This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, in nite dictionary. We show how to compute the estimator via semide nite programming and provide guarantees on its mean-square error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semide nite programming approach outperforms two classical spectral estimation techniques
- Compressed Sensing off the grid - Gongguo Tang, Badri Narayan Bhaskar, Parikshit Shah, Benjamin Recht
- Atomic Norm Denoising with applications to Line Spectral Estimation - Badri Narayan Bhaskar, Benjamin Recht
- Atomic Norm Denoising with applications to Line Spectral Estimation - Badri Narayan Bhaskar, Gongguo Tang, Benjamin Recht
- Sunday Morning Insight: The 200 Year Gap.
- Robust Near-Separable Nonnegative Matrix Factorization Using Linear Optimization - implementation -
- Robustness Analysis of HottTopixx, a Linear Programming Model for Factoring Nonnegative Matrices - implementation -
- Hott Topixx: Factoring nonnegative matrices with linear programs - implementation -
- Blind Deconvolution using Convex Programming - implementation -
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.