An ideal-observer framework to investigate signal detectability in diffuse optical imaging

Ideal Observer Computation by Use of Markov-Chain Monte Carlo With Generative Adversarial Networks

Medical imaging systems are often evaluated and optimized via objective, or task-specific, measures of image quality (IQ) that quantify the performance of an observer on a specific clinically-relevant task. The performance of the Bayesian Ideal Observer (IO) sets an upper limit among all observers, numerical or human, and has been advocated for use as a figure-of-merit (FOM) for evaluating and optimizing medical imaging systems. However, the IO test statistic corresponds to the likelihood ratio that is intractable to compute in the majority of cases. A sampling-based method that employs Markov-chain Monte Carlo (MCMC) techniques was previously proposed to estimate the IO performance. However, current applications of MCMC methods for IO approximation have been limited to a small number of situations where the considered distribution of to-be-imaged objects can be described by a relatively simple stochastic object model (SOM). As such, there remains an important need to extend the domain of applicability of MCMC methods to address a large variety of scenarios where IO-based assessments are needed but the associated SOMs have not been available. In this study, a novel MCMC method that employs a generative adversarial network (GAN)-based SOM, referred to as MCMC-GAN, is described and evaluated. The MCMC-GAN method was quantitatively validated by use of test-cases for which reference solutions were available. The results demonstrate that the MCMC-GAN method can extend the domain of applicability of MCMC methods for conducting IO analyses of medical imaging systems.

Modeling human observer detection in undersampled magnetic resonance imaging reconstruction with total variation and wavelet sparsity regularization

Purpose

Task-based assessment of image quality in undersampled magnetic resonance imaging provides a way of evaluating the impact of regularization on task performance. In this work, we evaluated the effect of total variation (TV) and wavelet regularization on human detection of signals with a varying background and validated a model observer in predicting human performance.

Approach

Human observer studies used two-alternative forced choice (2-AFC) trials with a small signal known exactly task but with varying backgrounds for fluid-attenuated inversion recovery images reconstructed from undersampled multi-coil data. We used a 3.48 undersampling factor with TV and a wavelet sparsity constraints. The sparse difference-of-Gaussians (S-DOG) observer with internal noise was used to model human observer detection. The internal noise for the S-DOG was chosen to match the average percent correct (PC) in 2-AFC studies for four observers using no regularization. That S-DOG model was used to predict the PC of human observers for a range of regularization parameters.

Results

We observed a trend that the human observer detection performance remained fairly constant for a broad range of values in the regularization parameter before decreasing at large values. A similar result was found for the normalized ensemble root mean squared error. Without changing the internal noise, the model observer tracked the performance of the human observers as the regularization was increased but overestimated the PC for large amounts of regularization for TV and wavelet sparsity, as well as the combination of both parameters.

Conclusions

For the task we studied, the S-DOG observer was able to reasonably predict human performance with both TV and wavelet sparsity regularizers over a broad range of regularization parameters. We observed a trend that task performance remained fairly constant for a range of regularization parameters before decreasing for large amounts of regularization.

Ideal-Observer Computation with anthropomorphic phantoms using Markov chain Monte Carlo

In medical imaging, it is widely recognized that image quality should be objectively evaluated based on performance in clinical tasks. To evaluate performance in signal-detection tasks, the ideal observer (IO) is optimal but also challenging to compute in clinically realistic settings. Markov Chain Monte Carlo (MCMC)-based strategies have demonstrated the ability to compute the IO using pre-computed projections of an anatomical database. To evaluate image quality in clinically realistic scenarios, the observer performance should be measured for a realistic patient distribution. This implies that the anatomical database should also be derived from a realistic population. In this manuscript, we propose to advance the MCMC-based approach towards achieving these goals. We then use the proposed approach to study the effect of anatomical database size on IO computation for the task of detecting perfusion defects in simulated myocardial perfusion SPECT images. Our preliminary results provide evidence that the size of the anatomical database affects the computation of the IO.

