Wavelet analysis is a branch of mathematics that has a broad area of application. It has its roots, in the streams like biomedical, neurosciences, etc.

Image compression is one of the most significant applications of wavelet. It is used in the field of signal processing also.

There are enormous applications of wavelets, other than the above-mentioned ones. In the first chapter, we have revealed the history of wavelets and mentioned the contributions of some eminent researchers in the field of wavelets.

We have given the basic definitions which are must begin with the wavelet -analysis. Also, we added appropriate examples wherever required to give a glimpse of the concept.

In Chapter 2, we have explored the study of the research paper entitled,” Convex Multiresolution Analysis “, due to Patrick L. Combettes and Jean-Christophe Pesquet, which was published in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.

20, no. 12, December 1998.

In support of definitions and results, we have constructed some examples. .