Study of Feasibility of Image Compression with Wavelets over Hexagonal Pixel Arrays using a Custom Photodetector Integrated Circuit

The use of hexagonal grids of pixels to represent digital images is a topic that has been studied for decades; however, despite its advantages there is relatively little work done on the subject. On the other hand, for the compression of images with rectangular grids, where there is far more research, the use of the wavelet transform is a strategy that allows high levels of performance to be achieved; two examples of image compression systems based on wavelets are the JPEG2000 standard and the IW44 algorithm used by DjVu, both currently still in use. In this work we are interested in evaluating the feasibility of a hexagonal grid image compression system using wavelets for implementation on a configurable sensor made of pixels on a hexagonal grid previously developed by our group. In order to do this, theoretical and implementation aspects of image compression with wavelets on hexagonal grids of pixels are studied first. A complete hexagonal image compression system is then implemented using Haar like wavelets and an adaptation of the coding algorithm for rectangular images SPIHT. To evaluate the performance of the proposed system, a comparison is made with its rectangular analogous version by testing with multiple images. Finally, a simple test is carried out on the configurable sensor that shows the it is possible to directly read the decomposition coefficients instead of reading pixel by pixel.