Dictionary Learning in Compressed Sensing using undersampled data in PET ... Imaging Physics, MD Anderson Cancer Center, Houston, TX 77030. Objective: ...
Dictionary Learning in Compressed Sensing using undersampled data in PET Imaging. SeyyedMajid Valiollahzadeh 1 ; John W. Clark, Jr 1 ; Osama R. Mawlawi 2 1. Electrical and computer Engineering, Rice University, Houston, Texas 77005 2. Imaging Physics, MD Anderson Cancer Center, Houston, TX 77030 Objective: Compressed sensing in PET imaging usually leverages the sparse representation of the acquired data in a predefined domain to help recover potential undersampling in the sinogram space. The majority of CS methods use analytical predefined sparsifying transforms such as wavelets, curvelets, and finite transforms. In this work, we evaluate the dictionary learning (DL) transform (sparsifying domain) to reconstruct PET images from partially sampled data and compare the results with a fully sampled image. Methods: Let xi D i where xi represents overlapping 4x4 pixel patches obtained from the partially sampled image, D is a matrix containing coefficients of the dictionary transform and is a sparse vector. Our objective is to optimize xi D i subject to the constraints that the coefficients be sparse and more importantly that D be bounded by a Poisson likelihood penalization. This optimization is performed iteratively in two steps for all patches concurrently: once we update columns of D while the coefficients are fixed and second we update the coefficient while D is fixed. Stopping criteria is based on 500 iterations. This algorithm was tested using an IEC image quality phantom containing 6 spheres with a sphere to background ratio of 10:1. 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 (11% off)- partially sampled (PS). The PS and DL-recovered images were compared to baseline by calculating the percent error in mean activity concentration (AC) in the 6 spheres and background. Results: The percent error in AC in the 6 spheres (largest - smallest) and background for PS (DL-recovered) images were -1(-0.9), -18(1.36), -24(3.9), -11(5.1), -9(9.1), -10(12.9), and 2(26.5) respectively. -22.5(6.3), -15.6(13.7), -19.6(7.8), -22.2(9.8), -14.2(25), -11.9(21.4), 33.3(22.2)
Baseline PS DL
Sphere 1 11.1 8.6 11.8
Sphere 2 10.9 9.2 12.4
Sphere 3 10.2 8.2 11
Sphere 4 8.1 6.3 8.9
Sphere 5 5.6 4.8 7.0
Sphere 6 4.2 3.7 5.1
Background 0.9 0.6 1.1
Conclusion: Poisson compressed sensing with DL seems to be a good approach to recover partially sampled PET data. This approach has implications towards reducing scanner cost while maintaining PET accurate image quantification.
