The Equivalent Quantum Efficiency of the Photographic Process

New Software for DQE Calculation in Digital Mammography Compliant with IEC 62220–1-2

Significant improvements in mammography systems have been achieved with the introduction of active matrix flat-panel digital detectors. The advent of this technology also makes it possible to implement computational methods for quantitative image analysis. This study describes new software created to perform detective quantum efficiency (DQE) calculations fully compliant with the IEC 62220–1-2 standard. Python-based software was developed that contains modules to calculate inverse conversion function, modulation transfer function (MTF), noise power spectrum (NPS), and DQE itself. A graphical user interface (GUI) and further add-ons make this software more user-friendly. Results are immediately displayed diagrammatically, and complete output data are exported to a .csv file. The code is available freely, as a compiled, executable file (.exe). The program was successfully tested using DICOM images obtained from mammography units from different manufacturers. This study also includes validation of the new software, based on comparisons of results obtained for the same set of data with two other, freely available programs.

Characterization of the hardened single line of sight camera at the National Ignition Facility

The hardened single line of sight camera has been recently characterized in preparation for its deployment on the National Ignition Facility. The latest creation based on the pulse-dilation technology leads to many new features and improvements over the previous-generation cameras to provide better quality measurements of inertial confinement fusion experiments, including during high neutron yield implosions. Here, we present the characterization data that illustrate the main performance features of this instrument, such as extended dynamic range and adjustable internal magnification, leading to improved spatial resolution.

A detective quantum efficiency for spectroscopic X-ray imaging detectors

PURPOSE

Spectroscopic X-ray detectors (SXDs) are under development for X-ray imaging applications. Recent efforts to extend the detective quantum efficiency (DQE) to SXDs impose a barrier to experimentation and/or do not provide a task-independent measure of detector performance. The purpose of this article is to define a task-independent DQE for SXDs that can be measured using a modest extension of established DQE-metrology methods.

METHODS

We defined a task-independent spectroscopic DQE and performed a simulation study to determine the relationship between the zero-frequency DQE and the ideal-observer signal-to-noise ratio (SNR) of low-frequency soft-tissue, bone, iodine, and gadolinium signals. In our simulations, we used calibrated models of the spatioenergetic response of cadmium telluride (CdTe) and cadmium-zinc-telluride (CdZnTe) SXDs. We also measured the zero-frequency DQE of a CdTe detector with two energy bins and of a CdZnTe detector with up to six energy bins for an RQA9 spectrum and compared with model predictions.

RESULTS

The spectroscopic DQE accounts for spectral distortions, energy-bin-dependent spatial resolution, interbin spatial noise correlations, and intrabin spatial noise correlations; it is mathematically equivalent to the squared SNR per unit fluence of the generalized least-squares estimate of the height of an X-ray impulse in a uniform noisy background. The zero-frequency DQE has a strong linear relationship with the ideal-observer SNR of low-frequency soft-tissue, bone, iodine, and gadolinium signals, and can be expressed in terms of the product of the quantum efficiency and a Swank noise factor that accounts for DQE degradation due to, for example, charge sharing (CS) and electronic noise. The spectroscopic Swank noise factor of the CdTe detector was measured to be 0.81 ± 0.04 and 0.83 ± 0.04 with and without anticoincidence logic for CS suppression, respectively. The spectroscopic Swank noise factor of the CdZnTe detector operated with four energy bins was measured to be 0.82 ± 0.02 which is within 5% of the theoretical value.

CONCLUSIONS

The spectroscopic DQE defined here is (1) task-independent, (2) can be measured using a modest extension of existing DQE-metrology methods, and (3) is predictive of the ideal-observer SNR of soft-tissue, bone, iodine, and gadolinium signals. For CT applications, the combination of CS and electronic noise in CdZnTe spectroscopic detectors will degrade the zero-frequency DQE by 10 %-20 % depending on the electronic noise level and pixel size.

Frequency-dependent signal and noise in spectroscopic x-ray imaging

Purpose

We present a new framework for theoretical analysis of the noise power spectrum (NPS) of photon‐counting x‐ray detectors, including simple photon‐counting detectors (SPCDs) and spectroscopic x‐ray detectors (SXDs), the latter of which use multiple energy thresholds to discriminate photon energies.

Methods

We show that the NPS of SPCDs and SXDs, including spatio‐energetic noise correlations, is determined by the joint probability density function (PDF) of deposited photon energies, which describes the probability of recording two photons of two different energies in two different elements following a single‐photon interaction. We present an analytic expression for this joint PDF and calculate the presampling and digital NPS of CdTe SPCDs and SXDs. We calibrate our charge sharing model using the energy response of a cadmium zinc telluride (CZT) spectroscopic x‐ray detector and compare theoretical results with Monte Carlo simulations.

Results

Our analysis shows that charge sharing increases pixel signal‐to‐noise ratio (SNR), but degrades the zero‐frequency signal‐to‐noise performance of SPCDs and SXDs. In all cases considered, this degradation was greater than 10%. Comparing the presampling NPS with the sampled NPS showed that degradation in zero‐frequency performance is due to zero‐frequency noise aliasing induced by charge sharing.

Conclusions

Noise performance, including spatial and energy correlations between elements and energy bins, are described by the joint PDF of deposited energies which provides a method of determining the photon‐counting NPS, including noise‐aliasing effects and spatio‐energetic effects in spectral imaging. Our approach enables separating noise due to x‐ray interactions from that associated with sampling, consistent with cascaded systems analysis of energy‐integrating systems. Our methods can be incorporated into task‐based assessment of image quality for the design and optimization of spectroscopic x‐ray detectors.

