In certain three-dimensional (3D) applications of photoacoustic computed tomography (PACT), including in vivo breast imaging, hemispherical measurement apertures that enclose the object within their convex hull are employed for data acquisition. Data acquired with such measurement geometries are referred to as half-scan data, as only half of a complete spherical measurement aperture is employed. Although previous studies have shown that half-scan data can uniquely and stably reconstruct the sought-after object, no associated closed-form reconstruction formula has been reported. To accurately reconstruct images from half-scan data, optimization-based iterative reconstruction methods can be employed; however, they are computationally expensive. To address this limitation, a learning-based filtered backprojection (FBP) reconstruction method, referred to as the half-scan FBP method, is developed in this work. Because the explicit form of the filtering operation in the half-scan FBP method is not currently known, a learning-based method is proposed to approximate it. The proposed method is systematically investigated by use of virtual imaging studies of 3D breast PACT that employ ensembles of numerical breast phantoms and a physics-based model of the data acquisition process. The method is subsequently applied to experimental data acquired in an in vivo breast PACT study. The results confirm that the half-scan FBP method can accurately reconstruct 3D images from half-scan data, while offering a substantial computational speed-up over iterative methods. Importantly, because the sought-after inverse mapping is well-posed, the reconstruction method remains accurate even when applied to data that differ considerably from those employed to learn the filtering operation.

Objective, task-based measures of image quality (IQ) have been widely advocated for assessing and optimizing medical imaging technologies. Besides signal detection theory-based measures, information-theoretic quantities have been proposed to quantify task-based IQ. For example, task-specific information (TSI), defined as the mutual information between an image and a task variable, represents an optimal measure of how informative an image is for performing a specified task. However, like the ideal observer from signal detection theory, TSI does not quantify the amount of task-relevant information in an image that can be exploited by a sub-ideal observer. A recently proposed relaxation of TSI, termed predictive $\mathcal {V}$ -information ( $\mathcal {V}$ -info), removes this limitation and can quantify the utility of an image with consideration of a specified family of sub-ideal observers. In this study, for the first time, we introduce and investigate $\mathcal {V}$ -info as an objective, task-specific IQ metric. To corroborate its usefulness, a stylized magnetic resonance image restoration problem is considered in which $\mathcal {V}$ -info is employed to quantify signal detection or discrimination performance. The presented experiments show that, for binary classification tasks, $\mathcal {V}$ -info varies consistently with the area under the receiver operating characteristic (ROC) curve in regimes where class separability changes with observer capacity or imaging conditions. However, unlike AUC, $\mathcal {V}$ -info remains sensitive in regimes where discrimination performance approaches saturation. In addition, $\mathcal {V}$ -info is readily applicable to multi-class ( $\gt {2}$ ) tasks where ROC analysis is less natural. These findings suggest that $\mathcal {V}$ -info can serve as a complementary task-based image quality measure alongside traditional signal detection theory-based metrics.

Computational wave imaging (CWI) extracts hidden structure and physical properties of a volume of material by analyzing wave signals that traverse that volume. Applications include seismic exploration of the Earth's subsurface, acoustic imaging and non-destructive testing in material science, and ultrasound computed tomography in medicine. Current approaches for solving CWI problems can be divided into two categories: those rooted in traditional physics, and those based on deep learning. Physics-based methods stand out for their ability to provide high-resolution and quantitatively accurate estimates of acoustic properties within the medium. However, they can be computationally intensive and are susceptible to ill-posedness and nonconvexity typical of CWI problems. Machine learning-based computational methods have recently emerged, offering a different perspective to address these challenges. Diverse scientific communities have independently pursued the integration of deep learning in CWI. This review discusses how contemporary scientific machine-learning (ML) techniques, and deep neural networks in particular, have been developed to enhance and integrate with traditional physics-based methods for solving CWI problems. We present a structured framework that consolidates existing research spanning multiple domains, including computational imaging, wave physics, and data science. This study concludes with important lessons learned from existing ML-based methods and identifies technical hurdles and emerging trends through a systematic analysis of the extensive literature on this topic.

