The direct calculation of parametric images from dynamic PET data using maximum-likelihood iterative reconstruction

Abstract

The aim of this work is to calculate, directly from projection data, concise images characterizing the spatial and temporal distribution of labelled compounds from dynamic PET data. Conventionally, image reconstruction and the calculation of parametric images are performed sequentially. By combining the two processes, low-noise parametric images are obtained, using a computationally feasible parametric iterative reconstruction (PIR) algorithm. PIR is performed by restricting the pixel time-activity curves to a positive linear sum of predefined time characteristics. The weights in this sum are then calculated directly from the PET projection data, using an iterative algorithm based on a maximum-likelihood iterative algorithm commonly used for tomographic reconstruction. The ability of the algorithm to extract known kinetic components from the raw data is assessed, using data from both a phantom experiment and clinical studies. The calculated parametric images indicate differential kinetic behaviour and have been used to aid in the identification of tissues which exhibit differences in the handling of labelled compounds. These parametric images should be helpful in defining regions of interest with similar functional behaviour, and with FDG Patlak analysis.

Dynamic PET Reconstruction Using Wavelet Regularization With Adapted Basis Functions

“…The 1-D prefilters are designed using the principle of consistent sampling and are given by the convolutional inverse of the cross-correlation sequence [47]. When we include this prefiltering step explicitly in the update equation we get (25) where denotes the prefiltering operation that maps an image from to following the consistent sampling methodology, represents the inverse operation. The projector on nonnegative functions works in the pixelized space and therefore corresponds to setting pixels with negative values to zero.…”

“…Several teams have investigated the use of nonuniform B-splines and have reported promising results [7]- [9], [23]. It has also been proposed to derive the temporal basis functions from the data itself [24], [25]. Our work differs from these approaches in that the proposed temporal basis functions form a (generalized) wavelet basis and in that we make use of a global sparsity constraint in the spatio-temporal wavelet domain.…”

Spatiotemporal reconstruction of list-mode PET data

“…In (10), is a standard normal, hence, its sum of squares is a random variable with degrees of freedom and, hence, has expectation .…”

“…This form encompasses the parametric imaging work of Matthews [10], Zibulevsky [11], and Snyder [2] and the mixture models of O'Sullivan [12]. We also note that Ollinger [13] used list-mode data to reconstruct rate functions as histograms with adaptive bin sizes; our work could be viewed as a continuous-time extension of this.…”

Direct 4D list mode parametric reconstruction for PET with a novel EM algorithm

“…Carson and Lange [2] also proposed an EM framework for direct parametric image reconstruction algorithm with a one tissue model. Subsequently, many direct kinetic estimation methods [3][4][5][6][7][8] for sinogram data have been produced. However, for a high-resolution scanner such as the HRRT with 4.5×10 9 potential lines of response, list mode data is preferred; this can reduce the data storage requirements while maintaining highest resolution by storing the measured attributes of each event in the list.…”