Journal of Biosciences and Medicines, 2013, 1, 6-9 JBM

http://dx.doi.org/10.4236/jbm.2013.12002 Published Online October 2013 (http://www.scirp.org/journal/jbm/)

OPEN ACCESS

Towards n ove l regularization approaches to PET i m age

reconstruction

E. Karali, D. Koutsouris

Department of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece

Email: ekarali76@hotmail.com

Received August 2013

ABSTRACT

The purpose of this study is to introduce a novel em-

pirical iterative algorithm for medical image recon-

struction, under the short name MRP-ISWLS (Me-

dian Root Prior Image Space Weighted Least Squares).

Further, we assess the performance of the new algo-

rithm by comparing it to the simultaneous version of

known MRP algorithms. All algorithms are com-

pared in terms of cross-correlation and CNRs (Con-

trast-to-Noise Ratios). As it turns out, MRP-ISWLS

presents higher CNRs than the known algorithms for

objects of different size. Also MRP-ISWLS has better

noise manipulation.

Keywords: Image Reconstruction; Positron Emission

Tomography (PET); Small Animal Imaging; Median

Root Prior (MRP)

1. INTRODUCTION

Iterative techniques are divided into two main categories:

algebraic and statistical. Statistical techniques are classi-

fied to maximum-likelihood algorithms and least squares

methods. The most famous maximum likelihood tech-

nique is the expectation maximization maximum likeli-

hood (EM-ML) algorithm, which was first presented by

Shepp and Vardi. Image Space Reconstruction Algorithm

(ISRA) is a least square reconstruction method intro-

duced by Daube-Witherspoon and Muehllehner. It shows

better noise manipulation than EM-ML. Another least

squares algorithm is the Weighted Least Square tech-

nique (WLS), due to Anderson et al. WLS assumes that

random independent noise variables present different

standard deviations. The matrix of these standard devia-

tions consists of the expected projection data. WLS ac-

celerates the reconstruction process and results in recon-

structed images of better spatial resolution [1-3].

For the reduction of the noise many regularization

methods have been proposed, which reduce drastically

the noise with a small image resolution reduction. These

methods take into account a priori information for the

radioactivity spatial distribution inside the object under

examination [1]. The success of a regularization method

depends on the mathematical formula of the prior. Me-

dian root prior (MRP) [4] belongs to the most popular

priors. It is derived from a Gaussian distribution with

mean value the median value of reconstructed image

pixels in the vicinity of pixel i. The use of MRP results in

noise component reduction while at the same time it

preserves the edges.

The purpose of this study is on the one hand to intro-

duce a new empirical MRP image reconstruction algo-

rithm, under the short name MRP-ISWLS (Median Root-

Prior-Image Space Weighted Least Squares). MRP-

ISWLS will be an MRP version of ISWLS (Image Space

Weigthed Least Squares), which was introduced in [5].

ISWLS has ISRA properties in noise manipulation and

WLS acceleration of reconstruction process. To assess

the performance of the new iterative reconstruction me-

thod we have used phantom data produced from simu-

lating a prototype small-animal PET system. We com-

pared reconstruction data with MRP-EM-ML, MRP-

ISRA and MRP-WLS following the OSL (One Step Late)

philoshophy [6]. The methods presented here are applied

to 2D sinograms. Moreov e r, the simultaneous version of

the aforementioned algorithms is implemented.

We note that simultaneous versions of reconstruction

algorithms, that is, algorithms where all image pixels are

simultaneously updated in every iteration, are of great

interest because of their ability to be implemented in

parallel computing architectures, which decreases dras-

tically the total reconstruction time [1].

2. THEORY

In general, every iterative method relies on the hypothe-

sis that the projection data y is linearly connected to the

image x of radiopharmaceutical spatial distribution, ac-

cording to the equation:

(1)

where

is a matrix that characterizes the PET system