Santosh Kulkarni

Channelized hotelling and human observer study of optimal smoothing in SPECT MAP reconstruction

We compared the performance of a channelized Hotelling observer (CHO) to that of human observers to determine an optimal smoothing parameter /spl beta/ for an SKE/BKE detection task in a SPECT MAP (maximum a posteriori) reconstruction. The study is motivated in part by the recent development of theoretical methods that can rapidly predict CHO signal-to-noise ratios (SNRs) for MAP reconstructions. We found that a CHO not adjusted for internal noise effects was less predictive of the optimal smoothing parameters than one that used human observer data to tune the CHO for internal noise. We used a three-channel, square profile, radially symmetric channel structure, and, for internal noise, a method that altered the diagonal elements of the channel covariance matrix. The human observer study for two different signals A and B showed that /spl beta/ in the range 0.5-10.0 produced high detectability as measured by high d/sub A//sup 2/, while the CHO without internal noise showed high SNR/sup 2/ for /spl beta/ in the wider range 0.01-10.0. The CHO at location A was modified by internal noise utilizing human data at A, so that the d/sub A//sup 2/ and SNR/sup 2/ overlapped well, but when these internal noise parameters from A were applied at B, the curves did not overlap well. Nevertheless, both modified CHOs predicted a /spl beta/ range in accord with human data. We conclude that CHOs may need some way of incorporating internal noise without having to conduct a human study in the first place to determine internal noise parameters.

A channelized Hotelling observer study of lesion detection in SPECT MAP reconstruction using anatomical priors

In emission tomography, anatomical side information, in the form of organ and lesion boundaries, derived from intra-patient coregistered CT or MR scans can be incorporated into the reconstruction. Our interest is in exploring the efficacy of such side information for lesion detectability. To assess detectability we used the SNR of a channelized Hotelling observer and a signal-known exactly/background-known exactly detection task. In simulation studies, we incorporated anatomical side information into a SPECT MAP (maximum a posteriori) reconstruction by smoothing within but not across organ or lesion boundaries. A non-anatomical prior was applied by uniform smoothing across the entire image. We investigated whether the use of anatomical priors with organ boundaries alone or with perfect lesion boundaries alone would change lesion detectability relative to the case of a prior with no anatomical information. Furthermore, we investigated whether any such detectability changes for the organ-boundary case would be a function of the distance of the lesion to the organ boundary. We also investigated whether any detectability changes for the lesion-boundary case would be a function of the degree of proximity, i.e. a difference in the radius of the true functional lesion and the radius of the anatomical lesion boundary. Our results showed almost no detectability difference with versus without organ boundaries at any lesion-to-organ boundary distance. Our results also showed no difference in lesion detectability with and without lesion boundaries, and no variation of lesion detectability with degree of proximity.

Aperture optimization in emission imaging using ideal observers for joint detection and localization

For the familiar 2-class detection problem (signal present/absent), ideal observers have been applied to optimization of pinhole and collimator parameters in planar emission imaging. Given photon noise and background and signal variabilities, such experiments show how to optimize an aperture to maximize detectability of the signal. Here, we consider a fundamentally different, more realistic task in which the observer is required to both detect and localize a signal. The signal is embedded in a variable background and is known except for location. We inquire whether the addition of a localization requirement changes conclusions on aperture optimization. We have previously formulated an ideal observer for this joint detection/localization task, and here apply it to the classic problem of determining an optimal pinhole diameter in a planar emission imaging system. We conclude that as search tolerance on localization decreases, the optimal pinhole diameter shrinks from that required by detection alone, and, in addition, task performance becomes more sensitive to fluctuations about the optimal pinhole diameter. As in the case for detection only, the optimal pinhole diameter shrinks as the amount of background variability grows and, in addition, conspicuity limits can be observed. Unlike the case for detection only, our task leads to a finite aperture size in the absence of background variability. For both tasks, the inclusion of background variability yields a finite aperture size.

Strategies to jointly optimize spect collimator and reconstruction parameters for a detection task

In systems like SPECT, raw data is obtained by the imaging system and then reconstructed and viewed by a human observer. We compare two approaches to optimizing SPECT for a detection task with a known signal in a statistically varying background. In a sequential approach, we optimize the collimator using an ideal observer applied to the sinogram. We then optimize the regularization of the reconstruction using a human-emulating channelized Hotelling observer (CHO). In a second approach, we use the CHO to jointly optimize the collimator and regularization. The performance of the joint approach exceeds that of the sequential approach. The collimator properties from the joint approach are closer to that of a commercial collimator than those of the sequential approach. Thus using the “best” collimator derived by an ideal observer leads to suboptimal net detection performance.

Effect on lesion detectability of proximity to anatomical boundaries in emission tomography

In emission tomography (ET) comprising PET and SPECT, anatomical information derived from intra-patient coregistered CT or MR scans can be incorporated into the ET reconstruction. The increasing availability of PET-CT and SPECT-CT has engendered renewed interest in anatomical priors. Our interest is in exploring the efficacy of such side information for lesion detectability. In simulation studies we used an idealized model of anatomical side information incorporated into a SPECT MAP (maximum a posteriori) reconstruction, and a channelized Hotelling observer (CHO) whose performance emulates that of humans in such detection tasks. We observed that detectability appears to vary little with or without anatomical side information unless the lesion is tightly constrained by anatomical boundaries. Our preliminary studies thus imply a limited utility for anatomical side information for this task.

