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Diffusion and Poisson flow models have shown impressive performance in a wide range of generative tasks, including low-dose CT image denoising. However, one limitation in general, and for clinical applications in particular, is slow sampling. Due to their iterative nature, the number of function evaluations (NFE) required is usually on the order of $10-10^3$, both for conditional and unconditional generation. In this paper, we present posterior sampling Poisson flow generative models (PPFM), a novel image denoising technique for low-dose and photon-counting CT that produces excellent image quality whilst keeping NFE=1. Updating the training and sampling processes of Poisson flow generative models (PFGM)++, we learn a conditional generator which defines a trajectory between the prior noise distribution and the posterior distribution of interest. We additionally hijack and regularize the sampling process to achieve NFE=1. Our results shed light on the benefits of the PFGM++ framework compared to diffusion models. In addition, PPFM is shown to perform favorably compared to current state-of-the-art diffusion-style models with NFE=1, consistency models, as well as popular deep learning and non-deep learning-based image denoising techniques, on clinical low-dose CT images and clinical images from a prototype photon-counting CT system.

Deep learning has proven to be important for CT image denoising. However, such models are usually trained under supervision, requiring paired data that may be difficult to obtain in practice. Diffusion models offer unsupervised means of solving a wide range of inverse problems via posterior sampling. In particular, using the estimated unconditional score function of the prior distribution, obtained via unsupervised learning, one can sample from the desired posterior via hijacking and regularization. However, due to the iterative solvers used, the number of function evaluations (NFE) required may be orders of magnitudes larger than for single-step samplers. In this paper, we present a novel image denoising technique for photon-counting CT by extending the unsupervised approach to inverse problem solving to the case of Poisson flow generative models (PFGM)++. By hijacking and regularizing the sampling process we obtain a single-step sampler, that is NFE=1. Our proposed method incorporates posterior sampling using diffusion models as a special case. We demonstrate that the added robustness afforded by the PFGM++ framework yields significant performance gains. Our results indicate competitive performance compared to popular supervised, including state-of-the-art diffusion-style models with NFE=1 (consistency models), unsupervised, and non-deep learning-based image denoising techniques, on clinical low-dose CT data and clinical images from a prototype photon-counting CT system developed by GE HealthCare.

Spectral imaging is the acquisition of multiple images of an object at different energy spectra. In mammography, dual-energy imaging (spectral imaging with two energy levels) has been investigated for several applications, in particular material decomposition, which allows for quantitative analysis of breast composition and quantitative contrast-enhanced imaging. Material decomposition with dual-energy imaging is based on the assumption that there are two dominant photon interaction effects that determine linear attenuation: the photoelectric effect and Compton scattering. This assumption limits the number of basis materials, i.e. the number of materials that are possible to differentiate between, to two. However, Rayleigh scattering may account for more than 10% of the linear attenuation in the mammography energy range. In this work, we show that a modified version of a scanning multi-slit spectral photon-counting mammography system is able to acquire three images at different spectra and can be used for triple-energy imaging. We further show that triple-energy imaging in combination with the efficient scatter rejection of the system enables measurement of Rayleigh scattering, which adds an additional energy dependency to the linear attenuation and enables material decomposition with three basis materials. Three available basis materials have the potential to improve virtually all applications of spectral imaging.

It has previously been shown that 2D spectral mammography can be used to discriminate between (likely benign) cystic and (potentially malignant) solid lesions in order to reduce unnecessary recalls in mammography. One limitation of the technique is, however, that the composition of overlapping tissue needs to be interpolated from a region surrounding the lesion. The purpose of this investigation was to demonstrate that lesion characterization can be done with spectral tomosynthesis, and to investigate whether the 3D information available in tomosynthesis can reduce the uncertainty from the interpolation of surrounding tissue. A phantom experiment was designed to simulate a cyst and a tumor, where the tumor was overlaid with a structure that made it mimic a cyst. In 2D, the two targets appeared similar in composition, whereas spectral tomosynthesis revealed the exact compositional difference. However, the loss of discrimination signal due to spread from the plane of interest was of the same strength as the reduction of anatomical noise. Results from a preliminary investigation on clinical tomosynthesis images of solid lesions yielded results that were consistent with the phantom experiments, but were still to some extent inconclusive. We conclude that lesion characterization is feasible in spectral tomosynthesis, but more data, as well as refinement of the calibration and discrimination algorithms, are needed to draw final conclusions about the benefit compared to 2D.

