Compressed sensing

Signal processing
(Candes et al. 2006)


Compressed sensing is a technique to recover a sparse signal from partial observations.

The signal is described as a $N$-dimensional vector \(\textbf{s}\). We make \(M\) measurements, where a measurements means a projection of the signal \(\textbf{s}\) onto some known vector. The result of all these measurements can be written as \(\textbf{y} = \textbf{Fs}\), where \(\textbf{F}\) is a \(M \times N\) matrix.

In the context of compressed sensing, we have \(M < N\). This results in an underdetermined linear system which usually has an infinite number of solutions.


  1. . . "Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information". IEEE Transactions on Information Theory 52 (2):489–509. DOI.
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