A global method for invertible integer DCT and integer wavelet algorithms

Invertible integer DCT algorithms

Matrix factorizations for reversible integer mapping

Reversible integer mapping is essential for lossless source coding by transformation. A general matrix factorization theory for reversible integer mapping of invertible linear transforms is developed in this paper. Concepts of the integer factor and the elementary reversible matrix (ERM) for integer mapping are introduced, and two forms of ERM—triangular ERM (TERM) and single-row ERM (SERM)—are...

Invertible update-then-predict integer lifting wavelet for lossless image compression

This paper presents a new wavelet family for lossless image compression by re-factoring the channel representation of the update-then-predict lifting wavelet, introduced by Claypoole, Davis, Sweldens and Baraniuk, into lifting steps. We name the new wavelet family as invertible update-then-predict integer lifting wavelets (IUPILWs for short). To build IUPILWs, we investigate some central issues...

Lossless Image Compression Using Integer to Integer Wavelet Transforms

Invertible wavelet transforms that map integers to integers are important for lossless representations. In this paper, we present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless im...

Integer DCT-based Image Coding

DCT-based image/video coding is still popular now. In this paper, a novel embedded image coding scheme based on integer reversible DCT is proposed. It integrates lossy and lossless coding schemes perfectly. The transform is implemented by factoring the float DCT transform matrix into a series of integer reversible transform matrices. We apply the series of matrices to image samples, and encode ...