Spectral imaging is a method in medical x-ray imaging to extract information about the object constituents by the material-specific energy dependence of x-ray attenuation. Contrast-enhanced spectral imaging has been thoroughly investigated, but unenhanced imaging may be more useful because it comes as a bonus to the conventional non-energy-resolved absorption image at screening; there is no additional radiation dose and no need for contrast medium. We have used a previously developed theoretical framework and system model that include quantum and anatomical noise to characterize the performance of a photon-counting spectral mammography system with two energy bins for unenhanced imaging. The theoretical framework was validated with synthesized images. Optimal combination of the energy-resolved images for detecting large unenhanced tumors corresponded closely, but not exactly, to minimization of the anatomical noise, which is commonly referred to as energy subtraction. In that case, an ideal-observer detectability index could be improved close to 50% compared to absorption imaging. Optimization with respect to the signal-to-quantum-noise ratio, commonly referred to as energy weighting, deteriorated detectability. For small microcalcifications or tumors on uniform backgrounds, however, energy subtraction was suboptimal whereas energy weighting provided a minute improvement. The performance was largely independent of beam quality, detector energy resolution, and bin count fraction. It is clear that inclusion of anatomical noise and imaging task in spectral optimization may yield completely different results than an analysis based solely on quantum noise.

Beam quality optimization in mammography traditionally considers detection of a target obscured by quantum noise on a homogenous background. It can be argued that this scheme does not correspond well to the clinical imaging task because real mammographic images contain a complex superposition of anatomical structures, resulting in anatomical noise that may dominate over quantum noise. Using a newly developed spectral mammography system, we measured the correlation and magnitude of the anatomical noise in a set of mammograms. The results from these measurements were used as input to an observer-model optimization that included quantum noise as well as anatomical noise. We found that, within this framework, the detectability of tumors and microcalcifications behaved very differently with respect to beam quality and dose. The results for small microcalcifications were similar to what traditional optimization methods would yield, which is to be expected since quantum noise dominates over anatomical noise at high spatial frequencies. For larger tumors, however, low-frequency anatomical noise was the limiting factor. Because anatomical structure has similar energy dependence as tumor contrast, optimal x-ray energy was significantly higher and the useful energy region wider than traditional methods suggest. Measurements on a tissue phantom confirmed these theoretical results. Furthermore, since quantum noise constitutes only a small fraction of the noise, the dose could be reduced substantially without sacrificing tumor detectability. Exposure settings used clinically are therefore not necessarily optimal for this imaging task. The impact of these findings on the mammographic imaging task as a whole is, however, at this stage unclear.

X-ray detectors made of crystalline silicon have several advantages including low dark currents, fast charge collection and high energy resolution. For high-energy x-rays, however, silicon suffers from its low atomic number, which might result in low detection efficiency, as well as low energy and spatial resolution due to Compton scattering. We have used a monte-carlo model to investigate the feasibility of a detector for pediatric CT with 30 to 40 mm of silicon using x-ray spectra ranging from 80 to 140 kVp. A detection efficiency of 0.74 was found at 80 kVp, provided the noise threshold could be set low. Scattered photons were efficiently blocked by a thin metal shielding between the detector units, and Compton scattering in the detector could be well separated from photo absorption at 80 kVp. Hence, the detector is feasible at low acceleration voltages, which is also suitable for pediatric imaging. We conclude that silicon detectors may be an alternative to other designs for this special case.

We present the first evaluation of a recently developed silicon-strip detector for photon-counting dual-energy breast tomosynthesis. The detector is well suited for tomosynthesis with high dose efficiency and intrinsic scatter rejection. A method was developed for measuring the spatial resolution of a system based on the detector in terms of the three-dimensional modulation transfer function (MTF). The measurements agreed well with theoretical expectations, and it was seen that depth resolution was won at the cost of a slightly decreased lateral resolution. This may be a justifiable trade-off as clinical images acquired with the system indicate improved conspicuity of breast lesions. The photon-counting detector enables dual-energy subtraction imaging with electronic spectrumsplitting. This improved the detectability of iodine in phantom measurements, and the detector was found to be stable over typical clinical acquisition times. A model of the energy resolution showed that further improvements are within reach by optimization of the detector.

Conventional energy filters for x-ray imaging are based on absorbing materials which attenuate low energy photons, sometimes combined with an absorption edge, thus also discriminating towards photons of higher energies. These filters are fairly inefficient, in particular for photons of higher energies, and other methods for achieving a narrower bandwidth have been proposed. Such methods include various types of monochromators, based on for instance mosaic crystals or refractive multi-prism x-ray lenses (MPL's). Prism-array lenses (PAL's) are similar to MPL's, but are shorter, have larger apertures, and higher transmission. A PAL consists of a number of small prisms arranged in columns perpendicular to the optical axis. The column height decreases along the optical axis so that the projection of lens material is approximately linear with a Fresnel phase-plate pattern superimposed on it. The focusing effect is one dimensional, and the lens is chromatic. Hence, unwanted energies can be blocked by placing a slit in the image plane of a desired energy. We present the first experimental and theoretical results on an energy filter based on a silicon PAL. The study includes an evaluation of the spectral shaping properties of the filter as well as a quantification of the achievable increase in dose efficiency compared to standard methods. Previously, PAL's have been investigated with synchrotron radiation, but in this study a medical imaging setup, based on a regular x-ray tube, is considered.

