Abstract: A front-end shared Haar transform is particularly adapted for cascade connection to an appended transform for providing lossless transform of an input data set, the appended transforms selected from the group consisting of an appended discrete cosine type-II (DCT-II) transform for forming a lossless DCT-II transform, an appended discrete cosine type-IV (DCT-IV) transform for forming a lossless DCT-IV transform, and an appended Haar transform for forming a lossless extended Haar transform.

Abstract: A shared lossless Haar transform and an appended discrete cosine transform type-II are combined to form a discrete cosine type-II transform in a parallel pipelined architecture for providing lossless data transformation.

Abstract: A shared lossless Haar transform and an appended type-IV discrete cosine transform are combined to form a lossless discrete cosine type-IV transform having a fast pipeline architecture for providing fast reversible lossless DCT-IV transform data.

Abstract: A shared lossless Haar transform and an appended Haar transform are combined to form a lossless extended Haar transform in a pipeline architecture for providing fast lossless compressed data that is reversible. The extended Haar transform also provide intrinsic decorrelation for decorrelating corrected randomly generated numbers.

Abstract: A system provides lossless split and merge processes of integer discrete cosine transform (DCT) transformed data such that the discrete cosine transform of one data block may be split into two half length DCT odd and even blocks for merging, with split and merge processes being lossless and are generated in the discrete cosine transformed domain. After splitting, the redundancy existing between the two integer discrete cosine transformed half data blocks allows one to approximately reconstruct the original data block in case one of the discrete cosine transformed half data block is lost during transmission.

Abstract: The integrated lifting transform provides both the lossy and lossless lifting wavelet transforms while sharing the same lifting chain for either lossy data compression or lossless data compression. The lifting steps can provide a lossless compression and a lossy compression directly from lossless compression while the integer-to-integer adaptive four-stage lifting wavelet transform provides the lossless compression with improved performance.

Abstract: The lifting transform reduces the number of lifting steps in lossless data compression while improving the overall rounding errors incurred in the real-to-integer conversion process at each of the lifting steps. The compression ratio increases when used for lossless image data compression. The lifting transform further saves memory space and decreases signal delay.

Abstract: An adaptive lifting transform provides lossless image data compression on an improved edge prediction process. The adaptive predictor works on pixel-by-pixel basis that does not need bookkeeping overhead, especially for integer-to-integer wavelet transform for reducing the number of lifting steps for use in JPEG2000 image compression.