With the increasing growth of technology and the entrance into the digital age, one has to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an efficient and effective manner, in order for it to be put to practical use. Wavelets provide a mathematical way of encoding information in such a way that it is layered according to level of detail. This layering facilitates approximations at various intermediate stages. These approximations can be stored using a lot less space than the original data. This paper aims at the analysis on image compression technique using Discrete Wavelet Transform (DWT) and Wavelet Packet Transform (WPT) with Set Partitioning in Hierarchical Tree (SPIHT). Finally a performance comparison is made between the techniques based on different parameters like Peak Signal to Noise Ratio (PSNR), Compression Ratio (CR), Mean Square Error (MSE) and Root Mean Square Error (RMSE).