Transcranial photoacoustic computed tomography presents challenges in human brain imaging due to skull-induced acoustic aberration. Existing full-wave image reconstruction methods rely on a unified elastic wave equa- tion for skull shear and longitudinal wave propagation, therefore demanding substantial computational resources. We propose an efficient discrete imaging model based on finite element discretization. The elastic wave equation for solids is solely applied to the hard-tissue skull region, while the soft-tissue or coupling-medium region that dominates the simulation domain is modeled with the simpler acoustic wave equation for liquids. The solid-liquid interfaces are explicitly modeled with elastic-acoustic coupling. Furthermore, finite element discretization allows coarser, irregular meshes to conform to object geometry. These factors significantly reduce the linear system size by 20 times to facilitate accurate whole-brain simulations with improved speed. We derive a matched forward-adjoint operator pair based on the model to enable integration with various optimization algorithms. We validate the reconstruction framework through numerical simulations and phantom experiments.

Deep generative models (DGMs) have the potential to revolutionize diagnostic imaging. Generative adversarial networks (GANs) are one kind of DGM which are widely employed. The overarching problem with deploying any sort of DGM in mission-critical applications is a lack of adequate and/or automatic means of assessing the domain-specific quality of generated images. In this work, we demonstrate several objective and human-interpretable tests of images output by two popular DGMs. These tests serve two goals: (i) ruling out DGMs for downstream, domain-specific applications, and (ii) quantifying hallucinations in the expected spatial context in DGM-generated images. The designed datasets are made public and the proposed tests could also serve as benchmarks and aid the prototyping of emerging DGMs. Although these tests are demonstrated on GANs, they can be employed as a benchmark for evaluating any DGM. Specifically, we designed several stochastic context models (SCMs) of distinct image features that can be recovered after generation by a trained DGM. Together, these SCMs encode features as per-image constraints in prevalence, position, intensity, and/or texture. Several of these features are high-order, algorithmic pixel-arrangement rules which are not readily expressed in covariance matrices. We designed and validated statistical classifiers to detect specific effects of the known arrangement rules. We then tested the rates at which two different DGMs correctly reproduced the feature context under a variety of training scenarios, and degrees of feature-class similarity. We found that ensembles of generated images can appear largely accurate visually, and show high accuracy in ensemble measures, while not exhibiting the known spatial arrangements. The main conclusion is that SCMs can be engineered, and serve as benchmarks, to quantify numerous per image errors, i.e., hallucinations, that may not be captured in ensemble statistics but plausibly can affect subsequent use of the DGM-generated images.

Diffusion models have emerged as a popular family of deep generative models (DGMs). In the literature, it has been claimed that one class of diffusion models-denoising diffusion probabilistic models (DDPMs)-demonstrate superior image synthesis performance as compared to generative adversarial networks (GANs). To date, these claims have been evaluated using either ensemble-based methods designed for natural images, or conventional measures of image quality such as structural similarity. However, there remains an important need to understand the extent to which DDPMs can reliably learn medical imaging domain-relevant information, which is referred to as 'spatial context' in this work. To address this, a systematic assessment of the ability of DDPMs to learn spatial context relevant to medical imaging applications is reported for the first time. A key aspect of the studies is the use of stochastic context models (SCMs) to produce training data. In this way, the ability of the DDPMs to reliably reproduce spatial context can be quantitatively assessed by use of post-hoc image analyses. Error-rates in DDPM-generated ensembles are reported, and compared to those corresponding to other modern DGMs. The studies reveal new and important insights regarding the capacity of DDPMs to learn spatial context. Notably, the results demonstrate that DDPMs hold significant capacity for generating contextually correct images that are 'interpolated' between training samples, which may benefit data-augmentation tasks in ways that GANs cannot.

Interpretability is highly desired for deep neural network-based classifiers, especially when addressing high-stake decisions in medical imaging. Commonly used post-hoc interpretability methods have the limitation that they can produce plausible but different interpretations of a given model, leading to ambiguity about which one to choose. To address this problem, a novel decision-theory-inspired approach is investigated to establish a self-interpretable model, given a pre-trained deep binary black-box medical image classifier. This approach involves utilizing a self-interpretable encoder-decoder model in conjunction with a single-layer fully connected network with unity weights. The model is trained to estimate the test statistic of the given trained black-box deep binary classifier to maintain a similar accuracy. The decoder output image, referred to as an equivalency map, is an image that represents a transformed version of the to-be-classified image that, when processed by the fixed fully connected layer, produces the same test statistic value as the original classifier. The equivalency map provides a visualization of the transformed image features that directly contribute to the test statistic value and, moreover, permits quantification of their relative contributions. Unlike the traditional post-hoc interpretability methods, the proposed method is self-interpretable, quantitative. Detailed quantitative and qualitative analyses have been performed with three different medical image binary classification tasks.

