EAGER: Ultra-FFAST Alias Codes for Sparse Spectrum Estimation: Next Generation Compressed Sensing

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This proposal targets the theoretical foundations and algorithmic design of ultra-large-scale sparse signal recovery and spectral estimation problems, with applications to fast MRI acquisition, low-power spectrum-sensing for cognitive radio, and low-power spectroscopy for deep-space exploration. While compressed sensing has recently emerged as a powerful framework for understanding the fundamental limits of sparse signal processing, current algorithms based on convex optimization, are difficult to scale efficiently. This proposal is motivated therefore to address the challenge of scale in the theory and design of sparse signal recovery problems, with the goal of enabling real-time processing capability. This proposal develops the mathematical foundations as well as practical sub-linear-time algorithms for ultra-large-scale sparse signal recovery and spectral estimation problems. The theory and algorithms are derived through an interdisciplinary mix of intellectual tools from coding theory, graph theory, number theory, and statistical signal processing. This leads to the proposal of new computational primitives dubbed as sparse-graph alias codes that are analogous to Low-Density-Parity-Check (LDPC) codes that have revolutionized modern communication systems. The proposed framework is envisioned to provide a similar impact on next-generation sparse signal processing systems with respect to (i) acquisition overhead; (ii) computational and energy efficiency; and (iii) performance guarantees and stability.