FPGA implementation of the pixel purity index algorithm

The Pixel Purity Index (PPI) is an algorithm employed in remote sensing for analyzing hyperspectral images. Particularly for low-resolution imagery, a single pixel usually covers several different materials, and its observed spectrum is (to a good approximation) a linear combination of a few pure spectral shapes. The PPI algorithm tries to identify these pure spectra by assigning a pixel purity index to each pixel in the image; the spectra for those pixels with a high index value are candidates for basis elements in the image decomposition. The PPI algorithm is extremely time consuming but is a good candidate for parallel hardware implementation due to its high volume of independent dot-product calculations. This article presents two parallel architectures we have developed and implemented on the Wildforce board. The first one is based on bit-serial arithmetic operators and the second deals with standard operators. Speed-up factors of up to 80 have been measured for these hand-coded architectures. In addition,the second version has been synthesized with the Streams-C compiler. The compiler translates a high level algorithm expressed in a parallel C extension into synthesizable VHDL. This comparison provides an interesting way of estimating the tradeoff between a traditional approach which tailors the design to get optimal performance and a fully automatic approach which aims to generate a correct design in minimal time.