Dual-energy subtraction imaging (DES) is a method to improve the detectability of contrast agents over a lumpy background. Two images, acquired at x-ray energies above and below an absorption edge of the agent material, are logarithmically subtracted, resulting in suppression of the signal from the tissue background and a relative enhancement of the signal from the agent. Although promising, DES is still not widely used in clinical practice. One reason may be the need for two distinctly separated x-ray spectra that are still close to the absorption edge, realized through dual exposures which may introduce motion unsharpness. In this study, electronic spectrum-splitting with a silicon-strip detector is theoretically and experimentally investigated for a mammography model with iodinated contrast agent. Comparisons are made to absorption imaging and a near-ideal detector using a signal-to-noise ratio that includes both statistical and structural noise. Similar to previous studies, heavy absorption filtration was needed to narrow the spectra at the expense of a large reduction in x-ray flux. Therefore, potential improvements using a chromatic multi-prism x-ray lens (MPL) for filtering were evaluated theoretically. The MPL offers a narrow tunable spectrum, and we show that the image quality can be improved compared to conventional filtering methods.

A photon-counting silicon strip detector with two energy thresholds was investigated for spectral X-ray imaging in a mammography system. Preliminary studies already indicate clinical benefit of the detector, and the purpose of the present study is optimization with respect to energy resolution. Factors relevant for the energy response were measured, simulated, or gathered from previous studies, and used as input parameters to a cascaded detector model. Threshold scans over several X-ray spectra were used to calibrate threshold levels to energy, and to validate the model. The energy resolution of the detector assembly was assessed to range over DeltaE/E = 0.12-0.26 in the mammography region. Electronic noise dominated the peak broadening, followed by charge sharing between adjacent detector strips, and a channel-to-channel threshold spread. The energy resolution may be improved substantially if these effects are reduced to a minimum. Anti-coincidence logic mitigated double counting from charge sharing, but erased the energy resolution of all detected events, and optimization of the logic is desirable. Pile-up was found to be of minor importance at typical mammography rates.

A multi-prism lens (MPL) is a refractive x-ray lens with one-dimensional focusing properties. If used as a pre-object collimator in a scanning system for medical x-ray imaging, it reduces the divergence of the radiation and improves on photon economy compared to a slit collimator. Potential advantages include shorter acquisition times, a reduced tube loading, or improved resolution. We present the first images acquired with an MPL in a prototype for a scanning mammography system. The lens showed a gain of flux of 1.32 compared to a slit collimator at equal resolution, or a gain in resolution of 1.31-1.44 at equal flux. We expect the gain of flux in a clinical set-up with an optimized MPL and a custom-made absorption filter to reach 1.67, or 1.45-1.54 gain in resolution.

Purpose: Spectral imaging is a method in medical x-ray imaging to extract information about the object constituents by the material-specific energy dependence of x-ray attenuation. The authors have investigated a photon-counting spectral imaging system with two energy bins for contrast-enhanced mammography. System optimization and the potential benefit compared to conventional non-energy-resolved absorption imaging was studied. Methods: A framework for system characterization was set up that included quantum and anatomical noise and a theoretical model of the system was benchmarked to phantom measurements. Results: Optimal combination of the energy-resolved images corresponded approximately to minimization of the anatomical noise, which is commonly referred to as energy subtraction. In that case, an ideal-observer detectability index could be improved close to 50% compared to absorption imaging in the phantom study. Optimization with respect to the signal-to-quantum-noise ratio, commonly referred to as energy weighting, yielded only a minute improvement. In a simulation of a clinically more realistic case, spectral imaging was predicted to perform approximately 30% better than absorption imaging for an average glandularity breast with an average level of anatomical noise. For dense breast tissue and a high level of anatomical noise, however, a rise in detectability by a factor of 6 was predicted. Another ~70-90% improvement was found to be within reach for an optimized system. Conclusions: Contrast-enhanced spectral mammography is feasible and beneficial with the current system, and there is room for additional improvements. Inclusion of anatomical noise is essential for optimizing spectral imaging systems.

