Hi Vishwaraj B Manur ,

If you think about surpassing the recovery guarantees of CS, it is indeed possible do that by exploiting statistical features of Multiple Measurement Vector (MMV) model (for example: correlation structure) along with CS algorithms. A seminal work can be found here for your starting point : Article Pushing the Limits of Sparse Support Recovery Using Correlat...

Hi

Please check the following work. It describes the process in details. I believe it will help you.

https://link.springer.com/chapter/10.1007/978-3-642-32112-2_14

Regards

Hi Md Sazal Miah ,

The article provided doesn't offer any generalized direction of CS, rather focused on a specific domain. Moreover, after 2012, the field CS saw astronomical growth in development as well. Regards.

Hello Md Sazal Miah and Shah Mahdi Hasan . Nope. I am not asking for alternatives or some evolution "inside" CS theory. I need a concept that completely overcome the CS theory. As I mentioned in question, Nyquist Criterion is overcome by CS theory, similarly is there any "XYZ theory" that succeeds the entire CS theory ? Thank you

Not that I know of. It is important to note that, lots of theoretical development happened beyond conventional CS framework but still use the phrase "Compressed Sensing" in their names. For example: Deep Compressed Sensing.

Dear Vishwaraj B Manur,

First of all, we should separate the concept of Sampling against the concept of Sensing. These two are not interchangeable!

1. Compressed Sensing theory states that it could recover a set of coefficients (which represents in a specific transform domain the useful information from the analyzed signal) from less samples than Nyquist sampling criteria in order to be able to reconstruct a signal (of course as it could be reconstructed from uniform samples by classical Shannon theory).

2. Compressive Sampling theory states that a signal can be sampled by a protocol (non-uniform sampling, random sampling, modulation and sampling, etc.) which will allow later to be reconstructed by means of a Compressed Sensing algorithm which knows about the used sampling protocol.

3. There are at least 4 sampling ways (according to Figure 2 from https://core.ac.uk/download/pdf/34645298.pdf ) to acquire the information from a signal. Take into account that practical CS is a lossy compression, and this is due to the non-ideal process which happens when the sampling process take place.