Performing tomographic reconstructions from a satellite looking toward Earth. Part 1: implementation and limitations.

For imaging instruments that are in space looking toward the Earth, there are a variety of nuisance signals that can get in the way of performing certain imaging tasks, such as reflections from clouds, reflections from the ground, and emissions from the OH-airglow layer. A method for separating these signals is to perform tomographic reconstructions from the collected data. A lingering struggle for this method is altitude-axis resolution and different methods for helping with it are discussed. An implementation of the maximum likelihood expectation maximization algorithm is given and analyzed.

Performing tomographic reconstructions from a satellite looking toward Earth. Part 2: analysis of image quality.

This paper is part 2 of two papers that explore performing tomographic reconstructions from a space platform. A simplified model of short-wave infrared emissions in the atmosphere is given. Simulations were performed that tested the effectiveness of reconstructions given signal amplitude, frequency, signal-to-noise ratio, number of iterations run, and others. Maximum likelihood expectation maximization is shown to be effective for reconstructing low signal cases.

Fisher information analysis of list-mode SPECT emission data for joint estimation of activity and attenuation distribution.

The potential to perform attenuation and scatter compensation (ASC) in single-photon emission computed tomography (SPECT) imaging without a separate transmission scan is highly significant. In this context, attenuation in SPECT is primarily due to Compton scattering, where the probability of Compton scatter is proportional to the attenuation coefficient of the tissue and the energy of the scattered photon and the scattering angle are related. Based on this premise, we investigated whether the SPECT scattered-photon data acquired in list-mode (LM) format and including the energy information can be used to estimate the attenuation map. For this purpose, we propose a Fisher-information-based method that yields the Cramer-Rao bound (CRB) for the task of jointly estimating the activity and attenuation distribution using only the SPECT emission data. In the process, a path-based formalism to process the LM SPECT emission data, including the scattered-photon data, is proposed. The Fisher information method was implemented on NVIDIA graphics processing units (GPU) for acceleration. The method was applied to analyze the information content of SPECT LM emission data, which contains up to first-order scattered events, in a simulated SPECT system with parameters modeling a clinical system using realistic computational studies with 2-D digital synthetic and anthropomorphic phantoms. The method was also applied to LM data containing up to second-order scatter for a synthetic phantom. Experiments with anthropomorphic phantoms simulated myocardial perfusion and dopamine transporter (DaT)-Scan SPECT studies. The results show that the CRB obtained for the attenuation and activity coefficients was typically much lower than the true value of these coefficients. An increase in the number of detected photons yielded lower CRB for both the attenuation and activity coefficients. Further, we observed that systems with better energy resolution yielded a lower CRB for the attenuation coefficient. Overall, the results provide evidence that LM SPECT emission data, including the scattered photons, contains information to jointly estimate the activity and attenuation coefficients.

Development of an ideal observer that incorporates nuisance parameters and processes list-mode data.

Observer models were developed to process data in list-mode format in order to perform binary discrimination tasks for use in an arms-control-treaty context. Data used in this study was generated using GEANT4 Monte Carlo simulations for photons using custom models of plutonium inspection objects and a radiation imaging system. Observer model performance was evaluated and presented using the area under the receiver operating characteristic curve. The ideal observer was studied under both signal-known-exactly conditions and in the presence of unknowns such as object orientation and absolute count-rate variability; when these additional sources of randomness were present, their incorporation into the observer yielded superior performance.

Correction of multiplexing artefacts in multi-pinhole SPECT through temporal shuttering, de-multiplexing of projections, and alternating reconstruction.

Objective.Single-photon emission computed tomography (SPECT) with pinhole collimators can provide high-resolution imaging, but is often limited by low sensitivity. Acquiring projections simultaneously through multiple pinholes affords both high resolution and high sensitivity. However, the overlap of projections from different pinholes on detectors, known as multiplexing, has been shown to cause artefacts which degrade reconstructed images.Approach.Multiplexed projection sets were considered here using an analytic simulation model of AdaptiSPECT-C-a brain-dedicated multi-pinhole SPECT system. AdaptiSPECT-C has fully adaptable aperture shutters, so can acquire projections with a combination of multiplexed and non-multiplexed frames using temporal shuttering. Two strategies for reducing multiplex artefacts were considered: an algorithm to de-multiplex projections, and an alternating reconstruction strategy for projections acquired with a combination of multiplexed and non-multiplexed frames. Geometric and anthropomorphic digital phantoms were used to assess a number of metrics.Main results.Both de-multiplexing strategies showed a significant reduction in image artefacts and improved fidelity, image uniformity, contrast recovery and activity recovery (AR). In all cases, the two de-multiplexing strategies resulted in superior metrics to those from images acquired with only mux-free frames. The de-multiplexing algorithm provided reduced image noise and superior uniformity, whereas the alternating strategy improved contrast and AR.Significance.The use of these de-multiplexing algorithms means that multi-pinhole SPECT systems can acquire projections with more multiplexing without degradation of images.

