We now move onto describe certain improvements over the algorithm that we have implemented in our project. We divide this chapter into two portions, one for Images and other for Audio.

Image Compression
 
For Image Compression, following improvements can be made:

• Non-separable filter banks could be tried and their affect noted. The bases functions for the 9/7 system that we used in our project are symmetric in the horizontal and vertical directions only. Non-Separable filter banks could improve on the symmetry of the basis functions.
• Also [Vetterli] speaks of a Quincunx downsampling approach, in which the downsampling removes odd diagonals. This approach may have more to offer than the normal horizontal & vertical downsampling.
• Loss Less source coding method could be improved upon. In particular, the Set Partitioning In Hierarchical Trees (SPIHT) by [Amir] could be used to enhance bit rate and output quality further. The method is especially suited to Wavelet Transform.
• Lattice Structures could be used to implement the linear phase 9/7 filters. Lattice structures are more immune to quantization effects in finite precision machines. Also, they can help reduce the complexity of the algorithm further.
• Another improvement in the Image Compression algorithm could be the incorporation of different quantization schemes into the algorithm including non-uniform quantizers, and vector quantizations.
• Effects of a large variety of wavelets could be observed and their results tabulated.
• Different measures for perceptual quality of image could be evolved.
• Wavelet Packet Transform can be explored.
• Algorithm could be modified to allow progressive transmission of images.
• JPEG style source coding method of the transform coefficients is another idea worth pursuing.

• The Bit allocation scheme could be modified to make it more sophisticated.
• Lattice structures could be used to provide a relative degree of immunity to noise, and to reduce the complexity further.
• Different wavelets and different number of levels could also be tried.
• Perceptual models of the human Auditory System could be incorported into the algorithm.
• Non-uniform quantization could be tried with audio as well.
• Since the MIPS requirement for the coder are small, a multi-channel system could be developed that would directly code into one bit-stream, two or more channels.
• SPHIT can be applied to 1-D audio signals as well.