Recovery of partially sampled PET images using compressed sensing

Methods: A uniform Ge-68 phantom (20 cm diameter and length) was imaged on a D-RX PET/CT scanner twice; once with all detectors operational (baseline) and once with 5 detector elements at each of 0, 90, 180 and 270 degrees turned off (partially sampled). The partially sampled (PS) sinogram was first decomposed into two different layers – cartoons and texture using Daubechie wavelets (6rh order) and 50% overlapping discrete cosine transform respectively. The sparsest possible solution for each layer was then determined using a soft thresholding algorithm. These solutions were subsequently converted to their corresponding layers, summed, and compared to the original PS sinogram. Comparison was done only for existing sinogram pixel values. This process was repeated iteratively until a RMS error of 5% or a total of 100 iterations was reached. For each iteration update, the values of the pixels corresponding to the missing detectors were obtained from the previous iteration while the remaining pixel values were extracted from the original sinogram (baseline scan). The resultant corrected sinograms where then reconstructed using OSEM and FB and the corresponding images for full and PS sinograms were compared using mean and max activity concentration in a ROI placed centrally over the phantom.