Random Sampling of Sparse Trigonometric Polynomials, II. Orthogonal Matching Pursuit versus Basis Pursuit

نویسندگان

  • Stefan Kunis
  • Holger Rauhut
چکیده

We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by Basis Pursuit has recently been studied by several authors, we provide theoretical results on the success probability of reconstruction via Thresholding and OMP for both a continuous and a discrete probability model for the sampling points. We present numerical experiments, which indicate that usually Basis Pursuit is significantly slower than greedy algorithms, while the recovery rates are very similar.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Sparse Recovery

List of included articles [1] H. Rauhut. Random sampling of sparse trigonometric polynomials. Appl. Comput. [2] S. Kunis and H. Rauhut. Random sampling of sparse trigonometric polynomials II-orthogonal matching pursuit versus basis pursuit. [3] H. Rauhut. Stability results for random sampling of sparse trigonometric polynomi-als. [4] H. Rauhut. On the impossibility of uniform sparse reconstruct...

متن کامل

Deterministic Sampling of Sparse Trigonometric Polynomials

One can recover sparse multivariate trigonometric polynomials from few randomly taken samples with high probability (as shown by Kunis and Rauhut). We give a deterministic sampling of multivariate trigonometric polynomials inspired by Weil’s exponential sum. Our sampling can produce a deterministic matrix satisfying the statistical restricted isometry property, and also nearly optimal Grassmann...

متن کامل

On the Impossibility of Uniform Sparse Reconstruction using Greedy Methods

It has previously shown that a trigonometric polynomial having at most M nonvanishing coefficients can be recovered from N = O(M log(D)) random samples by the greedy methods thresholding and orthogonal matching pursuit with high probability. In this note we show that these results cannot be made uniform in the sense that a single (random) sampling set cannot guarantee recovery of all such M -sp...

متن کامل

Wavelet Compressive Sampling Signal Reconstruction Using Upside-Down Tree Structure

This paper suggests an upside-down tree-based orthogonal matching pursuit UDT-OMP compressive sampling signal reconstruction method in wavelet domain. An upside-down tree for the wavelet coefficients of signal is constructed, and an improved version of orthogonal matching pursuit is presented. The proposed algorithm reconstructs compressive sampling signal by exploiting the upside-down tree str...

متن کامل

A dedicated greedy pursuit algorithm for sparse spectral modelling of music sound

A dedicated algorithm for sparse spectral modeling of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set call...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Foundations of Computational Mathematics

دوره 8  شماره 

صفحات  -

تاریخ انتشار 2008