In recent years, generative adversarial networks (GANs) have gained tremendous popularity for potential applications in medical imaging, such as medical image synthesis, restoration, reconstruction, translation, as well as objective image quality assessment. Despite the impressive progress in generating high-resolution, perceptually realistic images, it is not clear if modern GANs reliably learn the statistics that are meaningful to a downstream medical imaging application. In this work, the ability of a state-of-the-art GAN to learn the statistics of canonical stochastic image models (SIMs) that are relevant to objective assessment of image quality is investigated. It is shown that although the employed GAN successfully learned several basic first- and second-order statistics of the specific medical SIMs under consideration and generated images with high perceptual quality, it failed to correctly learn several per-image statistics pertinent to the these SIMs, highlighting the urgent need to assess medical image GANs in terms of objective measures of image quality.

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.

The ideal observer (IO) sets an upper performance limit among all observers and has been advocated for assessing and optimizing imaging systems. For general joint detection and estimation (detection-estimation) tasks, estimation ROC (EROC) analysis has been established for evaluating the performance of observers. However, in general, it is difficult to accurately approximate the IO that maximizes the area under the EROC curve. In this study, a hybrid method that employs machine learning is proposed to accomplish this. Specifically, a hybrid approach is developed that combines a multi-task convolutional neural network and a Markov-Chain Monte Carlo (MCMC) method in order to approximate the IO for detection-estimation tasks. Unlike traditional MCMC methods, the hybrid method is not limited to use of specific utility functions. In addition, a purely supervised learning-based sub-ideal observer is proposed. Computer-simulation studies are conducted to validate the proposed method, which include signal-known-statistically/background-known-exactly and signal-known-statistically/background-known-statistically tasks. The EROC curves produced by the proposed method are compared to those produced by the MCMC approach or analytical computation when feasible. The proposed method provides a new approach for approximating the IO and may advance the application of EROC analysis for optimizing imaging systems.

Obtaining a useful estimate of an object from highly incomplete imaging measurements remains a holy grail of imaging science. Deep learning methods have shown promise in learning object priors or constraints to improve the conditioning of an ill-posed imaging inverse problem. In this study, a framework for estimating an object of interest that is semantically related to a known prior image, is proposed. An optimization problem is formulated in the disentangled latent space of a style-based generative model, and semantically meaningful constraints are imposed using the disentangled latent representation of the prior image. Stable recovery from incomplete measurements with the help of a prior image is theoretically analyzed. Numerical experiments demonstrating the superior performance of our approach as compared to related methods are presented.

A variety of deep neural network (DNN)-based image denoising methods have been proposed for use with medical images. Traditional measures of image quality (IQ) have been employed to optimize and evaluate these methods. However, the objective evaluation of IQ for the DNN-based denoising methods remains largely lacking. In this work, we evaluate the performance of DNN-based denoising methods by use of task-based IQ measures. Specifically, binary signal detection tasks under signal-known-exactly (SKE) with background-known-statistically (BKS) conditions are considered. The performance of the ideal observer (IO) and common linear numerical observers are quantified and detection efficiencies are computed to assess the impact of the denoising operation on task performance. The numerical results indicate that, in the cases considered, the application of a denoising network can result in a loss of task-relevant information in the image. The impact of the depth of the denoising networks on task performance is also assessed. The presented results highlight the need for the objective evaluation of IQ for DNN-based denoising technologies and may suggest future avenues for improving their effectiveness in medical imaging applications.

Tomographic image reconstruction is generally an ill-posed linear inverse problem. Such ill-posed inverse problems are typically regularized using prior knowledge of the sought-after object property. Recently, deep neural networks have been actively investigated for regularizing image reconstruction problems by learning a prior for the object properties from training images. However, an analysis of the prior information learned by these deep networks and their ability to generalize to data that may lie outside the training distribution is still being explored. An inaccurate prior might lead to false structures being hallucinated in the reconstructed image and that is a cause for serious concern in medical imaging. In this work, we propose to illustrate the effect of the prior imposed by a reconstruction method by decomposing the image estimate into generalized measurement and null components. The concept of a hallucination map is introduced for the general purpose of understanding the effect of the prior in regularized reconstruction methods. Numerical studies are conducted corresponding to a stylized tomographic imaging modality. The behavior of different reconstruction methods under the proposed formalism is discussed with the help of the numerical studies.

