2012/02/08 by Chinmay Hegde, Richard G. Baraniuk, Hegde, Chinmay +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (stat.ML) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques #cs.IT #math.IT #stat.ML
paper · pdf · doi:10.48550/arxiv.1202.1595
20 pages, 3 figures. Submitted to IEEE Trans. Inform. Theory. Revised version (June 2012) : fixed typos in proofs
openalex publication_date 2012/02/08 · arxiv created 2012/06/08 · arxiv updated 2012/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a first order projected gradient method to recover the signal components. Despite the nonconvex nature of the recovery problem and the possibility of underdetermined measurements, SPIN provably recovers the signal components, provided that the signal manifolds are incoherent and that the measurement operator satisfies a certain restricted isometry property. SPIN significantly extends the scope of current recovery models and algorithms for low dimensional linear inverse problems and matches (or exceeds) the current state of the art in terms of performance.