Comparison of Lesion Detection and Quantification in MAP Reconstruction with Gaussian and Non-Gaussian Priors

Statistical image reconstruction methods based on maximum a posteriori (MAP) principle have been developed for emission tomography. The prior distribution of the unknown image plays an important role in MAP reconstruction. The most commonly used prior are Gaussian priors, whose logarithm has a quadratic form. Gaussian priors are relatively easy to analyze. It has been shown that the effect of a Gaussian prior can be approximated by linear filtering a maximum likelihood (ML) reconstruction. As a result, sharp edges in reconstructed images are not preserved. To preserve sharp transitions, non-Gaussian priors have been proposed. However, their effect on clinical tasks is less obvious. In this paper, we compare MAP reconstruction with Gaussian and non-Gaussian priors for lesion detection and region of interest quantification using computer simulation. We evaluate three representative priors: Gaussian prior, Huber prior, and Geman-McClure prior. We simulate imaging a prostate tumor using positron emission tomography (PET). The detectability of a known tumor in either a fixed background or a random background is measured using a channelized Hotelling observer. The bias-variance tradeoff curves are calculated for quantification of the total tumor activity. The results show that for the detection and quantification tasks, the Gaussian prior is as effective as non-Gaussian priors

Analysis of Observer Performance in Known-Location Tasks for Tomographic Image Reconstruction

We consider the task of detecting a statistically varying signal of known location on a statistically varying background in a reconstructed tomographic image. We analyze the performance of linear observer models in this task. We show that, if one chooses a suitable reconstruction method, a broad family of linear observers can exactly achieve the optimal detection performance attainable with any combination of a linear observer and linear reconstructor. This conclusion encompasses several well-known observer models from the literature, including models with a frequency-selective channel mechanism and certain types of internal noise. Interestingly, the "optimal" reconstruction methods are unregularized and in some cases quite unconventional. These results suggest that, for the purposes of designing regularized reconstruction methods that optimize lesion detectability, known-location tasks are of limited use.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85959/1/Fessler48.pd

Theoretical Evaluation of the Detectability of Random Lesions in Bayesian Emission Reconstruction

Detecting cancerous lesion is an important task in positron emission tomography (PET). Bayesian methods based on the maximum a posteriori principle (also called penalized maximum likelihood methods) have been developed to deal with the low signal to noise ratio in the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the prior parameters in Bayesian reconstruction control the resolution and noise trade-off and hence affect detectability of lesions in reconstructed images. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Most research has been based on Monte Carlo simulations, which are very time consuming. Building on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers, here we develop a theoretical approach for fast computation of lesion detectability in Bayesian reconstruction. The results can be used to choose the optimum hyperparameter for the maximum lesion detectability. New in this work is the use of theoretical expressions that explicitly model the statistical variation of the lesion and background without assuming that the object variation is (locally) stationary. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predications and the Monte Carlo results

Quantitative Statistical Methods for Image Quality Assessment

Quantitative measures of image quality and reliability are critical for both qualitative interpretation and quantitative analysis of medical images. While, in theory, it is possible to analyze reconstructed images by means of Monte Carlo simulations using a large number of noise realizations, the associated computational burden makes this approach impractical. Additionally, this approach is less meaningful in clinical scenarios, where multiple noise realizations are generally unavailable. The practical alternative is to compute closed-form analytical expressions for image quality measures. The objective of this paper is to review statistical analysis techniques that enable us to compute two key metrics: resolution (determined from the local impulse response) and covariance. The underlying methods include fixed-point approaches, which compute these metrics at a fixed point (the unique and stable solution) independent of the iterative algorithm employed, and iteration-based approaches, which yield results that are dependent on the algorithm, initialization, and number of iterations. We also explore extensions of some of these methods to a range of special contexts, including dynamic and motion-compensated image reconstruction. While most of the discussed techniques were developed for emission tomography, the general methods are extensible to other imaging modalities as well. In addition to enabling image characterization, these analysis techniques allow us to control and enhance imaging system performance. We review practical applications where performance improvement is achieved by applying these ideas to the contexts of both hardware (optimizing scanner design) and image reconstruction (designing regularization functions that produce uniform resolution or maximize task-specific figures of merit)

Quantitative Techniques for PET/CT: A Clinical Assessment of the Impact of PSF and TOF