Medical imaging systems are commonly assessed and optimized by use of objective measures of image quality (IQ). The Ideal Observer (IO) performance has been advocated to provide a figure-of-merit for use in assessing and optimizing imaging systems because the IO sets an upper performance limit among all observers. When joint signal detection and localization tasks are considered, the IO that employs a modified generalized likelihood ratio test maximizes observer performance as characterized by the localization receiver operating characteristic (LROC) curve. Computations of likelihood ratios are analytically intractable in the majority of cases. Therefore, sampling-based methods that employ Markov-Chain Monte Carlo (MCMC) techniques have been developed to approximate the likelihood ratios. However, the applications of MCMC methods have been limited to relatively simple object models. Supervised learning-based methods that employ convolutional neural networks have been recently developed to approximate the IO for binary signal detection tasks. In this paper, the ability of supervised learning-based methods to approximate the IO for joint signal detection and localization tasks is explored. Both background-known-exactly and background-known-statistically signal detection and localization tasks are considered. The considered object models include a lumpy object model and a clustered lumpy model, and the considered measurement noise models include Laplacian noise, Gaussian noise, and mixed Poisson-Gaussian noise. The LROC curves produced by the supervised learning-based method are compared to those produced by the MCMC approach or analytical computation when feasible. The potential utility of the proposed method for computing objective measures of IQ for optimizing imaging system performance is explored.

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.

It is widely accepted that the optimization of medical 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 specific task, such as detection or estimation of a signal (e.g., a tumor). For binary signal detection tasks, the Bayesian Ideal Observer (IO) sets an upper limit of observer performance and has been advocated for use in optimizing medical imaging systems and data-acquisition designs. Except in special cases, the determination of the IO test statistic is analytically intractable. Markov-chain Monte Carlo (MCMC) techniques can be employed to approximate the IO detection performance, but their reported applications have been limited to relatively simple object models. In cases where the IO test statistic is difficult to compute, the Hotelling Observer (HO) can be employed. To compute the HO test statistic, potentially large covariance matrices must be accurately estimated and subsequently inverted, which can present computational challenges. This paper investigates the supervised learning-based methodologies for approximating the IO and HO test statistics. Convolutional neural networks (CNNs) and single-layer neural networks (SLNNs) are employed to approximate the IO and HO test statistics, respectively. The numerical simulations were conducted for both signal-known-exactly (SKE) and signal-known-statistically (SKS) signal detection tasks. The considered background models include the lumpy object model and the clustered lumpy object model. The measurement noise models considered are Gaussian, Laplacian, and mixed Poisson-Gaussian. The performances of the supervised learning methods are assessed via receiver operating characteristic (ROC) analysis, and the results are compared to those produced by the use of traditional numerical methods or analytical calculations when feasible. The potential advantages of the proposed supervised learning approaches for approximating the IO and HO test statistics are discussed.

Accurate estimation of the initial pressure distribution in photoacoustic computed tomography (PACT) depends on knowledge of the sound speed distribution. However, the sound speed distribution is typically unknown. Further, the initial pressure and sound speed distributions cannot both, in general, be stably recovered from PACT measurements alone. In this work, a joint reconstruction (JR) method for the initial pressure distribution and a low-dimensional parameterized model of the sound speed distribution is proposed. By employing a priori information about the structure of the sound speed distribution, both the initial pressure and sound speed can be accurately recovered. The JR problem is solved by use of a proximal optimization method that allows constraints and nonsmooth regularization functions for the initial pressure distribution. The gradients of the cost function with respect to the initial pressure and sound speed distributions are calculated by use of an adjoint state method that has the same per-iteration computational cost as calculating the gradient with respect to the initial pressure distribution alone. This approach is evaluated through two-dimensional computer-simulation studies for a small animal imaging model and by application to experimental in vivo measurements of a mouse.

Photoacoustic computed tomography (PACT) is an emerging imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to an inverse source problem in which the initial pressure distribution is recovered from measurements of the radiated wavefield. A major challenge in transcranial PACT brain imaging is compensation for aberrations in the measured data due to the presence of the skull. Ultrasonic waves undergo absorption, scattering and longitudinal-to-shear wave mode conversion as they propagate through the skull. To properly account for these effects, a wave-equation-based inversion method should be employed that can model the heterogeneous elastic properties of the skull. In this work, a forward model based on a finite-difference time-domain discretization of the three-dimensional elastic wave equation is established and a procedure for computing the corresponding adjoint of the forward operator is presented. Massively parallel implementations of these operators employing multiple graphics processing units (GPUs) are also developed. The developed numerical framework is validated and investigated in computer19 simulation and experimental phantom studies whose designs are motivated by transcranial PACT applications.

