Analytical Approach to Channelized Hotelling Observer Performance for Regularized Tomographic Image Reconstruction

Our goal is to analyze regularized image reconstruction methods such as penalized likelihood with respect to the performance of the channelized Hotelling observer (CHO) in the task of detecting a small target signal in the reconstructed images, in the presence of a correlated random background. We derive here an approximation to the performance of the CHO by working entirely with continuous-space formulations and then discretizing the final result. This approach leads to an extension and a refinement of approximations that we previously derived in the discrete space.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85962/1/Fessler196.pd

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

Analysis of Unknown-Location Signal Detectability for Regularized Tomographic Image Reconstruction

Our goal is to optimize regularized image reconstruction methods for emission tomography with respect to the task of detecting small lesions of unknown location in the reconstructed images. We consider model observers whose decisions are based on finding the maximum value of a local test statistic over all possible lesion locations. We use tail probability approximations by Adler (AAP 2000) and Siegmund and Worsley (AS 1995) to evaluate the probabilities of false alarm and detection respectively for the observers of interest. We illustrate how these analytical tools can be used to optimize regularization with respect to the performance (at low probability of false alarm operating points) of a maximum channelized non-prewhitening observer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85961/1/Fessler221.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

Analysis of Observer Performance in Detecting Signals with Location Uncertainty for Regularized Tomographic Image Reconstruction

Our goal is to optimize regularized image reconstruction methods for emission tomography with respect to the task of detecting small lesions in the reconstructed images. To reflect medical practice realistically, we consider the location of the lesion to be unknown. This location uncertainty significantly complicates the mathematical analysis of model observer performance. We consider model observers whose decisions are based on finding the maximum value of a local test statistic over all possible locations. Khurd and Gindi (SPIE 2004) and Qi and Huesman (SPIE 2004) described analytical approximations of the moments of the local test statistics and used Monte Carlo simulations to evaluate the localization performance of such "maximum observers". We propose here an alternative approach, where tail probability approximations developed by Adler (AAP 2000) facilitate analytical evaluation of the detection performance of these observers. We illustrate how these approximations can be used to evaluate the probability of detection (for low probability of false alarm operating points) for the maximum channelized hotelling observer. Using our analyses, one can rank and optimize image reconstruction methods without requiring time-consuming Monte Carlo simulations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85960/1/Fessler205.pd

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

Recovery of total I-131 activity within focal volumes using SPECT and 3D OSEM

We experimentally investigated the SPECT recovery of I-131 activity in multiple spheres located simultaneously at different locations within a cylindrical phantom that had an elliptical cross section. The sphere volumes ranged from 209 cc down to 4.2 cc. A Prism 3000 camera and two types of parallel-hexagonal-hole collimation were employed: high energy (HE) and ultra high energy (UHE). Using appropriately-different 3D models of the point source response function for the two types of collimation, approximately the same recovery of activity could be achieved with either collimation by 3D OSEM reconstruction. The recovery coefficient was greater with no background activity in the phantom by 0.10, on average, compared to that with background. In the HE collimation case, the activity recovery was considerably better for all volumes using 3D OSEM reconstruction than it had been in the past using 1D SAGE reconstruction. Recovery-coefficient-based correction in a simulated patient case involving spherical tumours moderately improved the activity estimates (average error reduced from 14% to 9% for UHE collimation, and from 15% to 11% for HE collimation). For a test case with HE collimation, increasing the projection-image sampling density while decreasing the image voxel size increased the recovery coefficient by 0.075 on average, and, if used in a full set of calibration measurements of recovery coefficient versus volume, might lead to further improvement in accuracy for the patient case.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58098/2/pmb7_3_017.pd

Insight into the fundamental trade-offs of diffusion MRI from polarization-sensitive optical coherence tomography in ex vivo human brain

