In and ?j are the values of linear

In a MLAA framework, optimization is done by an iterative manner. Every
iteration starts with activity update trough a ‘maximum likelihood

Where

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

,

denotes the attenuation image  

 (µ1 …. µN) and activity image

 (?1….?N) 
and yi is the measured emission data.

 

 

where
µj and ?j are the values of linear attenuation
coef?cient and activity at position

. cij is the
sensitivity of detectors along LOR

 to activity in

 in a perfectly condition with no attenuation
for photons. li,j represent the effective
intersection length of voxel

 with LOR

. Considering the Poisson
nature of measured emission data, the cost function is best modeled as:

 

 

Algorithm: In PET the expected counts

 for line of response (LOR)

can be expressed as:

 

In this study, we aimed at improving the
performance of non–TOF MLAA by exploiting of an air mask and a BPM,
beside patient individual soft
tissue information provided via the MR segmented images on the attenuation
estimations. The algorithm is based on joint
estimation of attenuation and activity from the PET emission data, which
alternatively updates attenuation and activity through an iterative approach. We
called the new algorithm MLAA-TPA.

Recently, it has been shown that using ‘magnetic
resonance (MR)’ partial information about distribution of soft tissue as prior
knowledge in the ‘maximum
likelihood reconstruction of activity and attenuation (MLAA)’ algorithm, derive the likelihood function towards a
local maxima and make problem less ill-posed (MR-MLAA) ‘2’.
Although MR-MLAA compared to the
standard MR-based ‘attenuation correction (AC)’, had one step forward in PET quanti?cation by
detection of bone and air in
attenuation map, but since some misclassifications of air and bone, which can locally cause
bias in activity values is reported, the correctness of detection is more essential.
Generally, the efficiency
of the MR-MLAA algorithm can be affected by: a) the accuracy of MR segmentation, b)
the quality of registration
process between the various datasets, c) the anatomy complexity of the
reconstruction site and d) the count statistics of emission data.

Introduction:
Joint estimation of attenuation and activity based on the ‘maximum likelihood (ML)’ approach from the emission data only, is
an ill-posed problem due to cross-talk
between attenuation map and activity distribution. In the other hand
accurate quanti?cation reconstruction of the radiotracer activity
distribution in ‘positron emission tomography
(PET)’ mandates reliable ‘attenuation correction factors (ACF)’, in order to compensating the loss of detected photons
induced by the materials along ‘lines of response (LOR)’ ‘1’.

 

Simultaneous
reconstruction of attenuation and activity (MLAA) from emission data only, suffered
from the inherent cross-talk
between the estimated attenuation and activity distributions. In this paper, we
proposed an improved MLAA algorithm by utilizing
tissue prior atlas (TPA) and a Gibbs prior as priori knowledge. TPA imposing statistical condition as a supplement for individual magnetic resonance (MR) information on the reconstruction process of attenuation map. Hence along with soft tissue distribution, provided by
segmentation of MR images, an air mask and a bone probability map (BPM) breakdown the MR low-signal class into 4 subclasses in order to favor recognitions of air and bone. Estimations on attenuation coefficients are realized as a mix of
pseudo-Gaussian distributions. The proposed algorithm evaluated using simulated
3D emission data. The proposed MLAA-TPA algorithm compared with MR-MLAA algorithm proposed by Heußer et al. Our
results demonstrate that the performance of MR-MLAA algorithm highly depends on the accuracy of MR segmentation
which is well handled by MLAA-TPA. The quantification results well illustrated that the MLAA-TPA outperformed
the MR-MLAA
algorithm,
owing
to reduction of misclassification and more
precise tissue detection.