2017/01/23 by Mohammadreza Soltani, Chinmay Hegde, Soltani, Mohammadreza +1 · 2 citations
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 #stat.ML
paper · pdf · doi:10.48550/arxiv.1701.06597
arxiv created 2017/01/23 · openalex publication_date 2017/01/23 · arxiv updated 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an algorithm that stably estimate the underlying components under general structured sparsity assumptions on these components. Specifically, we show that for certain types of structured superposition models, our method provably recovers the components given merely n = O(s) samples where s denotes the number of nonzero entries in the underlying components. Moreover, our method achieves a fast (linear) convergence rate, and also exhibits fast (near-linear) per-iteration complexity for certain types of structured models. We also provide a range of simulations to illustrate the performance of the proposed algorithm.