting spatial resolution as defined by the Nyquist׳s detector criteria with an ideal point source. The geometric magnification employed in the microCTs provide a tradeoff between field of view and spatial resolution for a wide range of applications.

Research and application of forward imaging technology with systemic blur

Forward imaging technique is the base of the combined method for density reconstruction with forward calculation and inverse problem solution. This paper proposes the idea of girding the areal source as many point sources. Using the blurring window as the affecting factor of the detector blur, the projecting matrix from any point source to any detector pixel with X-ray trace technique is obtained, the projection equation for the radiographic system with areal source blur and detector blur is introduced. The projection equation is used to gain the same deviation information about the object edge as the experimental image. The forward projection equation is combined with the constrained conjugate gradient method to form a full procedure of density reconstruction, which is applied on a simulated image of French Test Object and an experimental image. The results show that using the projection equation, the affecting range of the blur is decreased and can be controlled in one or two pixels.

Noise, sampling, and the number of projections in cone-beam CT with a flat-panel detector.

To investigate the effect of the number of projection views on image noise in cone-beam CT (CBCT) with a flat-panel detector. This fairly fundamental consideration in CBCT system design and operation was addressed experimentally (using a phantom presenting a uniform medium as well as statistically motivated "clutter") and theoretically (using a cascaded systems model describing CBCT noise) to elucidate the contributing factors of quantum noise (σ(Q)), electronic noise (σ(E)), and view aliasing (σ(view)). Analysis included investigation of the noise, noise-power spectrum, and modulation transfer function as a function of the number of projections (N(proj)), dose (D(tot)), and voxel size (b(vox)). The results reveal a nonmonotonic relationship between image noise and N(proj) at fixed total dose: for the CBCT system considered, noise decreased with increasing N(proj) due to reduction of view sampling effects in the regime N(proj) <~200, above which noise increased with N(proj) due to increased electronic noise. View sampling effects were shown to depend on the heterogeneity of the object in a direct analytical relationship to power-law anatomical clutter of the form κ/f(β)--and a general model of individual noise components (σ(Q), σ(E), and σ(view)) demonstrated agreement with measurements over a broad range in N(proj), D(tot), and b(vox). The work elucidates fairly basic elements of CBCT noise in a manner that demonstrates the role of distinct noise components (viz., quantum, electronic, and view sampling noise). For configurations fairly typical of CBCT with a flat-panel detector (FPD), the analysis reveals a "sweet spot" (i.e., minimum noise) in the range N(proj) ~ 250-350, nearly an order of magnitude lower in N(proj) than typical of multidetector CT, owing to the relatively high electronic noise in FPDs. The analysis explicitly relates view aliasing and quantum noise in a manner that includes aspects of the object ("clutter") and imaging chain (including nonidealities of detector blur and electronic noise) to provide a more rigorous basis for commonly held intuition and heurism in CBCT system design and operation.

Generalized Least-Squares CT Reconstruction with Detector Blur and Correlated Noise Models.

The success and improved dose utilization of statistical reconstruction methods arises, in part, from their ability to incorporate sophisticated models of the physics of the measurement process and noise. Despite the great promise of statistical methods, typical measurement models ignore blurring effects, and nearly all current approaches make the presumption of independent measurements - disregarding noise correlations and a potential avenue for improved image quality. In some imaging systems, such as flat-panel-based cone-beam CT, such correlations and blurs can be a dominant factor in limiting the maximum achievable spatial resolution and noise performance. In this work, we propose a novel regularized generalized least-squares reconstruction method that includes models for both system blur and correlated noise in the projection data. We demonstrate, in simulation studies, that this approach can break through the traditional spatial resolution limits of methods that do not model these physical effects. Moreover, in comparison to other approaches that attempt deblurring without a correlation model, superior noise-resolution trade-offs can be found with the proposed approach.

Patient-Specific Minimum-Dose Imaging Protocols for Statistical Image Reconstruction in C-arm Cone-Beam CT Using Correlated Noise Injection.