Tomographic reconstruction has been a challenge for many imaging applications, and it is particularly problematic for count-limited modalities such as Positron Emission Tomography (PET). Recent advances in PET, including the incorporation of time-of-flight (TOF) information and modeling the variation of the point response across the imaging field (PSF), have resulted in significant improvements in image quality. While the effects of these techniques have been characterized with simulations and mathematical modeling, there has been relatively little work investigating the potential impact of such methods in the clinical setting. The objective of this work is to quantify these techniques in the context of realistic lesion detection and localization tasks for a medical environment. Mathematical observers are used to first identify optimal reconstruction parameters and then later to evaluate the performance of the reconstructions. The effect on the reconstruction algorithms is then evaluated for various patient sizes and imaging conditions. The findings for the mathematical observers are compared to, and validated by, the performance of three experienced nuclear medicine physicians completing the same task

Channelized Hotelling Observer Performance for Penalized-Likelihood Image Reconstruction

What type of regularization method is optimal for penalized-likelihood image reconstruction when the imaging task is signal detection based on a channelized Hotelling (CHO) observer? To answer such questions, one would like to have a simple analytical expression (even if approximate) for the performance (SNR) of the CHO observer given different reconstruction methods. Bonetto, Qi, and Leahy (IEEE T-NS, Aug. 2000) derived and validated one such expression for penalized-likelihood (aka MAP) reconstruction and the Signal Known Exactly (SKE) problem using linearizations and local shift-invariance approximations. This paper describes a further simplification of the analytical SNR expression for the more general case of a Gaussian-distributed signal. This simplification, based on frequency-domain decompositions, greatly reduces computation time and thus can facilitate analytical comparisons between reconstruction methods in the context of detection tasks. It also leads to the very interesting result that regularization is not essential in this context for a large family of linear observers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85971/1/Fessler177.pd

Analysis of Observer Performance in Unknown-Location Tasks for Tomographic Image Reconstruction

Our goal is to optimize regularized image reconstruction for emission tomography with respect to lesion detectability in the reconstructed images. We consider model observers whose decision variable is the maximum value of a local test statistic within a search area. Previous approaches have used simulations to evaluate the performance of such observers. We propose an alternative approach, where approximations of tail probabilities for the maximum of correlated Gaussian random fields facilitate analytical evaluation of detection performance. We illustrate how these approximations, which are reasonably accurate at low probability of false alarm operating points, can be used to optimize regularization with respect to lesion detectability.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85914/1/Fessler33.pd

Breast Tomosynthesis: Aspects on detection and perception of simulated lesions

The aim of this thesis was to investigate aspects on detectability of simulated lesions (microcalcifications and masses) in digital mammography (DM) and breast tomosynthesis (BT). Perception in BT image volumes were also investigated by evaluating certain reading conditions. The first study concerned the effect of system noise on the detection of masses and microcalcification clusters in DM images using a free-response task. System noise has an impact on image quality and is related to the dose level. It was found to have a substantial impact on the detection of microcalcification clusters, whereas masses were relatively unaffected. The effect of superimposed tissue in DM is the major limitation hampering the detection of masses. BT is a three-dimensional technique that reduces the effect of superimposed tissue. In the following two studies visibility was quantified for both imaging modalities in terms of the required contrast at a fixed detection performance (92% correct decisions). Contrast detail plots for lesions with sizes 0.2, 1, 3, 8 and 25 mm were generated. The first study involved only an in-plane BT slice, where the lesion centre appeared. The second study repeated the same procedure in BT image volumes for 3D distributed microcalcification clusters and 8 mm masses at two dose levels. Both studies showed that BT needs substantially less contrast than DM for lesions above 1 mm. Furthermore, the contrast threshold increased as the lesion size increased for both modalities. This is in accordance with the reduced effect of superimposed tissue in BT. For 0.2 mm lesions, substantially more contrast was needed. At equal dose, DM was better than BT for 0.2 mm lesions and microcalcification clusters. Doubling the dose substantially improved the detection in BT. Thus, system noise has a substantial impact on detection. The final study evaluated reading conditions for BT image volumes. Four viewing procedures were assessed: free scroll browsing only or combined with initial cine loops at frame rates of 9, 14 and 25 fps. They were viewed on a wide screen monitor placed in vertical or horizontal positions. A free-response task and eye tracking were utilized to record the detection performance, analysis time, visual attention and search strategies. Improved reading conditions were found for horizontally aligned BT image volumes when using free scroll browsing only or combined with a cine loop at the fastest frame rate