Publisher Summary This chapter discusses wavelet-based image compression. Compression schemes can be broadly classified as loss-less or lossy compression. Loss-less compression schemes assume no loss of information during a compression-decompression cycle. This is most suited to data that need to be reconstructed exactly. Lossy compression schemes allow a certain error during a compression-decompression cycle, as long as the information loss is tolerable (i.e. the quality of the data is acceptable). The degree of tolerance to information loss is dictated by the particular application and some distortion metric appropriate to the application at hand is employed to measure the quality of the compression. The chapter further introduces the fundamentals of image compression and overviews the various compression algorithms. It also reviews the transformation techniques used in image compression and describes image compression using optimal task-based and best-basis image compression algorithms.