An experimental method to directly measure DQE[Formula: see text] at k = 0 for 2D x-ray imaging systems

The zero-frequency detective quantum efficiency (DQE), viz., DQE0, is defined as the ratio between output and input squared signal-to-noise ratio of an imaging system. In 1963, R. Shaw applied Fourier analysis to generalize DQE0 to the frequency-dependent DQE, i.e. DQE[Formula: see text]. Under conditions specified by Shaw, DQE[Formula: see text] is the same as DQE0 at k  =  0. The experimental measurement of DQE[Formula: see text] involves the measurement of system modulation transfer function (MTF) and noise power spectrum (NPS). Although the measurement of MTF is straightforward, the experimental measurements of NPS[Formula: see text] encountered several challenges. As a result, some experimental methods may yield a nonphysical NPS value at k  =  0, which makes the measured DQE(k)| k=0 deviate from the true zero-frequency DQE. This work presents new results from three aspects: 1) system drift is a significant error source when a large number of independent image acquisitions are involved in measuring NPS and DQE; 2) a cascaded systems analysis shows that the drift induces a global positive offset to the measured autocovariance function, and the offset is quantitatively related to the NPS error at k  =  0; 3) based on the measured autocovariance data, drift-induced offset can be estimated, so that errors in the measured NPS(k)| k=0 and DQE(k)| k=0 can be corrected. Both numerical simulations with known ground truth for DQE0 and experimental studies were performed to validate the proposed measurement method. The results demonstrated that the method mitigates the undesirable influence of system drift in DQE(k)| k=0 and DQE0, allowing the measured values consistent with the classical definition of zero-frequency DQE.

An experimental method to correct drift-induced error in zero-frequency DQE measurement

In 1963, Shaw applied Fourier analysis to the zero-frequency DQE and developed the frequency-dependent DQE or DQE(k) and made it clear that DQE(k) is applicable to every frequency level within the system bandwidth, including the zero frequency. Over time, especially after entering the modern era of digital x-ray imaging, the experimental measurement methods of DQE(k) (particularly the measurements of the NPS which is an important element in DQE(k)) have evolved, and some measurement methods may generate nonphysical NPS and DQE results at k=0. As a result, an experimental DQE(k) curve is often cut off at certain low frequency above zero. This work presents a new experimental method to deal with two challenges: severe NPS(k=0) underestimation due to polynomial-based background detrending; severe NPS(k=0) overestimation due to the presence of faint but non-negligible system drift. Based on a theoretical analysis of the impact of drift to the measured autocovariance function, the error introduced by drift can be isolated, and corresponding correction can be applied to NPS(k=0). Both numerical simulation with known ground truth and experimental studies demonstrated that the proposed method enables accurate DQE(k=0) measurement.

Investigating the relationship between noise transfer inside the x-ray framing cameras and their imaging ability

We apply a cascaded linear model analysis to a micro-channel plate x-ray framing camera. We establish a theoretical expression of the Noise Power Spectrum (NPS) at the detector's output and assess its accuracy by comparing it to the NPS of Monte Carlo simulations of the detector's response to a uniform illumination. We also demonstrate that fitting the NPS of experimental data against a parametric model based on this expression can yield valuable information on the imaging ability of framing cameras, offering an alternative approach to the usual method employed to measure their modulation transfer functions.

MTF and DQE enhancement using an apodized-aperture x-ray detector design

PURPOSE

Acquisition of high-quality x-ray images using low patient exposures requires detectors with high detective quantum efficiency (DQE). We describe a novel apodized-aperture pixel (AAP) design that increases high-frequency modulation transfer function (MTF) and DQE values. The AAP design makes a separation of physical sensor elements from image pixels by using very small sensor elements (e.g., 0.010-0.025 mm) to synthesize desired larger image pixels (e.g., 0.1-0.2 mm).

METHODS

A cascaded systems model of signal and noise propagation is developed to describe the benefits of the AAP approach in terms of the MTF, Wiener noise power spectrum (NPS), and DQE. The theoretical model was validated experimentally using a CMOS/CsI detector with 0.05 mm sensor elements to synthesize 0.20 mm image pixels and a clinical Se detector with 0.07 mm sensor elements to synthesize 0.28 mm pixels. A Monte Carlo study and x-ray images of a star-pattern and rat leg are used to visually compare AAP images.

RESULTS

When used with a high-resolution converter layer and sensor elements one quarter the size of image pixels, the MTF is increased by 53% and the DQE by a factor of 2.3× at the image sampling cut-off frequency. Both simulated and demonstration images show improved detectability of high-frequency content and removal of aliasing artifacts. Evidence of Gibbs ringing is sometimes seen near high-contrast edges.

CONCLUSIONS

It is shown that the AAP approach preserves the MTF of the small sensor elements and attenuates frequencies above the image sampling cut-off frequency. This has the double benefit of improving the MTF while reducing both signal and noise aliasing, resulting in an increase of the DQE at high spatial frequencies. For optimal implementation, the converter layer must have very high spatial resolution and the detector must have low readout noise.

Linear System Models for Ultrasonic Imaging: Intensity Signal Statistics

Despite a great deal of work characterizing the statistical properties of radio frequency backscattered ultrasound signals, less is known about the statistical properties of demodulated intensity signals. Analysis of intensity is made more difficult by a strong nonlinearity that arises in the process of demodulation. This limits our ability to characterize the spatial resolution and noise properties of B-mode ultrasound images. In this paper, we generalize earlier results on two-point intensity covariance using a multivariate systems approach. We derive the mean and autocovariance function of the intensity signal under Gaussian assumptions on both the object scattering function and acquisition noise, and with the assumption of a locally shift-invariant pulse-echo system function. We investigate the limiting cases of point statistics and a uniform scattering field with a stationary distribution. Results from validation studies using simulation and data from a real system applied to a uniform scattering phantom are presented. In the simulation studies, we find errors less than 10% between the theoretical mean and variance, and sample estimates of these quantities. Prediction of the intensity power spectrum (PS) in the real system exhibits good qualitative agreement (errors less than 3.5 dB for frequencies between 0.1 and 10 cyc/mm, but with somewhat higher error outside this range that may be due to the use of a window in the PS estimation procedure). We also replicate the common finding that the intensity mean is equal to its standard deviation (i.e., signal-to-noise ratio = 1) for fully developed speckle. We show how the derived statistical properties can be used to characterize the quality of an ultrasound linear array for low-contrast patterns using generalized noise-equivalent quanta directly on the intensity signal.

