2017/01/23 by Mohammadreza Soltani, Chinmay Hegde, Soltani, Mohammadreza +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1701.06597
openalex publication_date 2017/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the demixing problem of two (or more) high-dimensional vectors\nfrom nonlinear observations when the number of such observations is far less\nthan the ambient dimension of the underlying vectors. Specifically, we\ndemonstrate an algorithm that stably estimate the underlying components under\ngeneral \structured sparsity assumptions on these components.\nSpecifically, we show that for certain types of structured superposition\nmodels, our method provably recovers the components given merely n =\n\O(s) samples where s denotes the number of nonzero entries in the\nunderlying components. Moreover, our method achieves a fast (linear)\nconvergence rate, and also exhibits fast (near-linear) per-iteration complexity\nfor certain types of structured models. We also provide a range of simulations\nto illustrate the performance of the proposed algorithm.\n