- tags
- Signal processing
- resources
- (Candes et al. 2006)

## Description

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.

## Bibliography

- E.J. Candes, J. Romberg, T. Tao. . "Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information".
*IEEE Transactions on Information Theory*52 (2):489–509. DOI.