A new method for accurately portraying the impact of low-dose imaging techniques in C-arm cone-beam CT (CBCT) is presented and validated, allowing identification of minimum-dose protocols suitable to a given imaging task on a patient-specific basis in scenarios that require repeat intraoperative scans. To accurately simulate lower-dose techniques and account for object-dependent noise levels (x-ray quantum noise and detector electronics noise) and correlations (detector blur), noise of the proper magnitude and correlation was injected into the projections from an initial CBCT acquired at the beginning of a procedure. The resulting noisy projections were then reconstructed to yield low-dose preview (LDP) images that accurately depict the image quality at any level of reduced dose in both filtered backprojection and statistical image reconstruction. Validation studies were conducted on a mobile C-arm, with the noise injection method applied to images of an anthropomorphic head phantom and cadaveric torso across a range of lower-dose techniques. Comparison of preview and real CBCT images across a full range of techniques demonstrated accurate noise magnitude (within ~5%) and correlation (matching noise-power spectrum, NPS). Other image quality characteristics (e.g., spatial resolution, contrast, and artifacts associated with beam hardening and scatter) were also realistically presented at all levels of dose and across reconstruction methods, including statistical reconstruction. Generating low-dose preview images for a broad range of protocols gives a useful method to select minimum-dose techniques that accounts for complex factors of imaging task, patient-specific anatomy, and observer preference. The ability to accurately simulate the influence of low-dose acquisition in statistical reconstruction provides an especially valuable means of identifying low-dose limits in a manner that does not rely on a model for the nonlinear reconstruction process or a model of observer performance.

SU‐E‐I‐94: Correction to Improve X‐Ray Focal Spot Measurements by Image Detector Blur Deconvolution

Purpose: To deconvolve the inherent blur of a standard flat panel detector (FPD) when measuring x‐ray focal spots and to evaluate the method for three focal spots and different magnifications. Methods: A 30 micron pinhole was used to get the images of three focal spots (small, medium and large) of an x‐ray tube using a FPD for different magnifications (3.16,2.66 and 2.16) implemented by varying the source to image distance. The tube parameters were kept low (50kVp) to avoid spurious effects like blooming, pinhole penetration, etc. The detector blur, characterized by its MTF was divided into the Fourier Transform of the focal spot images and Result inverse transformed to obtain a deconvolved focal spot spread function from which the full width at tenth maximum (FWTM) focal spot measurements were obtained and compared with those of the uncorrected original profiles. Results: We measured the corrected focal spot size for small, medium and large focal spot using FWTM to be 0.41mm, 0.57mm, and 1.54mm respectively. The corrected focal spot sizes demonstrated reduced values of up to 25%, 18% and .7% compared to the uncorrected for the small, medium, and large focal spots respectively. Also, we observed that the difference between the focal spot size before and after deconvolution increases with the decrease in magnification (smaller SIDs) supporting the fact that the effect of detector blur can be reduced significantly by using a higher magnification. Conclusion: For improved accuracy in x‐ray focal spot measurements, deconvolving the detector resolution characteristics can be used to get rid of the excessive blur which can also be minimized by using the maximum magnification possible. NIH Grant 2R01EB002873

A statistically defined anthropomorphic software breast phantom

Digital anthropomorphic breast phantoms have emerged in the past decade because of recent advances in 3D breast x-ray imaging techniques. Computer phantoms in the literature have incorporated power-law noise to represent glandular tissue and branching structures to represent linear components such as ducts. When power-law noise is added to those phantoms in one piece, the simulated fibroglandular tissue is distributed randomly throughout the breast, resulting in dense tissue placement that may not be observed in a real breast. The authors describe a method for enhancing an existing digital anthropomorphic breast phantom by adding binarized power-law noise to a limited area of the breast. Phantoms with (0.5 mm)(3) voxel size were generated using software developed by Bakic et al. Between 0% and 40% of adipose compartments in each phantom were replaced with binarized power-law noise (β = 3.0) ranging from 0.1 to 0.6 volumetric glandular fraction. The phantoms were compressed to 7.5 cm thickness, then blurred using a 3 × 3 boxcar kernel and up-sampled to (0.1 mm)(3) voxel size using trilinear interpolation. Following interpolation, the phantoms were adjusted for volumetric glandular fraction using global thresholding. Monoenergetic phantom projections were created, including quantum noise and simulated detector blur. Texture was quantified in the simulated projections using power-spectrum analysis to estimate the power-law exponent β from 25.6 × 25.6 mm(2) regions of interest. Phantoms were generated with total volumetric glandular fraction ranging from 3% to 24%. Values for β (averaged per projection view) were found to be between 2.67 and 3.73. Thus, the range of textures of the simulated breasts covers the textures observed in clinical images. Using these new techniques, digital anthropomorphic breast phantoms can be generated with a variety of glandular fractions and patterns. β values for this new phantom are comparable with published values for breast tissue in x-ray projection modalities. The combination of conspicuous linear structures and binarized power-law noise added to a limited area of the phantom qualitatively improves its realism.

Penalized maximum likelihood reconstruction for improved microcalcification detection in breast tomosynthesis.

