An EM algorithm for estimating SPECT emission and transmission parameters from emission data only

Abstract

A maximum-likelihood (ML) expectation-maximization (EM) algorithm (called EM-IntraSPECT) is presented for simultaneously estimating single photon emission computed tomography (SPECT) emission and attenuation parameters from emission data alone. The algorithm uses the activity within the patient as transmission tomography sources, with which attenuation coefficients can be estimated. For this initial study, EM-IntraSPECT was tested on computer-simulated attenuation and emission maps representing a simplified human thorax as well as on SPECT data obtained from a physical phantom. Two evaluations were performed. First, to corroborate the idea of reconstructing attenuation parameters from emission data, attenuation parameters (mu) were estimated with the emission intensities (lambda) fixed at their true values. Accurate reconstructions of attenuation parameters were obtained. Second, emission parameters lambda and attenuation parameters mu were simultaneously estimated from the emission data alone. In this case there was crosstalk between estimates of lambda and mu and final estimates of lambda and mu depended on initial values. Estimates degraded significantly as the support extended out farther from the body, and an explanation for this is proposed. In the EM-IntraSPECT reconstructed attenuation images, the lungs, spine, and soft tissue were readily distinguished and had approximately correct shapes and sizes. As compared with standard EM reconstruction assuming a fix uniform attenuation map, EM-IntraSPECT provided more uniform estimates of cardiac activity in the physical phantom study and in the simulation study with tight support, but less uniform estimates with a broad support. The new EM algorithm derived here has additional applications, including reconstructing emission and transmission projection data under a unified statistical model.

Attenuation correction using SPECT emission data only

“…An approach in the same spirit is [19]. In § we minimize the negative log-likelihood of a Gaussian law, and possible choices of the norm q D q will be discussed in the next section.…”

Simultaneous Reconstruction of Tissue Attenuation and Radioactivity Maps in SPECT

“…On the other hand, in practical situations, especially for pathological data sets, it is almost impossible to have the exact patient-dependent attenuation information a priori. In addition to the prior methods, the incorporation of consistency conditions and statistical modeling into simultaneous estimation of activity and attenuation map from emission data has received a large amount of attention [10,1,6]. These iterative reconstruction algorithms require careful modeling of the imaging system response model which is subject to a number of physical effects.…”

Advanced reconstruction of attenuation maps using SPECT emission data only

“…the Tikhonov Regularization in order to generate an adequately realistic estimation of the attenuation [12]. Others provide methods to consider noise properties during the reconstruction in form of modified gradient ascent-and EM-algorithms [13] [14].…”