Decoding by linear programming
IEEE Transactions on Information Theory
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We propose an efficient, deterministic algorithm designed to reconstruct images from real Radon-Transform and Attenuated Radon-Transform data. Its input consists in a small family of recorded signals, each sampling the same composite pboton or positron emission scene over a non-Gaussian, noisy cbannel. The reconstruction is performed by combining a novel numerical implementation of an analytical inversion formula [1] and a novel signal processing tecbnique, inspired by the work of Tao and Candes [2] on code reconstruction. Our approacb is proven to be optimal under a variety of realistic assumptions. We also indicate several medical imaging applications for which the new technology achieves high fidelity, even when dealing with real data subject to substantial non-Gaussian distortions.