The development of spectral X-ray computed tomography (CT) using binned photon-counting detectors has received great attention in recent years and has enabled selective imaging of contrast agents loaded with K-edge materials. A practical issue in implementing this technique is the mitigation of the high-noise levels often present in material-decomposed sinogram data. In this work, the spectral X-ray CT reconstruction problem is formulated within a multi-channel (MC) framework in which statistical correlations between the decomposed material sinograms can be exploited to improve image quality. Specifically, a MC penalized weighted least squares (PWLS) estimator is formulated in which the data fidelity term is weighted by the MC covariance matrix and sparsity-promoting penalties are employed. This allows the use of any number of basis materials and is therefore applicable to photon-counting systems and K-edge imaging. To overcome numerical challenges associated with use of the full covariance matrix as a data fidelity weight, a proximal variant of the alternating direction method of multipliers is employed to minimize the MC PWLS objective function. Computer-simulation and experimental phantom studies are conducted to quantitatively evaluate the proposed reconstruction method.

Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT.

Existing approaches to image reconstruction in photoacoustic computed tomography (PACT) with acoustically heterogeneous media are limited to weakly varying media, are computationally burdensome, and/or cannot effectively mitigate the effects of measurement data incompleteness and noise. In this work, we develop and investigate a discrete imaging model for PACT that is based on the exact photoacoustic (PA) wave equation and facilitates the circumvention of these limitations. A key contribution of the work is the establishment of a procedure to implement a matched forward and backprojection operator pair associated with the discrete imaging model, which permits application of a wide-range of modern image reconstruction algorithms that can mitigate the effects of data incompleteness and noise. The forward and backprojection operators are based on the k-space pseudospectral method for computing numerical solutions to the PA wave equation in the time domain. The developed reconstruction methodology is investigated by use of both computer-simulated and experimental PACT measurement data.

Photon-counting detector technology has enabled the first experimental investigations of energy-resolved computed tomography (CT) imaging and the potential use for K-edge imaging. However, limitations in regards to detecter technology have been imposing a limit to effective count rates. As a consequence, this has resulted in high noise levels in the obtained images given scan time limitations in CT imaging applications. It has been well recognized in the area of low-dose imaging with conventional CT that iterative image reconstruction provides a superior signal to noise ratio compared to traditional filtered backprojection techniques. Furthermore, iterative reconstruction methods also allow for incorporation of a roughness penalty function in order to make a trade-off between noise and spatial resolution in the reconstructed images. In this work, we investigate statistically-principled iterative image reconstruction from material-decomposed sinograms in spectral CT. The proposed reconstruction algorithm seeks to minimize a penalized likelihood-based cost functional, where the parameters of the likelihood function are estimated by computing the Fisher information matrix associated with the material decomposition step. The performance of the proposed reconstruction method is quantitatively investigated by use of computer-simulated and experimental phantom data. The potential for improved K-edge imaging is also demonstrated in an animal experiment.

Optoacoustic tomography (OAT) is a hybrid imaging modality that combines the advantages of optical and ultrasound imaging. Most existing reconstruction algorithms for OAT assume that the ultrasound transducers employed to record the measurement data are point-like. When transducers with large detecting areas and/or compact measurement geometries are utilized, this assumption can result in conspicuous image blurring and distortions in the reconstructed images. In this work, a new OAT imaging model that incorporates the spatial and temporal responses of an ultrasound transducer is introduced. A discrete form of the imaging model is implemented and its numerical properties are investigated. We demonstrate that use of the imaging model in an iterative reconstruction method can improve the spatial resolution of the optoacoustic images as compared to those reconstructed assuming point-like ultrasound transducers.

We analyze some relationships between the small- and smooth-phase conditions in propagation-based X-ray phase-contrast imaging. Although these conditions are generally well-understood, our analysis yields the identification of physical conditions under which they are mathematically equivalent. We also demonstrate that the smooth-phase condition depends not only on the imaging system resolution and object-to-detector distance, but also on the topography of the wavefield phase function.

