Is the basis of the sparse signal assumed known in compressed sensing?

1. What is signal sparsity?
2. What is meant by compressed sensing?
3. What is compressed sensing in image processing?
4. Why is compressed sensing important?

What is signal sparsity?

A signal is said to be sparse if it can be represented in a basis or frame (e.g Fourier, Wavelets, Curvelets, etc.) in which the curve obtained by plotting the obtained coefficients, sorted by their decreasing absolute values, exhibits a polynomial decay.

What is meant by compressed sensing?

Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.

What is compressed sensing in image processing?

Compressed sensing (CS) is an image acquisition method, where only few random measurements are taken instead of taking all the necessary samples as suggested by Nyquist sampling theorem. It is one of the most active research areas in the past decade.

Why is compressed sensing important?

Compressive sensing possesses several advantages, such as the much smaller need for sensory devices, much less memory storage, higher data transmission rate, many times less power consumption. Due to all these advantages, compressive sensing has been used in a wide range of applications.