Why is incoherence important for compressive sensing?

1. What is the importance of compressed sensing?
2. How does compressed sensing work?
3. What is compressive sensing theory?
4. What is the difference between compressed sensing and sampling?

What is the importance of compressed sensing?

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.

How does compressed sensing work?

Compressed sensing addresses the issue of high scan time by enabling faster acquisition by measuring fewer Fourier coefficients. This produces a high-quality image with relatively lower scan time. Another application (also discussed ahead) is for CT reconstruction with fewer X-ray projections.

What is compressive sensing theory?

The compressive sensing theory states that the signal can be reconstructed using just a small set of randomly acquired samples if it has a sparse (concise) representation in certain transform domain.

What is the difference between compressed sensing and sampling?

Compressed sensing is a new sampling theory, it is sampling randomly under the frequency far less than the Nyquist sampling frequency to obtain the partial information of the signal, and then restoring the whole signal through the nonlinear reconstruction algorithm.