Fourier Analysis of Noise Characteristics in Cone-Beam Microtomography Laboratory Scanners

GOAL

We investigate the signal and noise performance of an x-ray microtomography system that incorporates a complementary metal-oxide-semiconductor flat-panel detector as a projection image receptor.

METHODS

Signal and noise performance is analyzed in the Fourier domain using modulation-transfer function (MTF), noise-power spectrum (NPS), and noise-equivalent number of quanta (NEQ) with respect to magnification and different convolution kernels for image reconstruction.

RESULTS

Higher magnification provides lower NPS, and thus, higher NEQ performance in the transaxial planes from microtomography. A window function capable of smoothing the ramp filter edge to below one-half of the Nyquist limit results in better performance in terms of NPS and NEQ. The characteristics of convolution kernels do not affect signal and noise performance in longitudinal planes; hence, MTF performance mainly dominates the NEQ performance. The signal and noise performances investigated in this study are demonstrated with images obtained from the contrast phantom and postmortem mouse.

CONCLUSION

The results of our study could be helpful in developing x-ray microtomography systems based on flat-panel detectors.

Optimal frequency-based weighting for spectral x-ray projection imaging

The purpose of this work is to derive a weighting scheme that maximizes the frequency-dependent ideal observer signal-difference-to-noise ratio, commonly referred to as detectability index or Hotelling-SDNR, for spectral X-ray projection imaging. Starting from basic statistical decision theory, optimal frequency-dependent weights are derived for a multiple-bin system and the Hotelling-SDNR calculated. A 28% increase in detectability index is found for high frequency objects when applying optimal frequency-dependent weights instead of pixel-based weights to a simplified model of a silicon detector, decreasing towards 0% for low frequency objects. Simulation results indicate a potentially large increase in detectability for high-frequency object imaging using silicon detectors, thus meriting further evaluations on a real system.

Research in digital mammography and tomosynthesis at the University of Toronto

There have been major advances in the field of breast cancer imaging since the early 1970s, both in technological improvements and in the use of the methods of medical physics and image analysis to optimize image quality. The introduction of digital mammography in 2000 provided a marked improvement in imaging of dense breasts. In addition, it became possible to produce tomographic and functional images on modified digital mammography systems. Digital imaging also greatly facilitated the extraction of quantitative information from images. My laboratory has been fortunate in being able to participate in some of these exciting developments. I will highlight some of the areas of our research interest which include modeling of the image formation process, development of high-resolution X-ray detectors for digital mammography and investigating new methods for analyzing image quality. I will also describe our more recent work on developing new applications of digital mammography including tomosynthesis, contrast-enhanced mammography, and measurement of breast density. Finally, I will point to a new area for our research--the application of the techniques of medical imaging to making pathology more quantitative to contribute to use of biomarkers for better characterizing breast cancer and directing therapeutic decisions.

Objective assessment of sonographic quality I: task information

In this paper, we explore relationships between the performance of the ideal observer and information-based measures of class separability in the context of sonographic breast-lesion diagnosis. This investigation was motivated by a finding that, since the test statistic of the ideal observer in sonography is a quadratic function of the echo data, it is not generally normally distributed. We found for some types of boundary discrimination tasks often required for sonographic lesion diagnosis, the deviation of the test statistic from a normal distribution can be significant. Hence the usual relationships between performance and information metrics become uncertain. Using Monte Carlo studies involving five common sonographic lesion-discrimination tasks, we found in each case that the detectability index d(A)(2) from receiver operating characteristic analysis was well approximated by the Kullback-Leibler divergence J, a measure of clinical task information available from the recorded radio-frequency echo data. However, the lesion signal-to-noise ratio, SNR(I)(2), calculated from moments of the ideal observer test statistic, consistently underestimates d(A)(2) for high-contrast boundary discrimination tasks. Thus, in a companion paper, we established a relationship between image-quality properties of the imaging system and J in order to predict ideal performance. These relationships provide a rigorous basis for sonographic instrument evaluation and design.

Objective assessment of sonographic: quality II acquisition information spectrum

This paper describes a task-based, information-theoretic approach to the assessment of image quality in diagnostic sonography. We expand the Kullback-Leibler divergence metric J, which quantifies the diagnostic information contained within recorded radio-frequency echo signals, into a spatial-frequency integral comprised of two spectral components: one describes patient features for low-contrast diagnostic tasks and the other describes instrumentation properties. The latter quantity is the acquisition information spectrum (AIS), which measures the density of object information that an imaging system is able to transfer to the echo data at each spatial frequency. AIS is derived based on unique properties of acoustic scattering in tissues that generate object contrast. Predictions made by the J integral expression were validated through Monte Carlo studies using echo-signal data from simulated lesions. Our analysis predicts the diagnostic performance of any sonographic system at specific diagnostic tasks based on engineering properties of the instrument that constitute image quality.