Objective Task-Based Evaluation of Artificial Intelligence-Based Medical Imaging Methods:: Framework, Strategies, and Role of the Physician

Artificial intelligence-based methods are showing promise in medical imaging applications. There is substantial interest in clinical translation of these methods, requiring that they be evaluated rigorously. We lay out a framework for objective task-based evaluation of artificial intelligence methods. We provide a list of available tools to conduct this evaluation. We outline the important role of physicians in conducting these evaluation studies. The examples in this article are proposed in the context of PET scans with a focus on evaluating neural network-based methods. However, the framework is also applicable to evaluate other medical imaging modalities and other types of artificial intelligence methods.

Task-based assessment of binned and list-mode SPECT systems

In SPECT, list-mode (LM) format allows storing data at higher precision compared to binned data. There is significant interest in investigating whether this higher precision translates to improved performance on clinical tasks. Towards this goal, in this study, we quantitatively investigated whether processing data in LM format, and in particular, the energy attribute of the detected photon, provides improved performance on the task of absolute quantification of region-of-interest (ROI) uptake in comparison to processing the data in binned format. We conducted this evaluation study using a DaTscan brain SPECT acquisition protocol, conducted in the context of imaging patients with Parkinson's disease. This study was conducted with a synthetic phantom. A signal-known exactly/background-known-statistically (SKE/BKS) setup was considered. An ordered-subset expectation-maximization algorithm was used to reconstruct images from data acquired in LM format, including the scatter-window data, and including the energy attribute of each LM event. Using a realistic 2-D SPECT system simulation, quantification tasks were performed on the reconstructed images. The results demonstrated improved quantification performance when LM data was used compared to binning the attributes in all the conducted evaluation studies. Overall, we observed that LM data, including the energy attribute, yielded improved performance on absolute quantification tasks compared to binned data.

Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging

We propose a formalism to incorporate boundary conditions in a Neumann-series-based radiative transport equation. The formalism accurately models the reflection of photons at the tissue-external medium interface using Fresnel's equations. The formalism was used to develop a gradient descent-based image reconstruction technique. The proposed methods were implemented for 3D diffuse optical imaging. In computational studies, it was observed that the average root-mean-square error (RMSE) for the output images and the estimated absorption coefficients reduced by 38% and 84%, respectively, when the reflection boundary conditions were incorporated. These results demonstrate the importance of incorporating boundary conditions that model the reflection of photons at the tissue-external medium interface.

Use of Sub-Ensembles and Multi-Template Observers to Evaluate Detection Task Performance for Data That are Not Multivariate Normal

The Hotelling Observer (HO) is widely used to evaluate image quality in medical imaging. However, applying it to data that are not multivariate-normally (MVN) distributed is not optimal. In this paper, we apply two multi-template linear observer strategies to handle such data. First, the entire data ensemble is divided into sub-ensembles that are exactly or approximately MVN and homoscedastic. Next, a different linear observer template is estimated for and applied to each sub-ensemble. The first multi-template strategy, adapted from previous work, applies the HO to each sub-ensemble, calculates the area under the receiver operating characteristics curve (AUC) for each sub-ensemble, and averages the AUCs from all the sub-ensembles. The second strategy applies the Linear Discriminant (LD) to estimate test statistics for each sub-ensemble and calculates a single global AUC using the pooled test statistics from all the sub-ensembles. We show that this second strategy produces the maximum AUC when only shifting of the HO test statistics is allowed. We compared these strategies to the use of a single HO template for the entire data ensemble by applying them to the non-MVN data obtained from reconstructed images of a realistic simulated population of myocardial perfusion SPECT studies with the goal of optimizing the reconstruction parameters. Of the strategies investigated, the multi-template LD strategy yielded the highest AUC for any given set of reconstruction parameters. The optimal reconstruction parameters obtained by the two multi-template strategies were comparable and produced higher AUCs for each sub-ensemble than the single-template HO strategy.

