We are engaged in a variety of research projects related to to theoretical and computational aspects of imaging science. We are particularly interested in the development and adaptation of modern machine learning methods for advancing methodologies for imaging quality assessment imaging system optimization.

**Sparsity-Driven Ideal Observer**

It is widely accepted that optimization of imaging system performance should be guided by task-based measures of image quality (IQ). Conventional wisdom dictates that imaging hardware or data-acquisition designs should be optimized by use of an ideal observer (IO) 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 project, a sparsity-driven ideal observer (SDIO) that can be employed to optimize hardware by use of a stochastic object model describing object sparsity is being developed and investigated. The SDIO 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 SDIO test statistic, computational tools developed recently for variational Bayesian inference with sparse linear models are being adopted. Our preliminary studies have revealed that the SDIO can produce rank orderings of data-acquisition designs that differ from those produced by use of the Hotelling observer (HO).

# Uncertainty Estimation in for Sparse Image Reconstruction

Point estimates, such as the maximum a posteriori (MAP) estimate, are commonly computed in image reconstruction tasks. However, such point estimates provide no information about the range of highly probable solutions or uncertainty in the computed estimate. Bayesian inference methods that seek to compute the posterior probability distribution function (PDF) of the object can achieve exactly these things, but are generally too computationally burdensome to be applied to medical image reconstruction problems. Moreover, sampling methods, such as the Monte Carlo Markov Chain (MCMC) method, require considerable expertise to run in a proper way. In this project, computationally-efficient variational Bayesian inference approaches are being investigated for use in computing the posterior image variance. The posterior variance map provides valuable information that reveals how noise level, data-acquisition parameters, and specification of the object prior will affect the reliability of a reconstructed MAP image estimate. Our methodology assumes that the object prior is described by a Laplacian distribution, which corresponds to use of an l_{1}-norm-based penalty in the associated MAP estimator.

# Deep Learning-Based Numerical Observers

It is widely accepted that optimization of imaging system performance should be guided by task-based measures of image quality (IQ). Task-based measures of IQ quantify the ability of an observer to perform a specified medically relevant task. An upper performance limit for a binary signal detection task is achieved by the Bayesian ideal observer (IO), which is a numerical observer that employs complete knowledge of the object and noise statistics. However, computation of the IO detection performance is, in general, not analytically tractable. In this project, methodologies that employ convolutional neural networks (CNNs) to approximate the IO test statistic for both signal-known-exactly and signal-known-statistically binary detection tasks are being developed and investigated. A methodology for training a CNN to approximate the Hotelling Observer (HO) is also being developed. Both background-known-exactly and background-known-statistically cases are considered. The ROC curves produced by use of the CNN-based methods are being compared to those produced by use of the Markov-Chain Monte Carlo (MCMC) method or the analytically computed HO. The advantages of the proposed supervised learning approaches for approximating these numerical observer models are being investigated.