Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information

Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information (2006)

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by Emmanuel J. Candès , Justin Romberg , Terence Tao

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BibTeX

@MISC{Candès06robustuncertainty,
    author = {Emmanuel J. Candès and Justin Romberg and Terence Tao},
    title = {Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information},
    year = {2006}
}

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Abstract

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this paper is as follows. Suppose that is a superposition of spikes @ Aa @ A @ A obeying @�� A I for some constant H. We do not know the locations of the spikes nor their amplitudes. Then with probability at least I @ A, can be reconstructed exactly as the solution to the I minimization problem I aH @ A s.t. ” @ Aa ” @ A for all

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