  The primary goal of this work is to review the importance of data compression
and present a fast Fourier-based method for generating the deterministic
compression matrix in the area of deterministic compressed sensing. The
principle concepts of data compression such as general process of data
compression, sparse signals, coherence matrix and Restricted Isometry Property
(RIP) have been defined. We have introduced two methods of sparse data
compression. The first method is formed by utilizing a stochastic matrix which
is a common approach, and the second method is created by utilizing a
deterministic matrix which is proposed more recently. The main goal of this
work is to improve the execution time of the deterministic matrix generation.
The execution time is related to the generation method of the deterministic
matrix. Furthermore, we have implemented a software which makes it possible to
compare different methods of reconstructing data compression. To make this
comparison, it is necessary to draw and compare certain graphs, e.g. phase
transition, the ratio of output signal to noise and input signal to noise,
signal to noise output and also the ratio of percentage of accurate
reconstructing and order of sparse signals for various reconstructing methods.
To facilitate this process, the user would be able to draw his/her favorite
graphs in GUI environment.
