Numerical study of linear predictive coding for the compression of gray scale images

The subject of this thesis is a system for the lossless compression of data in the format of 512 X 512 8-bit gray-scale images. Linear predictive coding cascaded with Huffman coding (LPC_HUFF) is applied to four representative images to determine if the storage requirements could be lowered by reducing the statistical redundancy in the images. The images were compressed by filtering each image with its optimal prediction coefficients followed by Huffman encoding of the filtered image. The statistical properties of the filtered images were studied by examining the following statistical parameters: minimum and maximum values, histogram, standard deviation, and entropy. To measure the amount of data reduction, the size of the compressed image was compared to the size of the original images. The decompression stage of the LPC_HUFF system was implemented to verify that the system being studied compressed images without error. Using an FIR predictive filter the optimal predictor coefficients were found to be nearly identical especially for lower order filters. The transient response caused outlying values to appear in the histograms of the filtered images as the length of the impulse response increased; consequently, the magnitude of the minimum and maximum values, and the entropy increased with filter order. Since the entropy results show that a simple differencing approach was optimal, the images were filtered using a first order filter to reduce the redundancy. The compression ratio for the data files of the four representative images ranged between 0.5429 and 0.7619.