Uniform Quadratic Penalties Cause Nonuniform Spatial Resolution

Examines the spatial resolution properties of penalized maximum-likelihood image reconstruction methods by analyzing the local impulse response. The authors show that for emission image reconstruction using the ordinary uniform quadratic regularization penalty, the local impulse response is spatially variant. Paradoxically, the local resolution is poorest in high activity regions. The analysis leads naturally to a modified quadratic regularization penalty that achieves nearly uniform resolution. The modified penalty also provides a very practical method for choosing the smoothing parameter to obtain a specified resolution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85906/1/Fessler127.pd

Absence of a metallicity effect for ultra-short-period planets

Ultra-short-period (USP) planets are a newly recognized class of planets with periods shorter than one day and radii smaller than about 2 Earth radii. It has been proposed that USP planets are the solid cores of hot Jupiters that lost their gaseous envelopes due to photo-evaporation or Roche lobe overflow. We test this hypothesis by asking whether USP planets are associated with metal-rich stars, as has long been observed for hot Jupiters. We find the metallicity distributions of USP-planet and hot-Jupiter hosts to be significantly different ($p = 3\times 10^{-4}$), based on Keck spectroscopy of Kepler stars. Evidently, the sample of USP planets is not dominated by the evaporated cores of hot Jupiters. The metallicity distribution of stars with USP planets is indistinguishable from that of stars with short-period planets with sizes between 2--4~$R_\oplus$. Thus it remains possible that the USP planets are the solid cores of formerly gaseous planets smaller than Neptune.Comment: AJ, in pres

Robust Maximum- Likelihood Position Estimation in Scintillation Cameras

The classical maximum-likelihood (ML) estimator for the position of a scintillation event in a gamma camera, as derived by Gray and Macovski in 1976, requires exact knowledge of the light-spread function (LSF) of each photomultiplier tube. In practice, one must determine each LSF from noisy measurements corrupted by Poisson noise, quantization error, and electronic noise and bias. Since the ML position estimator involves derivatives of each LSF, even small measurement errors can result in degraded estimator performance. In this paper we derive a robust ML position estimator that accounts for the statistical uncertainty in LSF measurements. The form of the robust estimator diminishes contributions from the tails of the LSF, where the relative measurement errors are the largest.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85879/1/Fessler117.pd

Spatial Resolution Properties of Penalized-Likelihood Image Reconstruction: Space-Invariant Tomographs

This paper examines the spatial resolution properties of penalized-likelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems. Paradoxically, for emission image reconstruction, the local resolution is generally poorest in high-count regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized-likelihood methods.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85890/1/Fessler97.pd

Regularized Emission Image Reconstruction Using Imperfect Side Information

A spatially variant penalized-likelihood method for tomographic image reconstruction based on a weighted Gibbs penalty was investigated. The penalty weights are determined from structural side information, such as the locations of anatomical boundaries in high-resolution magnetic resonance images. Such side information will be imperfect in practice, and a simple simulation demonstrated the importance of accounting for the errors in boundary locations. Methods are discussed for prescribing the penalty weights when the side information is noisy. Simulation results suggest that even imperfect side information is useful for guiding spatially variant regularization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85869/1/Fessler110.pd

Design of a very high-resolution small animal PET scanner using a silicon scatter detector insert

A small animal positron emission tomography (PET) instrument using a high-resolution solid-state detector insert in a conventional PET system was investigated for its potential to achieve sub-millimeter spatial resolution for mouse imaging. Monte Carlo simulations were used to estimate the effect of detector configurations (thickness, length and radius) on sensitivity. From this initial study, a PET system having an inner cylindrical silicon detector (4 cm ID, 4 cm length and 1.6 cm thickness composed of 16 layers of 300 µm × 300 µm × 1 mm pads), for scattering, surrounded by an outer cylindrical BGO scintillation detector (17.6 cm ID, 16 cm length and 2 cm thickness segmented into 3 mm × 3 mm × 20 mm crystals), for capture was evaluated in detail. In order to evaluate spatial resolution, sensitivity and image quality of the PET system, 2D images of multiple point and cylinder sources were reconstructed with the simulation data including blurring from positron range and annihilation photon acollinearity using filtered backprojection (FBP). Simulation results for 18F demonstrate 340 µm FWHM at the center of the field of view with 1.0% sensitivity from the coincidence of single scattering events in both silicon detectors and 1.0 mm FWHM with 9.0% sensitivity from the coincidence of single scattering in the silicon and full energy absorption of the second photon in the BGO detector.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58095/2/pmb7_15_019.pd

A Fast Recursive Algorithm for Computing CR-Type Bounds for Image Reconstruction Problems

The authors describe a method for computing matrix CR bounds for image reconstruction problems using an iterative algorithm that avoids the intractable inversion of the Fisher matrix required by direct methods. The algorithm produces a close approximation to the CR bound, requiring only O(n2) floating point operations per pixel of interest, an order of magnitude savings relative to the O(n3) flops required by noniterative methods. To illustrate the utility of the iterative algorithm, a prototypical application is studied: the dependence of achievable reconstruction accuracy on angular and radial sampling.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85898/1/Fessler122.pd

Experimental Evaluation For Joint Estimation Approach

Single photon emission computed tomography (SPECT) provides a potential to perform in vivo quantification of the radioactivity and dose distributions in the process of evaluating radiopharmaceuticals. The inherent modest resolution in SPECT impedes the potential of accurate quantification. Previously, the authors investigated a joint estimation approach for combining SPECT functional information with high resolution, structurally correlated MRI anatomical information to improve the accuracy of SPECT quantification, and the computer simulation results showed that this approach can exploit MRI region information that matches the SPECT functional information and to reduce artifacts caused by mismatched MRI anatomical information. Here, the authors further describe the experimental evaluation of the joint estimation approach using actual SPECT and MRI imaging with an animal-sized phantom. They describe practical details in applying the joint estimation approach and present the experimental evaluation results of quantitative analysis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86000/1/Fessler144.pd

Incorporating MRI Region Information into SPECT Reconstruction Using Joint Estimation

Single photon emission computed tomographic images (SPECT) have relatively poor resolution. In an attempt to improve SPECT image quality, many methods have been developed for including anatomic information, extracted from higher resolution, structurally correlated magnetic resonance images (MRI), into the SPECT reconstruction process. These methods provide improved SPECT reconstruction accuracy if the anatomic information is perfectly correlated with the SPECT functional information. However there exist mismatches between MRI anatomical structures and SPECT functional structures due to different imaging mechanisms. It has been reported that if the MR structures are applied into SPECT, the mismatched part will cause artifacts. The paper describes a joint estimation approach which unifies MR information extraction and SPECT reconstruction processes to avoid these artifacts. Both qualitative and quantitative evaluations show that the method improves the SPECT reconstruction where the MR information matches and is robust to mismatched MR information.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86029/1/Fessler134.pd