Compressed Sensing (study)

From now on, I will start a self book study session on Compressed Sensing, which I consider to be an important math tool for future research.
I will start with the "Introduction to Compressed Sensing" by Mark A. Davenport et al.
The study notes will be constantly updated in the file "CS_notes", it is mainly a summary of my study progress of "Introduction to Compressed Sensing" with some additional background material for me to understand, thus most of the material in the notes belongs to Mark A. Davenport et al., it is important to note that.

The Compressed Sensing has two equally important part:
(1). Sensing Matrix M, this is vital for practical measurement design, and the construction of the sensing matrix M requires knowledge of the sparsity of the data we want to measure.
(2). Signal Recovery via l1-minimization.

Up to June 13th, I have finished the first part--properties and construction of sensing matrix. But it is really difficult to understand the theory, compared to the Shannon sampling theory. I think partly due to the writing and partly due to the early stage of Compressed Sensing itself.  Hope the later study can be easier.