# Compressed sensing

tags
Signal processing

## 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.

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