Wavelets provide a powerful and remarkably flexible set of tools for handling fundamental problems in science and engineering, such as audio de-noising, signal compression, object detection and fingerprint compression, image de-noising, image enhancement, image recognition, diagnostic heart trouble and speech recognition, to name a few. Here, we are going to concentrate on wavelet application in the field of Image Compression so as to observe how wavelet is implemented to be applied to an image in the process of compression, and also how mathematical aspects of wavelet affect the compression process and the results of it. Wavelet image compression is performed with various known wavelets with different mathematical properties. We study the insights of how wavelets in mathematics are implemented in a way to fit the engineering model of image compression.