Simultaneous reconstruction and segmentation algorithm for positron emission tomography and transmission tomography

Abstract

We present a new reconstruction algorithm for emission and transmission tomography. The algorithm performs maximum likelihood reconstruction and doubly stochastic segmentation simultaneously. The resulting reconstructions show promising edge-preservation as well as suppression of measurement noise.

Simultaneous tomographic reconstruction and segmentation with class priors

“…, K) are assumed to be known from previous studies; see §3.2. Moreover, following [9] we use an HMMFM to incorporate a spatial prior inspired by the framework introduced in [8].…”

“…The use of the TV function R TV (8) allows discontinuities in the probabilities for the classes associated with neighboring pixels -and one expects this to be well suited for the segmentation process. The use of the Tikhonov function R Tik (9) enforces some spatial smoothness of the probabilities among classes associated with neighboring pixels.…”

“…The underlying idea is then to approximate this function with a uni-modal approximation -a single Gaussian function -such that we can use standard methods from convex optimization. The first type of simplification was introduced in [8], and for each pixel x j it "lumps" the parameters δ jk , µ k and σ k into the parametersμ j ,σ j andδ j = 1, wherê The simplified function then takes the form (omitting an additive constant):…”

“…From a computational point of view, the TV regularization term R TV (8) in algorithm SRS-TV is more difficult to handle than the Tikhonov term R Tik (9) used in SRS-Tik. As a consequence, for SRS-TV the range of appropriate regularization parameters is quite small and the computing time is large, while for SRS-Tik the range for appropriate parameters is larger and the computing time is significantly smaller.…”

“…The same approach was applied to CT problems with limited data in [7]. Van de Sompel and Brady [8] proposed a related idea using a Hidden Markov Measure Field Model (HMMFM) [9] that "learns" information about the different types of objects or phases from the given data during the SRS process. Other papers that describe the use of a hidden Markov field are [10] and [11].…”