Figure of merit for task-based assessment of frequency-domain diffusive imaging.

A figure of merit (FOM) for frequency-domain diffusive imaging (FDDI) is theoretically developed adapting the concept of Hotelling observer signal-to-noise ratio. Different from conventionally used FOMs for FDDI, the newly developed FOM considers diffused intensities, modulation amplitudes, and phases in combination. The FOM applied to Monte Carlo simulations of signal- and background-known-exactly problems shows unique characteristics that are in agreement with findings in the literature. We believe that a task based assessment using the FOM improves the characterization of FDDI systems and allows for complete system optimization.

Simulating Silicon Photomultiplier Response to Scintillation Light.

The response of a Silicon Photomultiplier (SiPM) to optical signals is affected by many factors including photon-detection efficiency, recovery time, gain, optical crosstalk, afterpulsing, dark count, and detector dead time. Many of these parameters vary with overvoltage and temperature. When used to detect scintillation light, there is a complicated non-linear relationship between the incident light and the response of the SiPM. In this paper, we propose a combined discrete-time discrete-event Monte Carlo (MC) model to simulate SiPM response to scintillation light pulses. Our MC model accounts for all relevant aspects of the SiPM response, some of which were not accounted for in the previous models. We also derive and validate analytic expressions for the single-photoelectron response of the SiPM and the voltage drop across the quenching resistance in the SiPM microcell. These analytic expressions consider the effect of all the circuit elements in the SiPM and accurately simulate the time-variation in overvoltage across the microcells of the SiPM. Consequently, our MC model is able to incorporate the variation of the different SiPM parameters with varying overvoltage. The MC model is compared with measurements on SiPM-based scintillation detectors and with some cases for which the response is known a priori. The model is also used to study the variation in SiPM behavior with SiPM-circuit parameter variations and to predict the response of a SiPM-based detector to various scintillators.

Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach.

We present the implementation, validation, and performance of a Neumann-series approach for simulating light propagation at optical wavelengths in uniform media using the radiative transport equation (RTE). The RTE is solved for an anisotropic-scattering medium in a spherical harmonic basis for a diffuse-optical-imaging setup. The main objectives of this paper are threefold: to present the theory behind the Neumann-series form for the RTE, to design and develop the mathematical methods and the software to implement the Neumann series for a diffuse-optical-imaging setup, and, finally, to perform an exhaustive study of the accuracy, practical limitations, and computational efficiency of the Neumann-series method. Through our results, we demonstrate that the Neumann-series approach can be used to model light propagation in uniform media with small geometries at optical wavelengths.

Three-dimensional Neumann-series approach to model light transport in nonuniform media.

We present the implementation, validation, and performance of a three-dimensional (3D) Neumann-series approach to model photon propagation in nonuniform media using the radiative transport equation (RTE). The RTE is implemented for nonuniform scattering media in a spherical harmonic basis for a diffuse-optical-imaging setup. The method is parallelizable and implemented on a computing system consisting of NVIDIA Tesla C2050 graphics processing units (GPUs). The GPU implementation provides a speedup of up to two orders of magnitude over non-GPU implementation, which leads to good computational efficiency for the Neumann-series method. The results using the method are compared with the results obtained using the Monte Carlo simulations for various small-geometry phantoms, and good agreement is observed. We observe that the Neumann-series approach gives accurate results in many cases where the diffusion approximation is not accurate.

Signal detectability in diffusive media using phased arrays in conjunction with detector arrays.