Amorphous and polycrystalline photoconductors for direct conversion flat panel x-ray image sensors

In the last ten to fifteen years there has been much research in using amorphous and polycrystalline semiconductors as x-ray photoconductors in various x-ray image sensor applications, most notably in flat panel x-ray imagers (FPXIs). We first outline the essential requirements for an ideal large area photoconductor for use in a FPXI, and discuss how some of the current amorphous and polycrystalline semiconductors fulfill these requirements. At present, only stabilized amorphous selenium (doped and alloyed a-Se) has been commercialized, and FPXIs based on a-Se are particularly suitable for mammography, operating at the ideal limit of high detective quantum efficiency (DQE). Further, these FPXIs can also be used in real-time, and have already been used in such applications as tomosynthesis. We discuss some of the important attributes of amorphous and polycrystalline x-ray photoconductors such as their large area deposition ability, charge collection efficiency, x-ray sensitivity, DQE, modulation transfer function (MTF) and the importance of the dark current. We show the importance of charge trapping in limiting not only the sensitivity but also the resolution of these detectors. Limitations on the maximum acceptable dark current and the corresponding charge collection efficiency jointly impose a practical constraint that many photoconductors fail to satisfy. We discuss the case of a-Se in which the dark current was brought down by three orders of magnitude by the use of special blocking layers to satisfy the dark current constraint. There are also a number of polycrystalline photoconductors, HgI₂ and PbO being good examples, that show potential for commercialization in the same way that multilayer stabilized a-Se x-ray photoconductors were developed for commercial applications. We highlight the unique nature of avalanche multiplication in a-Se and how it has led to the development of the commercial HARP video-tube. An all solid state version of the HARP has been recently demonstrated with excellent avalanche gains; the latter is expected to lead to a number of novel imaging device applications that would be quantum noise limited. While passive pixel sensors use one TFT (thin film transistor) as a switch at the pixel, active pixel sensors (APSs) have two or more transistors and provide gain at the pixel level. The advantages of APS based x-ray imagers are also discussed with examples.

A spatio-temporal detective quantum efficiency and its application to fluoroscopic systems

PURPOSE

Fluoroscopic x-ray imaging systems are used extensively in spatio-temporal detection tasks and require a spatio-temporal description of system performance. No accepted metric exists that describes spatio-temporal fluoroscopic performance. The detective quantum efficiency (DQE) is a metric widely used in radiography to quantify system performance and as a surrogate measure of patient "dose efficiency". It has been applied previously to fluoroscopic systems with the introduction of a temporal correction factor. However, the use of a temporally-corrected DQE does not provide system temporal information and it is only valid under specific conditions, many of which are not likely to be satisfied by suboptimal systems. The authors propose a spatio-temporal DQE that describes performance in both space and time and is applicable to all spatio-temporal quantum-based imaging systems.

METHODS

The authors define a spatio-temporal DQE (two spatial-frequency axes and one temporal-frequency axis) in terms of a small-signal spatio-temporal modulation transfer function (MTF) and spatio-temporal noise power spectrum (NPS). Measurements were made on an x-ray image intensifier-based bench-top system using continuous fluoroscopy with an RQA-5 beam at 3.9 microR/frame and hardened 50 kVp beam (0.8 mm Cu filtration added) at 1.9 microR/frame.

RESULTS

A zero-frequency DQE value of 0.64 was measured under both conditions. Nonideal performance was noted at both larger spatial and temporal frequencies; DQE values decreased by approximately 50% at the cutoff temporal frequency of 15 Hz.

CONCLUSIONS

The spatio-temporal DQE enables measurements of decreased temporal system performance at larger temporal frequencies analogous to previous measurements of decreased (spatial) performance. This marks the first time that system performance and dose efficiency in both space and time have been measured on a fluoroscopic system using DQE and is the first step toward the generalized use of DQE on clinical fluoroscopic systems.

Microdome-gooved Gd(2)O(2)S:Tb scintillator for flexible and high resolution digital radiography

A flexible microdome-grooved Gd(2)O(2)S:Tb scintillator is simulated, fabricated, and characterized for digital radiography applications. According to Monte Carlo simulation results, the dome-grooved structure has a high spatial resolution, which is verified by X-ray image performance of the scintillator. The proposed scintillator has lower X-ray sensitivity than a nonstructured scintillator but almost two times higher spatial resolution at high spatial frequency. Through evaluation of the X-ray performance of the fabricated scintillators, we confirm that the microdome-grooved scintillator can be applied to next-generation flexible digital radiography systems requiring high spatial resolution.

A small-signal approach to temporal modulation transfer functions with exposure-rate dependence and its application to fluoroscopic detective quantum efficiency

The detective quantum efficiency (DQE) is a metric widely used in radiography to quantify system performance and as a surrogate measure of patient "dose efficiency." It has been applied previously to fluoroscopic systems with the introduction of a temporal correction factor. Calculation of this correction factor relies on measurements of the temporal modulation transfer function (MTF). However, the temporal MTF is often exposure-rate dependent, violating a necessary Fourier linearity requirement. The authors show that a Fourier analysis is appropriate for fluoroscopic systems if a "small-signal" approach is used. Using a semitransparent edge, a lag-corrected DQE is described and measured for an x-ray image intensifier-based fluoroscopic system under continuous (non-pulsed) exposure conditions. It was found that results were equivalent for both rising and falling-edge profiles independent of edge attenuation when effective attenuation was in the range of 0.1-0.6. This suggests that this range is appropriate for measuring the small-signal temporal MTF. In general, lag was greatest at low exposure rates. It was also found that results obtained using a falling-edge profile with a radiopaque edge were equivalent to the small-signal results for the test system. If this result is found to be true generally, it removes the need for the small-signal approach. Lag-corrected DQE values were validated by comparison with radiographic DQE values obtained using very long exposures under the same conditions. Lag was observed to inflate DQE measurements by up to 50% when ignored.

