On the linear independence of spikes and sines

Abstract

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof involves depends on an extrapolation argument of Bourgain and Tzafriri.

16 pages, 4 figures. Revision with new proof of major theorems

References in corpus (1)

• Sparsity and Incoherence in Compressive Sampling

Cited by in corpus (12)

• Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
• Peak Reduction and Clipping Mitigation by Compressive Sensing
• The achievable performance of convex demixing
• On uncertainty principles in the finite dimensional setting
• The Sparsity Gap: Uncertainty Principles Proportional to Dimension
• Sparsity and `Something Else': An Approach to Encrypted Image Folding
• Sharp recovery bounds for convex demixing, with applications
• Binary Discrete Fourier Transform and its Inversion
• Limiting Empirical Singular Value Distribution of Restrictions of Unitary Matrices
• Recovery of Sparsely Corrupted Signals
• Inversion of band-limited discrete Fourier transforms of binary images: Uniqueness and algorithms
• Discrete Uncertainty Principle in Quaternion Setting and Application in Signal Reconstruction