We investigate Hotelling observer performance (i.e., signal detectability) of a phased array system for tasks of detecting small inhomogeneities and distinguishing adjacent abnormalities in uniform diffusive media. Unlike conventional phased array systems where a single detector is located on the interface between two sources, we consider a detector array, such as a CCD, on a phantom exit surface for calculating the Hotelling observer detectability. The signal detectability for adjacent small abnormalities (2 mm displacement) for the CCD-based phased array is related to the resolution of reconstructed images. Simulations show that acquiring high-dimensional data from a detector array in a phased array system dramatically improves the detectability for both tasks when compared to conventional single detector measurements, especially at low modulation frequencies. It is also observed in all studied cases that there exists the modulation frequency optimizing CCD-based phased array systems, where detectability for both tasks is consistently high. These results imply that the CCD-based phased array has the potential to achieve high resolution and signal detectability in tomographic diffusive imaging while operating at a very low modulation frequency. The effect of other configuration parameters, such as a detector pixel size, on the observer performance is also discussed.

SVD for imaging systems with discrete rotational symmetry.

The singular value decomposition (SVD) of an imaging system is a computationally intensive calculation for tomographic imaging systems due to the large dimensionality of the system matrix. The computation often involves memory and storage requirements beyond those available to most end users. We have developed a method that reduces the dimension of the SVD problem towards the goal of making the calculation tractable for a standard desktop computer. In the presence of discrete rotational symmetry we show that the dimension of the SVD computation can be reduced by a factor equal to the number of collection angles for the tomographic system. In this paper we present the mathematical theory for our method, validate that our method produces the same results as standard SVD analysis, and finally apply our technique to the sensitivity matrix for a clinical CT system. The ability to compute the full singular value spectra and singular vectors will augment future work in system characterization, image-quality assessment and reconstruction techniques for tomographic imaging systems.

Maximum-Likelihood Estimation With a Contracting-Grid Search Algorithm.

A fast search algorithm capable of operating in multi-dimensional spaces is introduced. As a sample application, we demonstrate its utility in the 2D and 3D maximum-likelihood position-estimation problem that arises in the processing of PMT signals to derive interaction locations in compact gamma cameras. We demonstrate that the algorithm can be parallelized in pipelines, and thereby efficiently implemented in specialized hardware, such as field-programmable gate arrays (FPGAs). A 2D implementation of the algorithm is achieved in Cell/BE processors, resulting in processing speeds above one million events per second, which is a 20× increase in speed over a conventional desktop machine. Graphics processing units (GPUs) are used for a 3D application of the algorithm, resulting in processing speeds of nearly 250,000 events per second which is a 250× increase in speed over a conventional desktop machine. These implementations indicate the viability of the algorithm for use in real-time imaging applications.

Reconstruction-Aware Imaging System Ranking by Use of a Sparsity-Driven Numerical Observer Enabled by Variational Bayesian Inference.

It is widely accepted that optimization of imaging system performance should be guided by task-based measures of image quality. It has been advocated that imaging hardware or data-acquisition designs should be optimized by use of an ideal observer that exploits full statistical knowledge of the measurement noise and class of objects to be imaged, without consideration of the reconstruction method. In practice, accurate and tractable models of the complete object statistics are often difficult to determine. Moreover, in imaging systems that employ compressive sensing concepts, imaging hardware and sparse image reconstruction are innately coupled technologies. In this paper, a sparsity-driven observer (SDO) that can be employed to optimize hardware by use of a stochastic object model describing object sparsity is described and investigated. The SDO and sparse reconstruction method can, therefore, be "matched" in the sense that they both utilize the same statistical information regarding the class of objects to be imaged. To efficiently compute the SDO test statistic, computational tools developed recently for variational Bayesian inference with sparse linear models are adopted. The use of the SDO to rank data-acquisition designs in a stylized example as motivated by magnetic resonance imaging is demonstrated. This paper reveals that the SDO can produce rankings that are consistent with visual assessments of the reconstructed images but different from those produced by use of the traditionally employed Hotelling observer.

Objective assessment of the effects of tumor motion in radiation therapy.

