Abstract
In a pure estimation task, an object of interest is known to be present, and we wish to determine numerical values for parameters that describe the object. This paper compares the theoretical framework, implementation method, and performance of two estimation procedures. We examined the performance of these estimators for tasks such as estimating signal location, signal volume, signal amplitude, or any combination of these parameters. The signal is embedded in a random background to simulate the effect of nuisance parameters. First, we explore the classical Wiener estimator, which operates linearly on the data and minimizes the ensemble mean-squared error. The results of our performance tests indicate that the Wiener estimator can estimate amplitude and shape once a signal has been located, but is fundamentally unable to locate a signal regardless of the quality of the image. Given these new results on the fundamental limitations of Wiener estimation, we extend our methods to include more complex data processing. We introduce and evaluate a scanning-linear estimator that performs impressively for location estimation. The scanning action of the estimator refers to seeking a solution that maximizes a linear metric, thereby requiring a global-extremum search. The linear metric to be optimized can be derived as a special case of maximum a posteriori (MAP) estimation when the likelihood is Gaussian and a slowly varying covariance approximation is made.
Highlights
The evaluation of image quality is rigorously approached by first stipulating the scientific purpose the images are meant to serve
This measure of performance indicates that, when the signal location is distributed throughout the field of view (FOV), linear estimation is not good at finding it; when σc is 4.0mm (8 pixels) the ensemble mean squared error (EMSE)
We have described and evaluated two estimation procedures designed to minimize the EMSE under distinct statistical circumstances
Summary
The evaluation of image quality is rigorously approached by first stipulating the scientific purpose the images are meant to serve. These estimates are commonly calculated using simple mathematics on a reconstructed image, such as summing the pixel values within a userspecified region or selecting a maximum pixel value Such estimation procedures were invented to produce numbers quickly and but are not derived according to cost minimization and are usually not evaluated using quantitative measures of performance. The image is usually influenced by effects that interfere with pure measurements of the desired quantities Such effects are called nuisance parameters and can include features like non-targeted uptake in nuclear medical imaging, atmospheric turbulence in astronomical applications, or any attribute of the object that is not being estimated yet influences the image data in a manner that is statistical and cannot be accounted for as a simple correction factor.
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