In the classic formulation of photoacoustic tomography (PAT), two distinct descriptions of the imaging model have been employed for developing reconstruction algorithms. We demonstrate that the numerical and statistical properties of unweighted least-squares reconstruction algorithms associated with each imaging model are generally very different. Specifically, some PAT reconstruction algorithms, including many of the iterative algorithms previously explored, do not work directly with the raw measured pressure wavefields, but rather with an integrated data function that is obtained by temporally integrating the photoacoustic wavefield. The integration modifies the statistical distribution of the data, introducing statistical correlations among samples. This change is highly significant for iterative algorithms, many of which explicitly or implicitly seek to minimize a statistical cost function. In this work, we demonstrate that iterative reconstruction by least-squares minimization yields better resolution-noise tradeoffs when working with the raw pressure data than with the integrated data commonly employed. In addition, we demonstrate that the raw-data based approach is less sensitive to certain deterministic errors, such as dc offset errors.

Thermoacoustic tomography (TAT) is an emerging imaging technique with great potential for a wide range of biomedical imaging applications. In this paper, we propose and investigate reconstruction approaches for TAT that are based on the half-time reflectivity tomography paradigm. We reveal that half-time reconstruction approaches permit for the explicit control of statistically complementary information that can result in the optimal reduction of image variances. We also show that half-time reconstruction approaches can mitigate image artifacts due to heterogeneous acoustic properties of an object. Reconstructed images and numerical results produced from simulated and experimental TAT measurement data are employed to demonstrate these effects.

Reflectivity tomography is an imaging technique that seeks to reconstruct certain acoustic properties of a weakly scattering object. Besides being applicable to pure ultrasound imaging techniques, the reconstruction theory of reflectivity tomography is also pertinent to hybrid imaging techniques such as thermoacoustic tomography. In this work, assuming spherical scanning apertures, redundancies in the three-dimensional (3-D) reflectivity tomography data function are identified and formulated mathematically. These data redundancies are used to demonstrate that knowledge of the measured data function over half of its domain uniquely specifies the 3-D object function. This indicates that, in principle, exact image reconstruction can be performed using a "half-scan" data function, which corresponds to temporally untruncated measurements acquired on a hemi-spherical aperture, or using a "half-time" data function, which corresponds to temporally truncated measurements acquired on the entire spherical aperture. Both of these minimal scanning configurations have important biological imaging applications. An iterative reconstruction method is utilized for reconstruction of a simulated 3-D object from noiseless and noisy half-scan and half-time data functions.

Thermoacoustic tomography (TAT) is an emerging imaging technique with potential for a wide range of biomedical imaging applications. In this correspondence, we propose an infinite family of weighted expectation maximization (EM) algorithms for reconstruction of images from temporally truncated TAT measurement data. The weighted EM algorithms are equivalent mathematically to the conventional EM algorithm, but are shown to propagate data inconsistencies in different ways. Using simulated and experimental TAT measurement data, we demonstrate that suitable choices of weighted EM algorithms can effectively mitigate image artifacts that are attributable to temporal truncation of the TAT data function.

In reflectivity tomography, conventional reconstruction approaches require that measurements be acquired at view angles that span a full angular range of 2pi. It is often, however, advantageous to reduce the angular range over which measurements are acquired, in order, for example, to minimize artifacts due to movements of the imaged object. Moreover, in certain situations, it may not be experimentally possible to collect data over a 2pi angular range. We investigate the problem of reconstructing images from reduced-scan data in reflectivity tomography. By exploiting symmetries in the data function of reflectivity tomography, we demonstrate heuristically that an image function can be uniquely specified by reduced-scan data that correspond to measurements taken over an angular interval (possibly disjoint) that spans at least pi radians. We also identify sufficient conditions that permit for a stable reconstruction of image boundaries from reduced-scan data. Numerical results in computer-simulation studies indicate that images can be reconstructed accurately from reduced-scan data.

Diffraction tomography (DT) is an inversion technique that reconstructs the refractive index distribution of a scattering object. We previously demonstrated that by exploiting the redundant information in the DT data, the scattering object could be exactly reconstructed using measurements taken over the angular range [0, phimin], where pi < phimin < or = 3pi/2. In this paper, we reveal a relationship between the maximum scanning angle and image resolution when a filtered backpropagation (FBPP) reconstruction algorithm is employed for image reconstruction. Based on this observation, we develop short-scan FBPP algorithms that reconstruct a low-pass filtered scattering object from measurements acquired over the angular range [0, phi(c)], where phi(c) < phimin.