We examined the application of an iterative penalized maximum likelihood (PML) reconstruction method for improved detectability of microcalcifications (MCs) in digital breast tomosynthesis (DBT). Localized receiver operating characteristic (LROC) psychophysical studies with human observers and 2-D image slices were conducted to evaluate the performance of this reconstruction method and to compare its performance against the commonly used Feldkamp FBP algorithm. DBT projections were generated using rigorous computer simulations that included accurate modeling of the noise and detector blur. Acquisition dose levels of 0.7, 1.0, and 1.5 mGy in a 5-cm-thick compressed breast were tested. The defined task was to localize and detect MC clusters consisting of seven MCs. The individual MC diameter was 150 μm. Compressed-breast phantoms derived from CT images of actual mastectomy specimens provided realistic background structures for the detection task. Four observers each read 98 test images for each combination of reconstruction method and acquisition dose. All observers performed better with the PML images than with the FBP images. With the acquisition dose of 0.7 mGy, the average areas under the LROC curve (A(L)) for the PML and FBP algorithms were 0.69 and 0.43, respectively. For the 1.0-mGy dose, the values of A(L) were 0.93 (PML) and 0.7 (FBP), while the 1.5-mGy dose resulted in areas of 1.0 and 0.9, respectively, for the PML and FBP algorithms. A 2-D analysis of variance applied to the individual observer areas showed statistically significant differences (at a significance level of 0.05) between the reconstruction strategies at all three dose levels. There were no significant differences in observer performance for any of the dose levels.

WE-E-201B-05: Image Quality Improvement in Megavoltage Cone Beam CT Using an Ultrafast Ceramic Scintillator System

Purpose: To quantitatively and qualitatively assess improvement in megavoltage cone beam CT (MVCBCT) image quality afforded by a 4.2 MV imaging beam line (IBL) with a carbon electron target and new pixelated ultrafast ceramic scintillator (UFC) detector, relative to the 6 MV treatment beam line (TBL). Detector blur is reduced with the UFC since light generated in a pixel is less likely to escape laterally. Methods: A prototype IBL+UFC system was installed on a Siemens ONCOR linear accelerator equipped with the MVision™ IGRT system. A UFC strip consisting of four tiles and measuring ∼40 cm by ∼10 cm was installed on the flat panel imager, with the long dimension in the cross‐plane direction. Phantom images were acquired at doses from 2–60 cGy with the TBL, IBL with conventional scintillator, and IBL+UFC. Several head and neck, thoracic, and pelvic patients were imaged with the three systems at doses from 2–15 cGy. Results: Phantom images indicate that the IBL+UFC images have lower noise and higher contrast than the IBL and TBL images. The contrast‐to‐noise ratio (CNR) for the IBL was 1.5–2 times higher than for the TBL, and the IBL+UFC CNR was 1.5–2 times better than for the IBL at all doses. CNR saturated near 30 cGy for the IBL+UFC and at 60 cGy or greater for the IBL and TBL. IBL+UFC patient images showed improved soft tissue contrast at all doses and sites examined. Conclusions: The IBL+UFC combination increases the CNR by up to a factor of four relative to the TBL with the conventional scintillator, and a factor of two relative to the IBL with the conventional scintillator. Imagenoise and soft tissue contrast in head and neck, thoracic, and pelvic patients improved dramatically in the IBL+UFC images relative to the TBL images. Sponsored partially by Siemens Oncology Care Systems.

A fast, angle‐dependent, analytical model of CsI detector response for optimization of 3D x‐ray breast imaging systems

