I am new in the field of compressive sensing, I've read many papers explaining that compressive sensing is used widely in sparse signal reconstruction. I've tried to understand how compressive sensing is used in signal processing, but I couldn't understand the concept.
According to the paper On some common compressive sensing recovery algorithms and applications - Review paper in page 2, THE MATHEMATICAL BACKGROUND OF THE COMPRESSIVE SENSING CONCEPT, I got the best description for compressing sensing mathematical concept. Assuming we are dealing with signal $x$ with length $N$, that is sparse in time domain. So according to equation 5, we can write the system equation as $Y = AX$, where $A$ is the CS matrix. My questions,
1- What is the signal $x$ with length $N$ which we want to reconstruct ? Is it $X$ or $Y$ ? And what does $A$ represent?
2- Is there any tutorial or file which explain that point with details and in easy way?