The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, we demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.

Reflection mode diffraction tomography (RM DT) is an inversion scheme used to reconstruct the acoustical refractive index distribution of a scattering object. In this work, we reveal the existence of statistically complementary information inherent in the backscattered data and propose reconstruction algorithms that exploit this information for achieving a bias-free reduction of image variance in RM DT images. Such a reduction of image variance can potentially enhance the detectability of subtle image features when the signal-to-noise ratio of the measured scattered data is low in RM DT. The proposed reconstruction algorithms are mathematically identical, but they propagate noise and numerical errors differently. We investigate theoretically, and validate numerically, the noise properties of images reconstructed using one of the reconstruction algorithms for several different multifrequency sources and uncorrelated data noise.

Adaptive smoothing approaches are particularly useful because the amount of smoothing imposed on the data is determined automatically from the statistical characteristics of subsets of the data itself. Although efficient methods are available for performing adaptive smoothings on one-dimensional (1-D) data, extension of these 1-D adaptive smoothing methods to higher dimensions is often difficult because of the lack of a theoretical edifice and prohibitively large computational requirements. Previously, a method was developed that reduces the dimensions of a data function by exploiting its Fourier transform properties and thus achieves an effective multidimensional smoothing by use of low-dimensional smoothing methods. The purpose of this letter is to extend this work and demonstrate the possibility of achieving a higher-dimensional smoothing by applying lower-dimensional smoothing operations on the partial orthogonal expansion coefficients of the data function.

It is well understood that binary classifiers have two implicit objective functions (sensitivity and specificity) describing their performance. Traditional methods of classifier training attempt to combine these two objective functions (or two analogous class performance measures) into one so that conventional scalar optimization techniques can be utilized. This involves incorporating a priori information into the aggregation method so that the resulting performance of the classifier is satisfactory for the task at hand. We have investigated the use of a niched Pareto multiobjective genetic algorithm (GA) for classifier optimization. With niched Pareto GA's, an objective vector is optimized instead of a scalar function, eliminating the need to aggregate classification objective functions. The niched Pareto GA returns a set of optimal solutions that are equivalent in the absence of any information regarding the preferences of the objectives. The a priori knowledge that was used for aggregating the objective functions in conventional classifier training can instead be applied post-optimization to select from one of the series of solutions returned from the multiobjective genetic optimization. We have applied this technique to train a linear classifier and an artificial neural network (ANN), using simulated datasets. The performances of the solutions returned from the multiobjective genetic optimization represent a series of optimal (sensitivity, specificity) pairs, which can be thought of as operating points on a receiver operating characteristic (ROC) curve. All possible ROC curves for a given dataset and classifier are less than or equal to the ROC curve generated by the niched Pareto genetic optimization.

Smoothing methods are often used for discerning underlying patterns and structure concealed by statistical noise within a dataset. Adaptive smoothing approaches are particularly useful because the amount of smoothing imposed on the data is determined automatically from the statistical characteristics of subsets of the data itself. We show theoretically that an effective N-dimensional smoothing can be achieved by utilization of a series of non-identical n-dimensional (n

Computerized detection schemes have the potential of increasing diagnostic accuracy in medical imaging by alerting radiologists to lesions that they initially overlooked. These schemes typically employ multiple parameters such as threshold values or filter weights to arrive at a detection decision. In order for the system to have high performance, the values of these parameters need to be set optimally. Conventional optimization techniques are designed to optimize a scalar objective function. The task of optimizing the performance of a computerized detection scheme, however, is clearly a multiobjective problem: we wish to simultaneously improve the sensitivity and false-positive rate of the system. In this work we investigate a multiobjective approach to optimizing computerized rule-based detection schemes. In a multiobjective optimization, multiple objectives are simultaneously optimized, with the objective now being a vector-valued function. The multiobjective optimization problem admits a set of solutions, known as the Pareto-optimal set, which are equivalent in the absence of any information regarding the preferences of the objectives. The performances of the Pareto-optimal solutions can be interpreted as operating points on an optimal free-response receiver operating characteristic (FROC) curve, greater than or equal to the points on any possible FROC curve for a given dataset and detection scheme. It is demonstrated that generating FROC curves in this manner eliminates several known problems with conventional FROC curve generation techniques for rule-based detection schemes. We employ the multiobjective approach to optimize a rule-based scheme for clustered microcalcification detection that has been developed in our laboratory.