In the first study comparing high angular resolution diffusion MRI (dMRI) in the human brain to axonal orientation measurements from polarization-sensitive optical coherence tomography (PSOCT), we compare the accuracy of orientation estimates from various dMRI sampling schemes and reconstruction methods. We find that, if the reconstruction approach is chosen carefully, single-shell dMRI data can yield the same accuracy as multi-shell data, and only moderately lower accuracy than a full Cartesian-grid sampling scheme. Our results suggest that current dMRI reconstruction approaches do not benefit substantially from ultra-high b-values or from very large numbers of diffusion-encoding directions. We also show that accuracy remains stable across dMRI voxel sizes of 1 ​mm or smaller but degrades at 2 ​mm, particularly in areas of complex white-matter architecture. We also show that, as the spatial resolution is reduced, axonal configurations in a dMRI voxel can no longer be modeled as a small set of distinct axon populations, violating an assumption that is sometimes made by dMRI reconstruction techniques. Our findings have implications for in vivo studies and illustrate the value of PSOCT as a source of ground-truth measurements of white-matter organization that does not suffer from the distortions typical of histological techniques.Published versio

Update on HE vs UHE Collimation for Focal Total-activity Quantification in I-131 SPECT Using 3D OSEM

We calibrated a scintillation camera for the counts-to-activity conversion factor, CF, by measuring a phantom consisting of a sphere containing a known 131-I activity placed within an elliptical cylinder. Within a 3D OSEM reconstruction algorithm, we employed a depth-dependent detector-response model based on smooth fits to the point-source-response function. Using the ultra-high-energy (UHE) collimator and 100 iterations, the recovery coefficient, RC, appeared to be 1 for any sphere volume down to 20 cm3. The CF changed only a small amount as the background-over-target activity concentration ratio, b, increased for both UHE and high-energy (HE) collimation. Tests of activity quantification were carried out with an anthropomorphic phantom simulating a 100 cm3 spherical tumor centrally located inferior to the lungs. With 3D OSEM reconstruction, using the global-average CF and no RC-based correction, mean bias in the simulated-tumor activity estimate over 20 realizations was -7.4% with UHE collimation, and -9.4% with HE collimation. For comparison, with 1D SAGE reconstruction, using the CF corresponding to the experimental estimate of b and RC-based correction, the mean bias was worse, -10.7% for UHE collimation, but better, -4.3 %, for HE collimation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85907/1/Fessler190.pd

Determining Total I-131 Activity Within a VoI Using SPECT, a UHE Collimator, OSEM, and a Constant Conversion Factor

Accurate determination of activity within a volume of interest is needed during radiopharmaceutical therapies. Single-photon emission computed tomography(SPECT) is employed but requires a method to convert counts to activity. We use a phantom-based conversion; that is, we image an elliptical cylinder containing a sphere that has a known amount of 131-I activity inside. The regularized space alternating generalized expectation (SAGE) algorithm employing a strip-integral detector-response model was employed for reconstruction in previous patient evaluations. With that algorithm and a high-energy collimator, the estimates for sphere activity varied with changes in: 1) the level of uniform background activity in the cylinder; 2) the image resolution due to different values of the radius of rotation R; and 3) the volume of the sphere. When one used those to convert reconstructed counts within a patient tumor into an activity estimate, the resultant value may have been in error because of patient-phantom mismatch. As a potential remedy, in this paper, we use an ordered subsets expectation maximization (OSEM) algorithm with a 3-D depth-dependent detector-response model and an ultra-high-energy collimator. Results after 100 OSEM iterations and using a maximum counts registration show the estimates for sphere activity: 1) have a dependence on the level of background activity with a slope whose absolute magnitude is typically only 0.37 times that with SAGE; 2) are independent of R; and 3) are independent of sphere volume down to and including a sphere volume of 20 cm3. We conclude that using a global-average conversion factor to relate counts to activity and no volume-based correction might be reasonable with OSEM. For a test of that conclusion, target activity is estimated for an anthropomorphic phantom containing a 100 cm3 spherical tumor centrally located inferior to the lungs. With OSEM-based quantification, using: 1) a global-average conversion factor and 2) no volume-based correction, mean bias in the simulated-tumor activity estimate over 20 realizations is -7.37% (relative standard deviation =5.93%). With SAGE-based quantification using: 1) the conversion factor corresponding to the experimental estimate of ba- ckground and 2) volume-based correction, the mean bias is -10.7% (relative standard deviation =2.37%). The mean bias is smaller in a statistically significant way and relative standard deviation is not more than a factor of 2.5 bigger with OSEM compared to SAGE. In addition, with OSEM, a patient image apparently shows more highly resolved features, and the activity estimates for two tumors are increased by an average of 10%, relative to results with SAGE.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85985/1/Fessler57.pd