Accurate models of detector blur are crucial for performing meaningful optimizations of three-dimensional (3D) x-ray breast imaging systems as well as for developing reconstruction algorithms that faithfully reproduce the imaged object anatomy. So far, x-ray detector blur has either been ignored or modeled as a shift-invariant symmetric function for these applications. The recent development of a Monte Carlo simulation package called MANTIS has allowed detailed modeling of these detector blur functions and demonstrated the magnitude of the anisotropy for both tomosynthesis and breast CT imaging systems. Despite the detailed results that MANTIS produces, the long simulation times required make inclusion of these results impractical in rigorous optimization and reconstruction algorithms. As a result, there is a need for detector blur models that can be rapidly generated. In this study, the authors have derived an analytical model for deterministic detector blur functions, referred to here as point response functions (PRFs), of columnar CsI phosphor screens. The analytical model is x-ray energy and incidence angle dependent and draws on results from MANTIS to indirectly include complicated interactions that are not explicitly included in the mathematical model. Once the mathematical expression is derived, values of the coefficients are determined by a two-dimensional (2D) fit to MANTIS-generated results based on a figure-of-merit (FOM) that measures the normalized differences between the MANTIS and analytical model results averaged over a region of interest. A smaller FOM indicates a better fit. This analysis was performed for a monochromatic x-ray energy of 25 keV, a CsI scintillator thickness of 150 microm, and four incidence angles (0 degrees, 15 degrees, 30 degrees, and 45 degrees). The FOMs comparing the analytical model to MANTIS for these parameters were 0.1951 +/- 0.0011, 0.1915 +/- 0.0014, 0.2266 +/- 0.0021, and 0.2416 +/- 0.0074 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. As a comparison, the same FOMs comparing MANTIS to 2D symmetric Gaussian fits to the zero-angle PRF were 0.6234 +/- 0.0020, 0.9058 +/- 0.0029, 1.491 +/- 0.012, and 2.757 +/- 0.039 for the same set of incidence angles. Therefore, the analytical model matches MANTIS results much better than a 2D symmetric Gaussian function. A comparison was also made against experimental data for a 170 microm thick CsI screen and an x-ray energy of 25.6 keV. The corresponding FOMs were 0.3457 +/- 0.0036, 0.3281 +/- 0.0057, 0.3422 +/- 0.0023, and 0.3677 +/- 0.0041 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. In a previous study, FOMs comparing the same experimental data to MANTIS PRFs were found to be 0.2944 +/- 0.0027, 0.2387 +/- 0.0039, 0.2816 +/- 0.0025, and 0.2665 +/- 0.0032 for the same set of incidence angles. The two sets of derived FOMs, comparing MANTIS-generated PRFs and experimental data to the analytical model, demonstrate that the analytical model is able to reproduce experimental data with a FOM of less than two times that comparing MANTIs and experimental data. This performance is achieved in less than one millionth the computation time required to generate a comparable PRF with MANTIS. Such small computation times will allow for the inclusion of detailed detector physics in rigorous optimization and reconstruction algorithms for 3D x-ray breast imaging systems.

A practical exposure-equivalent metric for instrumentation noise in x-ray imaging systems

The performance of high-sensitivity x-ray imagers may be limited by additive instrumentation noise rather than by quantum noise when operated at the low exposure rates used in fluoroscopic procedures. The equipment-invasive instrumentation noise measures (in terms of electrons) are generally difficult to make and are potentially not as helpful in clinical practice as would be a direct radiological representation of such noise that may be determined in the field. In this work, we define a clinically relevant representation for instrumentation noise in terms of noise-equivalent detector entrance exposure, termed the instrumentation noise-equivalent exposure (INEE), which can be determined through experimental measurements of noise-variance or signal-to-noise ratio (SNR). The INEE was measured for various detectors, thus demonstrating its usefulness in terms of providing information about the effective operating range of the various detectors. A simulation study is presented to demonstrate the robustness of this metric against post-processing, and its dependence on inherent detector blur. These studies suggest that the INEE may be a practical gauge to determine and compare the range of quantum-limited performance for clinical x-ray detectors of different design, with the implication that detector performance at exposures below the INEE will be instrumentation-noise limited rather than quantum-noise limited.

TU‐EE‐A4‐05: Comparison of Backprojection and a Penalized Maximum Likelihood Algorithm for Detection of Microcalcifications in Breast Tomosynthesis.

Tomosynthesis is proving to be a valuable tool for generating three dimensional images of the breast with only a limited number of projection angles. The image quality of the resulting tomosynthesis slices can potentially be improved by using more optimal acquisition geometries and/or improved reconstruction techniques. In this paper we compare the performance of a standard back‐projection (BP) algorithm with an algorithm that maximizes a penalized likelihood (PML) objective function using an optimization transfer principle leading to a simultaneous update algorithm. To compare reconstruction algorithms, a computer simulation is used to model the breast tomosynthesis geometry and human observer performance in detecting micro‐calcification clusters is evaluated. The simulation modeled the compressed breast using a structured breast phantom, with randomly inserted clusters of spherical “micro‐calcifications”. Clinically realistic x‐ray spectra were generated and x‐ray transport through the breast phantom was modeled using ray‐tracing combined with the focal spot and the detector blur of a 200 micron CsI scintillator. The iterative reconstruction used a simultaneous update algorithm where the non‐quadratic penalized likelihood objective function (which is difficult to maximize) is replaced by a surrogate paraboloidal function. A Huber prior was used as the potential function with the ability to control edge preserving factors and smoothness. A standard back‐projection technique that is computationally faster (in comparison to the iterative method) was used as a comparison. To evaluate microcalcification detection accuracy of the methods, an N‐alternative forced choice (NAFC) based observer study was performed. The results of NAFC studies performed with 3 observers and 63 pairs of images for each method shows that the PML based technique gave a percent correct improvement by 0.32 over the FB technique. The observers read the PML based images about 4 times faster than the FB technique indicating higher visibility of calcifications in the former.