A moving slanted-edge method to measure the temporal modulation transfer function of fluoroscopic systems

Lag in fluoroscopic systems introduces a frame-averaging effect that reduces measurements of image noise and incorrectly inflates measurements of the detective quantum efficiency (DQE). A correction can be implemented based on measurements of the temporal modulation transfer function (MTF). We introduce a method of measuring the temporal MTF under fluoroscopic conditions using a moving slanted edge, a generalization of the slanted-edge method used to measure the (spatial) MTF, providing the temporal MTF of the entire imaging system. The method uses a single x-ray exposure, constant edge velocity, and assumes spatial and temporal blurring are separable. The method was validated on a laboratory x-ray image intensifier (XRII) system by comparison with direct measurements of the XRII optical response, showing excellent agreement over the entire frequency range tested (+/- 100 Hz). With proper access to linearized data and continuous fluoroscopy, this method can be implemented in a clinical setting on both XRII and flat-panel detectors. It is shown that the temporal MTF of the CsI-based validation system is a function of exposure rate. The rising-edge response showed more lag than the falling edge, and the temporal MTF decreased with decreasing exposure rate. It is suggested that a small-signal approach, in which the range of exposure rates is restricted to a linear range by using a semitransparent moving edge, would be appropriate for measuring the DQE of these systems.

Investigation of the signal behavior at diagnostic energies of prototype, direct detection, active matrix, flat-panel imagers incorporating polycrystalline HgI2

Active matrix, flat-panel x-ray imagers based on a-Si:H thin-film transistors offer many advantages and are widely utilized in medical imaging applications. Unfortunately, the detective quantum efficiency (DQE) of conventional flat-panel imagers incorporating scintillators or a-Se photoconductors is significantly limited by their relatively modest signal-to-noise ratio, particularly in applications involving low x-ray exposures or high spatial resolution. For this reason, polycrystalline HgI2 is of considerable interest by virtue of its low effective work function, high atomic number and the possibility of large-area deposition. In this study, a detailed investigation of the properties of prototype, flat-panel arrays coated with two forms of this high-gain photoconductor are reported. Encouragingly, high x-ray sensitivity, low dark current and spatial resolution close to the theoretical limits were observed from a number of prototypes. In addition, input-quantum-limited DQE performance was measured from one of the prototypes at relatively low exposures. However, high levels of charge trapping, lag and polarization, as well as pixel-to-pixel variations in x-ray sensitivity are of concern. While the results of the current study are promising, further development will be required to realize prototypes exhibiting the characteristics necessary to allow practical implementation of this approach.

Physical characterization of a scanning photon counting digital mammography system based on Si-strip detectors

The physical performance of a scanning multislit full field digital mammography system was determined using basic image quality parameters. The system employs a direct detection detector comprised of linear silicon strip sensors in an edge-on geometry connected to photon counting electronics. The pixel size is 50 microm and the field of view 24 x 26 cm2. The performance was quantified using the presampled modulation transfer function, the normalized noise power spectrum and the detective quantum efficiency (DQE). Compared to conventional DQE methods, the scanning geometry with its intrinsic scatter rejection poses additional requirements on the measurement setup, which are investigated in this work. The DQE of the photon counting system was found to be independent of the dose level to the detector in the 7.6-206 microGy range. The peak DQE was 72% and 73% in the scan and slit direction, respectively, measured with a 28 kV W-0.5 mm Al anode-filter combination with an added 2 mm Al filtration.

Signal and noise transfer properties of photoelectric interactions in diagnostic x-ray imaging detectors

Image quality in diagnostic x-ray imaging is ultimately limited by the statistical properties governing how, and where, x-ray energy is deposited in a detector. This in turn depends on the physics of the underlying x-ray interactions. In the diagnostic energy range (10-100 keV), most of the energy deposited in a detector is through photoelectric interactions. We present a theoretical model of the photoelectric effect that specifically addresses the statistical nature of energy absorption by photoelectrons, K and L characteristic x rays, and Auger electrons. A cascaded-systems approach is used that employs a complex structure of parallel cascades to describe signal and noise transfer through the photoelectric effect in terms of the modulation transfer function, Wiener noise power spectrum, and detective quantum efficiency (DQE). The model was evaluated by comparing results with Monte Carlo calculations for x-ray converters based on amorphous selenium (a-Se) and lead (Pb), representing both low and high-Z materials. When electron transport considerations can be neglected, excellent agreement (within 3%) is obtained for each metric over the entire diagnostic energy range in both a-Se and Pb detectors up to 30 cycles/mm, the highest frequency tested. The cascaded model overstates the DQE when the electron range cannot be ignored. This occurs at approximately two cycles/mm in a-Se at an incident photon energy of 80 keV, whereas in Pb, excellent agreement is obtained for the DQE over the entire diagnostic energy range. However, within the context of mammography (20 keV) and micro-computed tomography (40 keV), the effects of electron transport on the DQE are negligible compared to fluorescence reabsorption, which can lead to decreases of up to 30% and 20% in a-Se and Pb, respectively, at 20 keV; and 10% and 5%, respectively, at 40 keV. It is shown that when Swank noise is identified in a Fourier model, the Swank factor must be frequency dependent. This factor decreases quickly with frequency, and in the case of a-Se and Pb, decreases by up to a factor of 3 at five cycles/mm immediately above the K edge. The frequency-dependent Swank factor is also equivalent to what we call the "photoelectric DQE," which describes signal and noise transfer through photoelectric interactions.

Diagnostic imaging over the last 50 years: research and development in medical imaging science and technology

Over the last 50 years, diagnostic imaging has grown from a state of infancy to a high level of maturity. Many new imaging modalities have been developed. However, modern medical imaging includes not only image production but also image processing, computer-aided diagnosis (CAD), image recording and storage, and image transmission, most of which are included in a picture archiving and communication system (PACS). The content of this paper includes a short review of research and development in medical imaging science and technology, which covers (a) diagnostic imaging in the 1950s, (b) the importance of image quality and diagnostic performance, (c) MTF, Wiener spectrum, NEQ and DQE, (d) ROC analysis, (e) analogue imaging systems, (f) digital imaging systems, (g) image processing, (h) computer-aided diagnosis, (i) PACS, (j) 3D imaging and (k) future directions. Although some of the modalities are already very sophisticated, further improvements will be made in image quality for MRI, ultrasound and molecular imaging. The infrastructure of PACS is likely to be improved further in terms of its reliability, speed and capacity. However, CAD is currently still in its infancy, and is likely to be a subject of research for a long time.

