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Evaluation of Penalizing Functions in Compressed Sensing to Recover Undersampled Data in PET Imaging

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S Valiollahzadeh

S Valiollahzadeh1*, J Clark1, O Mawlawi2, (1) Electrical and Computer Engineering, RICE University, Houston, Texas, (2) Department of Imaging Physics, MD Anderson Cancer Ctr., Houston, TX

SU-E-I-83 Sunday 3:00PM - 6:00PM Room: Exhibit Hall

Purpose:
Previously we proposed the use of compressed sensing (CS) techniques to recover partially sampled data in PET imaging (Valiollahzadeh et al IEEE MIC 2012). Here we compare the effect of various penalizing functions on the accuracy of the recovered activity concentration (AC) in PET images

Methods:
The recovery of partially sampled data using CS techniques requires minimizing a cost function describing a sparse model while being subject to the constraint of a partially observed data set. In this work we define the cost function as the summation of two terms: a Poisson log likelihood function to model the noise, and a penalty term to represent the sparse model. Four sparse models were evaluated: a TV model which assumes the image has a sparse representation in the finite difference domain; a linear combination of a wavelet and TV (WT) model; a recursive dyadic partitions (RDP) model which which estimates the structure of an image; and a variant of RDP that utilizes a cyclespun translation invariant version known as RDPTI. These 4 algorithms were tested using an IEC phantom containing 6 spheres (10:1 ratio). The phantom was imaged on a D-RX PET/CT scanner twice; once with all detectors operational (baseline) and once with 4 detector blocks at each of 0, 90, 180 and 270° turned off to create a partially sampled (PS) image. The PS image was corrected using the 4 different algorithms and the resultant images were compared to baseline by evaluating the mean AC in the spheres and background.

Results:
The average percent error in AC for the spheres (background) for the TV, WT, RDP and RDPI algorithms were 12.6(5.3), 4.3(5.1), 8.9(7.6), and 10.7(13)% respectively.

Conclusion:
WT gave the most accurate AC and the least spurious artifacts suggesting its superior performance over the other algorithms.

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