Implementation of Direct Indexing and 2-V Golomb Coding of Lattice Vectors for Image Compression

Indexing of code vectors is a most difficult task in lattice vector quantization. In this work we focus on the problem of efficient indexing and coding of indexes. Index assignment to the quantized lattice vectors is computed by direct indexing method, through which a vector can be represented by a scalar quantity which represents the index of that vector. This eliminates the need of calculating the prefix i.e. index of the radius ( R) or norm and suffix i.e. the index of the position of vector on the shell of radius R, also eliminates index assignment to the suffix based on lattice point enumeration or leader’s indexing . Two value golomb coding is used to enumerate indices of quantized lattice vectors. We use analytical means to emphasize the dominance of two value golomb code over one value golomb code. This method is applied to achieve image compression. Indexes of particular subband of test images like barbara, peppers and boat are coded using 2-value golomb coding (2-V GC) and compression ratio is calculated. We demonstrate the effectiveness of the 2-V GC while the input is scanned columnwise as compare to rowwise. Experimentally we also show that good compression ratio is achieved when only higher order bits of the indexes are encoded instead of complete bits

Re-Ordered FEGC and Block Based FEGC for Inverted File Compression

Data compression has been widely used in many Information Retrieval based applications like web search engines, digital libraries, etc. to enable the retrieval of data to be faster. In these applications, universal codes (Elias codes (EC), Fibonacci code (FC), Rice code (RC), Extended Golomb code (EGC), Fast Extended Golomb code (FEGC) etc.) have been preferably used than statistical codes (Huffman codes, Arithmetic codes etc). Universal codes are easy to be constructed and decoded than statistical codes. In this paper, the authors have proposed two methods to construct universal codes based on the ideas used in Rice code and Fast Extended Golomb Code. One of the authors’ methods, Re-ordered FEGC, can be suitable to represent small, middle and large range integers where Rice code works well for small and middle range integers. It is also competing with FC, EGC and FEGC in representing small, middle and large range integers. But it could be faster in decoding than FC, EGC and FEGC. The authors’ another coder, Block based RFEGC, uses local divisor rather than global divisor to improve the performance (both compression and decompression) of RFEGC. To evaluate the performance of the authors’ coders, the authors have applied their methods to compress the integer values of the inverted files constructed from TREC, Wikipedia and FIRE collections. Experimental results show that their coders achieve better performance (both compression and decompression) for those files which contain significant distribution of middle and large range integers.