A radiative transfer equation-based image-reconstruction method incorporating boundary conditions for diffuse optical imaging

Developing reconstruction methods for diffuse optical imaging requires accurate modeling of photon propagation, including boundary conditions arising due to refractive index mismatch as photons propagate from the tissue to air. For this purpose, we developed an analytical Neumann-series radiative transport equation (RTE)-based approach. Each Neumann series term models different scattering, absorption, and boundary-reflection events. The reflection is modeled using the Fresnel equation. We use this approach to design a gradient-descent-based analytical reconstruction algorithm for a three-dimensional (3D) setup of a diffuse optical imaging (DOI) system. The algorithm was implemented for a three-dimensional DOI system consisting of a laser source, cuboidal scattering medium (refractive index > 1), and a pixelated detector at one cuboid face. In simulation experiments, the refractive index of the scattering medium was varied to test the robustness of the reconstruction algorithm over a wide range of refractive index mismatches. The experiments were repeated over multiple noise realizations. Results showed that by using the proposed algorithm, the photon propagation was modeled more accurately. These results demonstrated the importance of modeling boundary conditions in the photon-propagation model.

A three-step reconstruction method for fluorescence molecular tomography based on compressive sensing

Fluorescence molecular tomography (FMT) is a promising tool for real time in vivo quantification of neurotransmission (NT) as we pursue in our BRAIN initiative effort. However, the acquired image data are noisy and the reconstruction problem is ill-posed. Further, while spatial sparsity of the NT effects could be exploited, traditional compressive-sensing methods cannot be directly applied as the system matrix in FMT is highly coherent. To overcome these issues, we propose and assess a three-step reconstruction method. First, truncated singular value decomposition is applied on the data to reduce matrix coherence. The resultant image data are input to a homotopy-based reconstruction strategy that exploits sparsity via ℓ₁ regularization. The reconstructed image is then input to a maximum-likelihood expectation maximization (MLEM) algorithm that retains the sparseness of the input estimate and improves upon the quantitation by accurate Poisson noise modeling. The proposed reconstruction method was evaluated in a three-dimensional simulated setup with fluorescent sources in a cuboidal scattering medium with optical properties simulating human brain cortex (reduced scattering coefficient: 9.2 cm^-1, absorption coefficient: 0.1 cm^-1) and tomographic measurements made using pixelated detectors. In different experiments, fluorescent sources of varying size and intensity were simulated. The proposed reconstruction method provided accurate estimates of the fluorescent source intensity, with a 20% lower root mean square error on average compared to the pure-homotopy method for all considered source intensities and sizes. Further, compared with conventional ℓ₂ regularized algorithm, overall, the proposed method reconstructed substantially more accurate fluorescence distribution. The proposed method shows considerable promise and will be tested using more realistic simulations and experimental setups.

Radiance and photon noise: imaging in geometrical optics, physical optics, quantum optics and radiology

The statistics of detector outputs produced by an imaging system are derived from basic radiometric concepts and definitions. We show that a fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular, and wavelength variables. We begin the paper by recalling the concept of radiance in geometrical optics, radiology, physical optics, and quantum optics. The propagation and conservation laws for radiance in each of these domains are reviewed. Building upon these concepts, we distinguish four categories of imaging detectors that all respond in some way to the incident radiance, including the new category of photon-processing detectors (capable of measuring radiance on a photon-by-photon basis). This allows us to rigorously show how the concept of radiance is related to the statistical properties of detector outputs and to the information content of a single detected photon. A Monte-Carlo technique, which is derived from the Boltzmann transport equation, is presented as a way to estimate probability density functions to be used in reconstruction from photon-processing data.

RADIANCE AND PHOTON NOISE: Imaging in geometrical optics, physical optics, quantum optics and radiology

A fundamental way of describing a photon-limited imaging system is in terms of a Poisson random process in spatial, angular and wavelength variables. The mean of this random process is the spectral radiance. The principle of conservation of radiance then allows a full characterization of the noise in the image (conditional on viewing a specified object). To elucidate these connections, we first review the definitions and basic properties of radiance as defined in terms of geometrical optics, radiology, physical optics and quantum optics. The propagation and conservation laws for radiance in each of these domains are reviewed. Then we distinguish four categories of imaging detectors that all respond in some way to the incident radiance, including the new category of photon-processing detectors. The relation between the radiance and the statistical properties of the detector output is discussed and related to task-based measures of image quality and the information content of a single detected photon.