Generalization of the image space reconstruction algorithm

Abstract

The image space reconstruction algorithm (ISRA) has been shown to be a non-negative least squares estimator, and was introduced as an alternative iterative image reconstruction method for positron emission tomography (PET) data. The implementation of ISRA is straightforward: the ratio of the backprojected measured data to that of the backprojected expected data is used to multiplicatively update the current image estimate. This work starts with a modified weighted least squares objective function to derive a more general form of the ISRA algorithm, which importantly accommodates weighting of the backprojection. Simply by changing the choice of backprojection weighting factors at a given iteration, both the well known ML-EM (maximum likelihood expectation maximization) algorithm as well as the standard ISRA, are obtained as special cases. ML-EM corresponds to using the current estimate of the expected data as the weights for backprojection, and ISRA corresponds to the case of unit weighting during backprojection. Of particular interest however,is that the framework naturally suggests the existence of many alternative reconstruction algorithms through alternative data weighting choices. By changing the weighting factors, a performance improvement over ISRA is obtained, as well as a slight performance improvement compared to ML-EM (for the task of accurate region quantification which is considered in this work). Specifically, these improvements are obtained, for example, by using a spatially-smoothed copy of the measured data as weighting factors during backprojection.

Recent advances in combined Positron Emission Tomography and Magnetic Resonance Imaging

“…The MLEM is presented as a particular case of RAMLA. In [221], both ISRA and MLEM were presented from the point of view of a gradient descent algorithm of a weighted least-squares objective function, with properly chosen descent steps. In terms of noise models, the weighted least squares can be viewed as the log-likelihood of a gaussian model of the noise.…”

Ionospheric‐thermospheric UV tomography: 1. Image space reconstruction algorithms

“…Variants of this algorithm were used to correct early Hubble Space Telescope images for aberrations resulting from the improper figure of the primary mirror [Hanisch et al, 1997]. A second ISRA, which we call the Least Squares Positive Definite (LSPD) algorithm, has been discovered independently by several researchers [Reader et al, 2011;Jansson, 1997;Gold, 1964], and the authors, although we have not found this algorithm, has a specific name in the literature. The RL algorithm is designed to handle measurements that follow the Poisson distribution, while the LSPD algorithm is tailored to measurements that follow the normal distribution.…”

Scattering correction through a space-variant blind deconvolution algorithm

“…In this work, the optimization is done with a modified nonnegative least-square estimator, the ISRA. [10][11][12] In the first step, the PSF is updated by applying the ISRA E Q -T A R G E T ; t e m p : i n t r a l i n k -; s e c 2 . 1 ; 3 2 6 ; 3 6 9…”