Extension of x-ray imaging linear systems analysis to detectors with energy discrimination capability

A figure of merit, the broad-spectrum generalized detective quantum efficiency, which describes the performance of digital detectors designed for broad-spectrum x-ray imaging is derived from linear response theory. This measure of the imaging efficacy of an x-ray sensor is obtained when detector contrast modulation in the domain of x-ray energy is introduced in the Fourier-based analysis of digital systems. A method is proposed to scale existing figures of merit according to the energy-dependent response of the detector and the spectral shape of the x-ray beam. The new figure of merit obtained with this method provides an extended description of system performance when comparing energy-integrating, single-photon counting, and future energy-sensitive x-ray imaging sensors. The applicability of this linear system analysis is restricted to the tasks of low-contrast object detection in radiography. The method for scaling the figure of merit to take into consideration broad-spectrum conditions is applied to mammography for future energy-dependent detectors. An approximation valid in the typical mammographic x-ray energy range is used to calculate the broad-spectrum generalized detective quantum efficiency at zero spatial frequency, for several mammographic x-ray spectra. X-ray energy weighting in mammography is investigated in the context of simulated tumors and microcalcifications detection by comparing this figure of merit, calculated for different detector technologies, under ideal imaging conditions, at zero spatial frequency.

Detection performance theory for ultrasound imaging systems

A rigorous statistical theory for characterizing the performance of medical ultrasound systems for lesion detection tasks is developed. A design strategy for optimizing ultrasound systems should be to adjust parameters for maximum information content, which is obtained by maximizing the ideal observer performance. Then, given the radio-frequency data, image and signal processing algorithms are designed to extract as much diagnostically relevant information as possible. In this paper, closed-form and low-contrast approximations of ideal observer performance are derived for signal known statistically detection tasks. The accuracy of the approximations are tested by comparing with Monte Carlo techniques. A metric borrowed and modified from photon imaging, Generalized Noise Equivalent Quanta, is shown to be a useful and measurable target-independent figure of merit when adapted for ultrasound systems. This theory provides the potential to optimize design tradeoffs for detection tasks. For example it may help us understand how to push the limits of specific features, such as spatial resolution, without significantly compromising overall detection performance.

Computational engine for development of complex cascaded models of signal and noise in X-ray imaging systems

The detective quantum efficiency (DQE) is generally accepted as the primary metric of signal-to-noise performance in medical X-ray imaging systems. Simple theoretical models of the Wiener noise power spectrum (NPS) and DQE can be developed using a cascaded-systems approach to assess particular system designs and establish operational benchmarks. However, the cascaded approach is often impractical for the development of comprehensive models due to the complexity and extremely large number of algebraic terms that must be manipulated to describe signal and noise transfer. We have developed a computational engine that overcomes this limitation. Using a predefined library of elementary physical processes, complex models are assembled and input-output relationships established using a graphical interface. A novel recursive algorithm is described that allows the signal and noise analyses of models with arbitrary complexity including the use of multiple parallel cascades. Symbolic mathematics is used to develop analytic expressions for the NPS and DQE. The algorithm is validated by manual calculation for simple models and by Monte Carlo calculation for complex models. We believe our approach enables the use of complex cascaded models to design better detectors with improved image quality.

An energy- and depth-dependent model for x-ray imaging

In this paper, we model an x-ray imaging system, paying special attention to the energy- and depth-dependent characteristics of the inputs and interactions: x rays are polychromatic, interaction depth and conversion to optical photons is energy-dependent, optical scattering and the collection efficiency depend on the depth of interaction. The model we construct is a random function of the point process that begins with the distribution of x rays incident on the phosphor and ends with optical photons being detected by the active area of detector pixels to form an image. We show how the point-process representation can be used to calculate the characteristic statistics of the model. We then simulate a Gd2O2S:Tb phosphor, estimate its characteristic statistics, and proceed with a signal-detection experiment to investigate the impact of the pixel fill factor on detecting spherical calcifications (the signal). The two extremes possible from this experiment are that SNR2 does not change with fill factor or changes in proportion to fill factor. In our results, the impact of fill factor is between these extremes, and depends on the diameter of the signal.

Performance of electronic portal imaging devices (EPIDs) used in radiotherapy: Image quality and dose measurements

The aim of our study was to compare the image and dosimetric quality of two different imaging systems. The first one is a fluoroscopic electronic portal imaging device (first generation), while the second is based on an amorphous silicon flat-panel array (second generation). The parameters describing image quality include spatial resolution [modulation transfer function (MTF)], noise [noise power spectrum (NPS)], and signal-to-noise transfer [detective quantum efficiency (DQE)]. The dosimetric measurements were compared with ionization chamber as well as with film measurements. The response of the flat-panel imager and the fluoroscopic-optical device was determined performing a two-step Monte Carlo simulation. All measurements were performed in a 6 MV linear accelerator photon beam. The resolution (MTF) of the fluoroscopic device (f 1/2 = 0.3 mm(-1)) is larger than of the amorphous silicon based system (f 1/2 = 0.21 mm(-1)), which is due to the missing backscattered photons and the smaller pixel size. The noise measurements (NPS) show the correlation of neighboring pixels of the amorphous silicon electronic portal imaging device, whereas the NPS of the fluoroscopic system is frequency independent. At zero spatial frequency the DQE of the flat-panel imager has a value of 0.008 (0.8%). Due to the minor frequency dependency this device may be almost x-ray quantum limited. Monte Carlo simulations verified these characteristics. For the fluoroscopic imaging system the DQE at low frequencies is about 0.0008 (0.08%) and degrades with higher frequencies. Dose measurements with the flat-panel imager revealed that images can only be directly converted to portal dose images, if scatter can be neglected. Thus objects distant to the detector (e.g., inhomogeneous dose distribution generated by a modificator) can be verified dosimetrically, while objects close to a detector (e.g., a patient) cannot be verified directly and must be scatter corrected prior to verification. This is justified by the response of the flat-panel imaging device revealing a strong dependency at low energies.