PURPOSE: Internal organ motion reduces the accuracy and efficacy of radiation therapy. However, there is a lack of tools to objectively (based on a medical or scientific task) assess the dosimetric consequences of motion, especially on an individual basis. We propose to use therapy operating characteristic (TOC) analysis to quantify the effects of motion on treatment efficacy for individual patients. We demonstrate the application of this tool with pancreatic stereotactic body radiation therapy (SBRT) clinical data and explore the origin of motion sensitivity. METHODS: The technique is described as follows. (a) Use tumor-motion data measured from patients to calculate the motion-convolved dose of the gross tumor volume (GTV) and the organs at risk (OARs). (b) Calculate tumor control probability (TCP) and normal tissue complication probability (NTCP) from the motion-convolved dose-volume histograms. (c) Construct TOC curves from TCP and NTCP models. (d) Calculate the area under the TOC curve (AUTOC) and use it as a figure of merit for treatment efficacy. We used tumor motion data measured from patients to calculate the relation between AUTOC and motion magnitude for 25 pancreatic SBRT treatment plans. Furthermore, to explore the driving factor of motion sensitivity of a given plan, we compared the dose distribution of motion-sensitive plans and motion-robust plans and studied the dependence of motion sensitivity to motion directions. RESULTS: Our technique is able to recognize treatment plans that are sensitive to motion. Under the presence of motion, the treatment efficacy of some plans changes from providing high tumor control and low risks of complications to providing no tumor control and high risks of side effects. Several treatment plans experience falloffs in AUTOC at a smaller magnitude of motion than other plans. In our dataset, a potential indicator of a motion-sensitive treatment plan is that the duodenum is in proximity to the tumor in the SI direction. CONCLUSIONS: The TOC framework can serve as a tool to quantify the effects of internal organ motion in radiation therapy. With pancreatic SBRT clinical data, we applied this tool to study the change in treatment efficacy induced by motion for individual treatment plans. This framework could potentially be used clinically to understand the effects of motion in an individual patient and to design a patient-specific motion management plan. This framework could also be used in research to evaluate different components of the treatment process, such as motion-management techniques, treatment-planning algorithms, and treatment margins.

A prototype instrument for single pinhole small animal adaptive SPECT imaging.

The authors have designed and constructed a small-animal adaptive SPECT imaging system as a prototype for quantifying the potential benefit of adaptive SPECT imaging over the traditional fixed geometry approach. The optical design of the system is based on filling the detector with the region of interest for each viewing angle, maximizing the sensitivity, and optimizing the resolution in the projection images. Additional feedback rules for determining the optimal geometry of the system can be easily added to the existing control software. Preliminary data have been taken of a phantom with a small, hot, offset lesion in a flat background in both adaptive and fixed geometry modes. Comparison of the predicted system behavior with the actual system behavior is presented, along with recommendations for system improvements.

A Task-Based Approach to Adaptive and Multimodality Imaging: Computation techniques are proposed for figures-of-merit to establish feasibility and optimize use of multiple imaging systems for disease diagnosis and treatment-monitoring.

Multimodality imaging is becoming increasingly important in medical imaging. Since the motivation for combining multiple imaging modalities is generally to improve diagnostic or prognostic accuracy, the benefits of multimodality imaging cannot be assessed through the display of example images. Instead, we must use objective, task-based measures of image quality to draw valid conclusions about system performance. In this paper, we will present a general framework for utilizing objective, task-based measures of image quality in assessing multimodality and adaptive imaging systems. We introduce a classification scheme for multimodality and adaptive imaging systems and provide a mathematical description of the imaging chain along with block diagrams to provide a visual illustration. We show that the task-based methodology developed for evaluating single-modality imaging can be applied, with minor modifications, to multimodality and adaptive imaging. We discuss strategies for practical implementing of task-based methods to assess and optimize multimodality imaging systems.

Task-based design of a synthetic-collimator SPECT system used for small animal imaging.

