This paper demonstrates compression of an image using wavelet packet decomposition. One reasonable criterion for selecting decomposition for the compression of image is the additive cost function. The entropy based cost function used here to select the best basis is the log-energy entropy metric. The algorithm checks the entropy of decomposed nodes (child nodes) with entropy of node, which has been decomposed (parent node) and takes decision of decomposition of a node. An adaptive thresholding is used for quantization. The wavelet packet coefficients are classified as important or unimportant depending on whether its value lies above or below the threshold value. After the data has been quantized into a finite set of values, it can be encoded using an entropy coder to give additional compression. Results are compared in terms of encoding time, decoding time, signal to noise ratio, root mean square error value and compression ratio.