Signal detectability in digital radiography: spatial domain figures of merit

The usefulness of Fourier-based measures of imaging performance has come into question for the evaluation of digital imaging systems. Figures of merit such as detective quantum efficiency (DQE) based on Fourier domain parameters are relevant for linear, shift-invariant systems with stationary noise. However, no digital imaging system is shift invariant, and realistic images do not satisfy the stationarity condition. Our methods for the task-based evaluation of imaging systems, based on signal detectability in the spatial domain, do not require such assumptions. We have computed the performance of ideal and quasi-ideal observers for the task of signal detection in digital radiography. Signal detectability in terms of an observer signal-to-noise-ratio (SNR) has been compared to results obtained from a Monte Carlo simulation of the digital image-acquisition process. The simulation incorporates the effects of random amplification and secondary quantum blur, integration over pixel area, and electronic noise. The observer figures of merit that have been previously shown to bracket human performance directly specify the usefulness of the images for the stated diagnostic task. In addition, the observer figures of merit give a task-dependent measure of imaging system efficiency in terms of the ratio of an output SNR2 to an input SNR2. Thus, the concept of "detective quantum efficiency" reappears in a natural way but based in the spatial domain and not dependent on shift invariance and stationarity assumptions. With respect to the optimum amount of system blur, our simulations indicate that under certain task-dependent conditions, large signals are fairly insensitive to blur in the x-ray transducer, while an optimum blur is found for small signals.

Noise aliasing in interline-video-based fluoroscopy systems

Video-based imaging systems for continuous (nonpulsed) x-ray fluoroscopy use a variety of video formats. Conventional video-camera systems may operate in either interlaced or progressive-scan modes, and CCD systems may operate in interline- or frame-transfer modes. A theoretical model of the image noise power spectrum corresponding to these formats is described. It is shown that with respect to frame-transfer or progressive-readout modes, interline or interlaced cameras operating in a frame-integration mode will result in a spectral shift of 25% of the total image noise power from low spatial frequencies to high. In a field-integration mode, noise power is doubled with most of the increase occurring at high spatial frequencies. The differences are due primarily to the effect of noise aliasing. In interline or interlaced formats, alternate lines are obtained with each video field resulting in a vertical sampling frequency for noise that is one half of the physical sampling frequency. The extent of noise aliasing is modified by differences in the statistical correlations between video fields in the different modes. The theoretical model is validated with experiments using an x-ray image intensifier and CCD-camera system. It is shown that different video modes affect the shape of the noise-power spectrum and therefore the detective quantum efficiency. While the effect on observer performance is not addressed, it is concluded that in order to minimize image noise at the critical mid-to-high spatial frequencies for a specified x-ray exposure, fluoroscopic systems should use only frame-transfer (CCD camera) or progressive-scan (conventional video) formats.

Parallel cascades: new ways to describe noise transfer in medical imaging systems

A generalized approach to describing transfer of the noise power spectrum through medical imaging systems has been developed over the past several years in which image-forming processes are represented in terms of a cascade of amplified point processes. Until recently, this approach has been restricted to serial cascades only. Here we develop a generalized expression for the cross covariance of amplified point processes and an expression for the cross spectral density for wide-sense stationary conditions. These results extend the generalized transfer-theory approach to include the description of more complex image-forming processes involving parallel cascades of quantum amplification processes. This parallel-cascade approach is used to develop a theoretical expression for noise-power transfer in a simple radiographic screen that includes the effect of characteristic x-ray reabsorption. The result confirms earlier work by Metz and Vyborny, who showed that reabsorption increases image noise and decreases the detective quantum efficiency at low spatial frequencies. Use of the transfer-theory approach facilitates a straightforward generalization to many new digital imaging systems including conventional angiographic and active-matrix flat-panel systems.

Screen-film and digital mammography. Image quality and radiation dose considerations

Factors affecting image quality and patient dose in screen-film and digital mammography have been discussed. Some proposed parameters for judging image quality and breast exposure measurements and dose calculations relating to changes in image quality factors have been reviewed. It is important to remember that the goal in making a mammogram is to obtain as much diagnostic information as possible at the lowest dose compatible with that information. As noted previously, this necessitates compromises (i.e., an optimization of factors that affect image quality). These include beam quality, compression, imaging geometry, grids, receptor characteristics, processing of the film or digital image, and display and viewing conditions. If this is done correctly, a high-quality mammogram can be obtained at a reasonably low dose to the patient. The goal is not simply to use as low a dose as possible, because if this is done there is a large risk of degrading the performance of mammography in detecting or accurately characterizing small, node-negative cancers.

Analysis of the detective quantum efficiency of a developmental detector for digital mammography

We are developing a modular detector for applications in full field digital mammography and for diagnostic breast imaging. The detector is based on a design that has been refined over the past decade for applications in x-ray crystallography [Kalata et al., Proc. SPIE 1345, 270-279 (1990); Phillips et al. ibid. 2009, 133-138 (1993), Phillips et al., Nucl. Instrum. Methods Phys. Rev. A 334, 621-630 (1993)]. The full field mammographic detector, currently undergoing clinical evaluation, is formed from a 19 cm x 28 cm phosphor screen, read out by a 2 x 3 array of butted charge-coupled device (CCD) modules. Each 2k x 2k CCD is optically coupled to the phosphor via a fiber optic taper with dimensions of 9.4 cm x 9.4cm at the phosphor. This paper describes the imaging performance of a two-module prototype, built using a similar design. In this paper we use cascaded linear systems analysis to develop a model for calculating the spatial frequency dependent noise power spectrum (NPS) and detective quantum efficiency (DQE) of the detector using the measured modulation transfer function (MTF). We compare results of the calculation with the measured NPS and DQE of the prototype. Calculated and measured DQEs are compared over a range of clinically relevant x-ray exposures and kVps. We find that for x-ray photon energies between 10 and 28 keV, the detector gain ranges between 2.5 and 3.7 CCD electrons per incident x-ray, or approximately 5-8 electrons per absorbed x ray. Using a Mo/Mo beam and acrylic phantom, over a detector entrance exposure range of approximately 10 to 80 mR, the volume under the measured 2-d NPS of the prototype detector is proportional to the x-ray exposure, indicating quantum limited performance. Substantial agreement between the calculated and measured values was obtained for the frequency and exposure dependent NPS and DQE over a range of tube voltage from 25 to 30 kVp.