PURPOSE: In traditional multipinhole SPECT systems, image multiplexing - the overlapping of pinhole projection images - may occur on the detector, which can inhibit quality image reconstructions due to photon-origin uncertainty. One proposed system to mitigate the effects of multiplexing is the synthetic-collimator SPECT system. In this system, two detectors, a silicon detector and a germanium detector, are placed at different distances behind the multipinhole aperture, allowing for image detection to occur at different magnifications and photon energies, resulting in higher overall sensitivity while maintaining high resolution. The unwanted effects of multiplexing are reduced by utilizing the additional data collected from the front silicon detector. However, determining optimal system configurations for a given imaging task requires efficient parsing of the complex parameter space, to understand how pinhole spacings and the two detector distances influence system performance. METHODS: In our simulation studies, we use the ensemble mean-squared error of the Wiener estimator (EMSEW ) as the figure of merit to determine optimum system parameters for the task of estimating the uptake of an 123 I-labeled radiotracer in three different regions of a computer-generated mouse brain phantom. The segmented phantom map is constructed by using data from the MRM NeAt database and allows for the reduction in dimensionality of the system matrix which improves the computational efficiency of scanning the system's parameter space. To contextualize our results, the Wiener estimator is also compared against a region of interest estimator using maximum-likelihood reconstructed data. RESULTS: Our results show that the synthetic-collimator SPECT system outperforms traditional multipinhole SPECT systems in this estimation task. We also find that image multiplexing plays an important role in the system design of the synthetic-collimator SPECT system, with optimal germanium detector distances occurring at maxima in the derivative of the percent multiplexing function. Furthermore, we report that improved task performance can be achieved by using an adaptive system design in which the germanium detector distance may vary with projection angle. Finally, in our comparative study, we find that the Wiener estimator outperforms the conventional region of interest estimator. CONCLUSIONS: Our work demonstrates how this optimization method has the potential to quickly and efficiently explore vast parameter spaces, providing insight into the behavior of competing factors, which are otherwise very difficult to calculate and study using other existing means.

Hardware assessment using the multi-module, multi-resolution system (M3R): a signal-detection study.

The multi-module, multi-resolution system (M3R) is used for hardware assessment in objective, task-based signal detection studies in projection data. A phantom capable of generating multiple realizations of a random textured background is introduced. Measured backgrounds from this phantom are used along with simulated lumpy and uniform backgrounds to investigate signal-to-noise ratio as a function of exposure time. Results are shown to agree with theoretical predictions, exhibiting a power-law like dependence previously seen for studies performed either in simulation or without an imaging system, and help validate the use of simulated lumpy backgrounds in observer studies. A second study looks at signal-detection performance, measured by AUC (area under the receiver operating characteristic curve), in lumpy backgrounds for 20 M3R aperture combinations as a function of lump size and signal size. Observer performance reveals an improvement in AUC for certain ranges of signal and lump combinations through the use of multiplexed, multiple-pinhole apertures, indicating a need for task-specific aperture optimization. The channelized Hotelling observer is used with Laguerre-Gauss channels for both observer studies. Methods for selection of number of channels and channel width are discussed.

The multi-module, multi-resolution system (M3R): a novel small-animal SPECT system.

We have designed and built an inexpensive, high-resolution, tomographic imaging system, dubbed the multi-module, multi-resolution system, or M3R. Slots machined into the system shielding allow for the interchange of pinhole plates, enabling the system to operate over a wide range of magnifications and with virtually any desired pinhole configuration. The flexibility of the system allows system optimization for specific imaging tasks and also allows for modifications necessary due to improved detectors, electronics, and knowledge of system construction (e.g., system sensitivity optimization). We provide an overview of M3R, focusing primarily on system design and construction, aperture construction, and calibration methods. Reconstruction algorithms will be described and reconstructed images presented.

Assessing computed tomography image quality for combined detection and estimation tasks.

Maintaining or even improving image quality while lowering patient dose is always the desire in clinical computed tomography (CT) imaging. Iterative reconstruction (IR) algorithms have been designed to allow for a reduced dose while maintaining or even improving an image. However, we have previously shown that the dose-saving capabilities allowed with IR are different for different clinical tasks. The channelized scanning linear observer (CSLO) was applied to study clinical tasks that combine detection and estimation when assessing CT image data. The purpose of this work is to illustrate the importance of task complexity when assessing dose savings and to move toward more realistic tasks when performing these types of studies. Human-observer validation of these methods will take place in a future publication. Low-contrast objects embedded in body-size phantoms were imaged multiple times and reconstructed by filtered back projection (FBP) and an IR algorithm. The task was to detect, localize, and estimate the size and contrast of low-contrast objects in the phantom. Independent signal-present and signal-absent regions of interest cropped from images were channelized by the dense-difference of Gauss channels for CSLO training and testing. Estimation receiver operating characteristic (EROC) curves and the areas under EROC curves (EAUC) were calculated by CSLO as the figure of merit. The one-shot method was used to compute the variance of the EAUC values. Results suggest that the IR algorithm studied in this work could efficiently reduce the dose by [Formula: see text] while maintaining an image quality comparable to conventional FBP reconstruction warranting further investigation using real patient data.