What is measurement matrix in compressive sensing?
The measurement matrix is one of most essential parts in compressive sensing. For this application, the measurement matrix decides each time which part of the IR light will be reflected and finally reach the CNT detector. Correctly selected measurements will lead to fewer measurements and a clear reconstructed image.
Compressive sensing (also known as compressive sampling or sparse signal sampling), a relatively new field of signal processing that has emerged over the last two decades. Based on the idea that many signals, particularly in the natural world, are sparse or compressible in some domain.
The scientific background of compressive sensing lies in the field of information theory and signal processing.
Particularly in the development of the Shannon-Nyquist sampling theorem. The Shannon-Nyquist theorem states that in order to perfectly reconstruct a signal. It must become sampled at a rate of at least twice its highest frequency component. While this theorem is fundamental to digital signal processing, it can be quite inefficient in situations where the signal has a sparse representation.
Compressive sensing seeks to overcome this inefficiency by exploiting the sparsity or compressibility of the signal in some domain. The basic idea is to acquire a small number of linear measurements of the signal. A number sufficient to recover the underlying sparse representation. Accomplished by designing a sensing matrix that maps the high-dimensional signal to a low-dimensional space. While preserving enough information to allow for accurate recovery of the signal.
The development of compressive sensing has become driven by advances in mathematics and computer science. Moreover, particularly in the areas of linear algebra, optimization, and information theory. It has found applications in a wide range of fields. Including image and video processing, radar and sonar imaging, medical imaging, and lastly, more recently, in machine learning and data science.
What is measurement matrix in compressive sensing?