Monte Carlo simulations of the imaging performance of metal plate/phosphor screens used in radiotherapy

The imaging performance of metal plate/phosphor screens which are used for the creation of portal images in radiotherapy is investigated by using Monte Carlo simulations. To this end the modulation transfer function, the noise power spectrum and the detective quantum efficiency [DQE(f)] are calculated for different metals and phosphors and different thicknesses of metal and phosphor for a range of spatial resolutions. The interaction of x-rays with the metal plate/phosphor screen is modeled with the EGS4 electron gamma shower code. Optical transport in the phosphor is modeled by simulating scattering and reabsorption events of individual optical photons. It is shown that metals with a high atomic number perform better than lighter metals in maximizing the DQE(f). It is furthermore shown that the DQE(f) for the metal plate/phosphor screen alone is nearly x-ray quantum absorption limited up to spatial frequencies of 0.4 cycles/mm. In addition, it is argued that the secondary quantum sink of optical photons imposed by the optical chain (mirror, lenses and video camera) leads to a significant degradation of the signal-to-noise ratio at spatial frequencies which are most important for successful registration of portal images. Therefore, the conclusion is that a replacement of the optical chain by a flat array of photodiodes placed directly under the phosphor will lead to a substantial improvement in image quality of portal images.

An investigation of the imaging characteristics of the Y2O2S:Eu3+ phosphor for application in X-ray detectors of digital mammography

Y2O2S:Eu laboratory prepared screens were evaluated as mammographic image receptors and were compared to similarly prepared screens of Gd2O2S:Tb and Y2O2S:Tb phosphor materials, often used in X-ray imaging detectors. The evaluation was performed by determining the Modulation Transfer Function (MTF) and the spatial frequency dependent Detective Quantum Efficiency (DQE). Y2O2S:Eu exhibited higher DQE values at low frequencies and given its good spectral matching with digital optical detectors, it may be appropriate for use in X-ray digital mammography.

Recent developments in breast imaging

A review of breast imaging has already appeared in 1982 in this journal. Consequently, the present article concentrates on a discussion of only those developments of a more recent nature. Although the emphasis is placed on the physical aspects of the different imaging methods concerned, the essential factors relating to the clinical background and the associated radiation risk are also outlined. The completeness of detail depends on the present clinical importance of the method under discussion. X-ray mammography, which is still the most important breast imaging technique and has proved to be an effective method for breast cancer screening, is therefore treated in greater detail. Since the early 1980s, ultrasound B-mode scanning has evolved to an indispensable adjunct to x-ray mammography. For Doppler sonography, diaphanography, contrast-enhanced MRI, CT and DSA, the visualization of a tumour depends essentially on the enhanced vascularity of the lesion. Whether this will prove to be a reliable indicator for malignancy remains to be shown in controlled clinical studies. Common to all imaging systems is the increasing use of digital methods for signal processing, which also offers the possibility of computer-aided diagnosis by texture analysis and pattern recognition.

Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance

Figures of merit for image quality are derived on the basis of the performance of mathematical observers on specific detection and estimation tasks. The tasks include detection of a known signal superimposed on a known background, detection of a known signal on a random background, estimation of Fourier coefficients of the object, and estimation of the integral of the object over a specified region of interest. The chosen observer for the detection tasks is the ideal linear discriminant, which we call the Hotelling observer. The figures of merit are based on the Fisher information matrix relevant to estimation of the Fourier coefficients and the closely related Fourier crosstalk matrix introduced earlier by Barrett and Gifford [Phys. Med. Biol. 39, 451 (1994)]. A finite submatrix of the infinite Fisher information matrix is used to set Cramer-Rao lower bounds on the variances of the estimates of the first N Fourier coefficients. The figures of merit for detection tasks are shown to be closely related to the concepts of noise-equivalent quanta (NEQ) and generalized NEQ, originally derived for linear, shift-invariant imaging systems and stationary noise. Application of these results to the design of imaging systems is discussed.

SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory

A method of measuring the image quality of medical imaging equipment is considered within the framework of statistical decision theory. In this approach, images are regarded as random vectors and image quality is defined in the context of the image information available for performing a specified detection or discrimination task. The approach provides a means of measuring image quality, as related to the detection of an image detail of interest, without reference to the actual physical mechanisms involved in image formation and without separate measurements of signal transfer characteristics or image noise. The measurement does not, however, consider deterministic errors in the image; they need a separate evaluation for imaging modalities where they are of concern. The detectability of an image detail can be expressed in terms of the ideal observer's signal-to-noise ratio (SNR) at the decision level. Often a good approximation to this SNR can be obtained by employing sub-optimal observers, whose performance correlates well with the performance of human observers as well. In this paper the measurement of SNR is based on implementing algorithmic realizations of specified observers and analysing their responses while actually performing a specified detection task of interest. Three observers are considered: the ideal prewhitening matched filter, the non-prewhitening matched filter, and the DC-suppressing non-prewhitening matched filter. The construction of the ideal observer requires an impractical amount of data and computing, except for the most simple imaging situations. Therefore, the utilization of sub-optimal observers is advised and their performance in detecting a specified signal is discussed. Measurement of noise and SNR has been extended to include temporally varying images and dynamic imaging systems.