Human observer efficiency for signal detection and localization in emission tomographic images

For the medically relevant task of joint detection and localization of a signal (lesion) in an emission computed tomographic (ECT) images, it is of interest to measure the efficiency, defined as the relative task performance of a human observer vs that of an ideal observer. Low efficiency implies that improvements in reconstruction algorithms may be possible and also that an ideal observer might be suitably handicapped to derive a model observer that emulates human performance. In our experiments, we use a simplified “filtered noise model” proposed in [1] that simplifies the complex ideal observer calculations. This model is used to emulate the tomographic reconstruction process where the correlation structure of the reconstructed images is a combination of quantum noise and the noise due to background variability both modulated by a form of regularization implemented during the reconstruction process. A two-alternative forced choice (2AFC) test is used to obtain the performance of the human observers. We also introduce two efficiency definitions appropriated for the underlining joint detection-localization tasks. Experimental results show that both the ideal observer and the human observer perform badly in localizing the exact center of the signal but much better in obtaining the rough location of the signal. The human efficiency depends strongly on the amount of smoothing in the image, with efficiency dropping for both over-smoothed case and under-smoothed case. Human efficiency increases approximately monotonically with signal intensity. We compared these results with a signal-known-exactly case and observed similar trends.

Rapid optimization of SPECT scatter correction using model LROC observers

The problem we address is the optimization and comparison of window-based scatter correction (SC) methods in SPECT for maximum a posteriori reconstructions. While sophisticated reconstruction-based SC methods are available, the commonly used window-based SC methods are fast, easy to use, and perform reasonably well. Rather than subtracting a scatter estimate from the measured sinogram and then reconstructing, we use an ensemble approach and model the mean scatter sinogram in the likelihood function. This mean scatter sinogram estimate, computed from satellite window data, is itself inexact (noisy). Therefore two sources of noise, that due to Poisson noise of unscattered photons and that due to the model error in the scatter estimate, are propagated into the reconstruction. The optimization and comparison is driven by a figure of merit, the area under the LROC curve (ALROC) that gauges performance in a signal detection plus localization task. We use model observers to perform the task. This usually entails laborious generation of many sample reconstructions, but in this work, we instead develop a theoretical approach that allows one to rapidly compute ALROC given known information about the imaging system and the scatter correction scheme. A critical step in the theory approach is to predict additional (above that due to to the propagated Poisson noise of the primary photons) contributions to the reconstructed image covariance due to scatter (model error) noise. Simulations show that our theory method yields, for a range of search tolerances, LROC curves and ALROC values in close agreement to that obtained using model observer responses obtained from sample reconstruction methods. This opens the door to rapid comparison of different window-based SC methods and to optimizing the parameters (including window placement and size, scatter sinogram smoothing kernel) of the SC method.

Effects of image quantization and regularization on lesion detectability in SPECT MAP reconstruction

In penalized likelihood methods for SPECT, the degree of smoothing /spl beta/ controls a noise-resolution tradeoff and would seem to be a crucial parameter in controlling image quality as measured by the SNR of a channelized Hotelling observer (CHO) in an SKE/BKE lesion detection task. Application of the CHO to a floating point reconstruction shows a very weak dependence of SNK and /spl beta/, however, and this dependence is only slightly changed if we modify the floating point reconstruction to the 8-bit quantized version that would be viewed by a human observer. SKE/BKE human studies show a fairly different behavior than that of the CHO, resulting in a strong dependence of SNR on /spl beta/. Attempts to account for the discrepancy by modeling quantization noise in the CHO fail. We repeat the human and model observer studies at more extreme levels of quantization and note some interesting effects.

Statistical Properties of SPECT MAP Reconstruction Incorporating Window Based Scatter Correction

In SPECT, the sinogram contains scatter counts that degrade the reconstructed image quality. We develop theoretical expressions to predict the reconstructed mean, covariance, and local point-spread function for SPECT MAP (maximum a posteriori) reconstructions. These expressions apply to window-based scatter correction methods, such as the triple-energy-window method, where the scatter correction is incorporated directly into the forward imaging model as an affine term. In addition this forward imaging model is incorporated directly in the MAP objective. We model a scatter estimate as a noisy quantity so that the reconstruction is driven by both photon noise in the photopeak and the noise in the scatter estimate. We use sample reconstruction methods to validate our theoretical expressions. We compare the speed of our theoretical methods to that of methods based on sample reconstructions. Such theoretical formulae could be used to rapidly assess the impact of different scatter correction strategies on image quality.

Effects of background complexity on LROC analysis of SPECT

We investigate image quality assessment for SPECT for the case where the human observer must detect and locate a lesion in the noisy reconstructed image. The lesion can appear anywhere in a search region which may contain a complex background of hot and cold structures. Our hypothesis is that as the spatial complexity of the background increases, the performance of the human observer decreases. In this study, the background is not random, but is fixed. We consider four backgrounds with increasing complexity. Human performance is measured using a two-alternative forced-choice (2AFC) test. From the 2AFC results, one can compute a measure of human performance, the area under LROC curve. We observe that the human performance degrades as the background complexity increases despite the fact that the true background image is available to the observer during the 2AFC test. Therefore, the human apparently has a difficult time learning complex backgrounds. We also compute the performance of an ideal observer for this task, and show that it is insensitive to background complexity.