Randomized Projections for Improved Sensing and Imaging in Positron Emission Tomography

Positron Emission Tomography (PET) aims at recovering the metabolic activity of an organ of interest. Established algorithms implemented in contemporary PET scans are based on an approximation of the inverse Radon transform, resulting in a suboptimal estimate. In this context, the Bluebild algorithm is proposed to recover the metabolic activity through a mathematical model that reformulates the inversion problem in a continuous framework. The procedure involves computing the in- verse of a very large and dense Gram matrix, increasing significantly the computational cost and numerical instability of the algorithm. In this project, we investigate the use of Gaussian random projections as means of reducing the high dimensionality of the PET scan data, and consequently of the Gram matrix. We show that the conditioning of the Gram matrix is improved in expectation, making the recovery more stable and resilient to noise. Simulations are used to as- sess the accuracy of the estimate as well as the conditioning of the Gram matrix. Finally, we show that the results with the Bluebild framework are more accurate than the state-of-the-art algorithms.