In recent decades, developments in detectors for X-ray imaging have improved dose efficiency. This has been accomplished with for example, structured scintillators such as columnar CsI, or with direct detectors where the X rays are converted to electric charge carriers in a semiconductor. Scattered radiation remains a major noise source, and fairly inefficient anti-scatter grids are still a gold standard. Hence, any future development should include improved scatter rejection. In recent years, photon-counting detectors have generated significant interest by several companies as well as academic research groups. This method eliminates electronic noise, which is an advantage in low-dose applications. Moreover, energy-sensitive photon-counting detectors allow for further improvements by optimising the signal-to-quantum-noise ratio, anatomical background subtraction or quantitative analysis of object constituents. This paper reviews state-of-the-art photon-counting detectors, scatter control and their application in diagnostic X-ray medical imaging. In particular, spectral imaging with photon-counting detectors, pitfalls such as charge sharing and high rates and various proposals for mitigation are discussed.

Chromatic properties of the multi-prism and prism-array X-ray lenses (MPL and PAL) can potentially be utilized for efficient energy filtering and dose reduction in mammography. The line-shaped foci of the lenses are optimal for coupling to photon-counting silicon strip detectors in a scanning system. A theoretical model was developed and used to investigate the benefit of two lenses compared with an absorption-filtered reference system. The dose reduction of the MPL filter was ~15% compared with the reference system at matching scan time, and the spatial resolution was higher. The dose of the PAL-filtered system was found to be ~20% lower than for the reference system at equal scan time and resolution, and only ~20% higher than for a monochromatic beam. An investigation of some practical issues remains, including the feasibility of brilliant-enough X-ray sources and manufacturing of a polymer PAL.

Knowledge of x-ray attenuation is essential for developing and evaluating x-ray imaging technologies. For instance, techniques to distinguish between cysts and solid tumours at mammography screening would be highly desirable to reduce recalls, but the development requires knowledge of the x-ray attenuation for cysts and tumours. We have previously measured the attenuation of cyst fluid using photon-counting spectral mammography. Data on x-ray attenuation for solid breast lesions are available in the literature, but cover a relatively wide range, likely caused by natural spread between samples, random measurement errors, and different experimental conditions. In this study, we have adapted the previously developed spectral method to measure the linear attenuation of solid breast lesions. A total of 56 malignant and 5 benign lesions were included in the study. The samples were placed in a holder that allowed for thickness measurement. Spectral (energy-resolved) images of the samples were acquired and the image signal was mapped to equivalent thicknesses of two known reference materials, which can be used to derive the x-ray attenuation as a function of energy. The spread in equivalent material thicknesses was relatively large between samples, which is likely to be caused mainly by natural variation and only to a minor extent by random measurement errors and sample inhomogeneity. No significant difference in attenuation was found between benign and malignant solid lesions, or between different types of malignant lesions. The separation between cyst-fluid and tumour attenuation was, however, significant, which suggests it may be possible to distinguish cystic from solid breast lesions, and the results lay the groundwork for a clinical trial. [cropped]

Effective collecting area, angular resolution, field of view and energy response are fundamental attributes of X-ray telescopes. The performance of state-of-the-art telescopes is currently restricted by Wolter optics, especially for hard X-rays. In this paper, we report the development of a new approach - the Stacked Prism Lens, which is lightweight, modular and has the potential for a significant improvement in effective area, while retaining high angular resolution. The proposed optics is built by stacking discs embedded with prismatic rings, created with photoresist by focused UV lithography. We demonstrate the SPL approach using a prototype lens which was manufactured and characterized at a synchrotron radiation facility. The design of a potential satellite-borne X-ray telescope is outlined and the performance is compared to contemporary missions.

An important question when developing photon-counting detectors for computed tomography is how to select energy thresholds. In this work thresholds are optimized by maximizing signal-difference-to-noise ratio squared (SDNR2) in an optimally weighted image and signal-to-noise ratio squared (SNR2) in a gadolinium basis image in a silicon-strip detector and a cadmium zinc telluride (CZT) detector, factoring in pileup and imperfect energy response in both detectors. To investigate to what extent one single set of thresholds could be applied in various imaging tasks, the robustness of optimal thresholds with 2 to 8 bins is examined with the variation of phantom thicknesses and target materials. In contrast to previous studies, the optimal threshold locations don't always increase with increasing attenuation if pileup is included. Optimizing the thresholds for a 30 cm phantom yields near-optimal SDNR2 or SNR2 regardless of target tissue types and surrounding attenuation for both detectors. Having more than 3 bins reduces the need for changing the thresholds depending on anatomies and tissues. Using around 6 bins or 8 bins may give near-optimal SDNR2 or SNR2 without generating an unnecessarily large amount of data.