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: 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 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 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: 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.

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: 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: Fast Hadamard transforms (FHT) are implemented using a pipelined architecture having an input stage, a processing stage, and an output stage, the FHT having a single internal loop back between the output stage and the input stage, the processing stage having at least one Hadamard processing unit. The FHT implementations provided both forward and inverse transformations, and, lossless normalized and lossfull unnormalized transformations, while the FHT implementation includes only multiplexers, demultiplexer, latches, and shift registers, and while, the processing unit stage includes processing units using only shift registers and effective adders, for fast, low power, and low weight Hadamard transform implementations.

Abstract: Discrete Cosine Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain for enabling recursive merges and splits in transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. In the split transform process, whole transformed data is split using combinational processing into first and second transformed data halves in the transform domain as a true split. In the merge transform process, first and second transform halves are merged using combinational processing into a merged transformed data whole in the transform domain. In either case, time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole.

Abstract: Fast Fourier Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the Fourier transform domain for enabling recursive merges and splits in Fourier transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. Whole transformed data is split using combinational processing into transformed data halves in the transform domain as a true split. Transform halves are merged using combinational processing into whole merged transformed data in the transform domain. Time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole. The split halves can be merged by the merge process combinational processing and the merged whole are split by the split process combinational processing.

Abstract: A generalized radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain enabling recursive merges and splits in transform domain data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. Whole transformed data is split using combinational processing into transformed data halves in the transform domain as a true split. The transformed halves are merged using combinational processing into whole merged transformed data in the transform domain. Time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole. The split halves can be merged by the merge process combinational processing and the merged whole can be split by the split process combinational processing.

Abstract: Fast Hartley Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves for enabling recursive merges and splits in Hartley transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward Hartley transform processing is firstly transform processed followed by combinational processing. Whole transformed data is split using combinational processing into transformed data halves in the Hartley transform domain as a true split. The transformed halves are merged using combinational processing into whole merged transformed data in the Hartley transform domain. Time or spatial domain input data can be transformed into the Hartley transform domain in the form of split halves or merged whole. The split halves can be merged by the merge process combinational processing and the merged whole can be split by the split process combinational processing.

Abstract: Discrete Karhunen-Loeve Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the KLT domain for enabling recursive merges and splits in the KLT domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. Whole transformed data is split using combinational processing into transformed halves in the transform domain as a true split. Transformed halves are merged using combinational processing into whole merged transformed data in the transform domain. Time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole. The split halves are merged by the merge process combinational processing and the merged whole are split by the split process combinational processing.

Abstract: Discrete Sine Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the DST transform domain for enabling recursive merges and splits in DST transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. Whole transformed data is split using combinational processing into transformed data halves in the transform domain as a true split. The transformed halves are merged using combinational processing into whole merged transformed data in the transform domain. Time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole. The split halves are merged by the merge process combinational processing and the merged whole are split by the split process combinational processing.

Abstract: Discrete Sine Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain for enabling recursive merges and splits in transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. In the split transform process, whole transformed data is split using combinational processing into first and second transformed data halves in the transform domain as a true split. In the merge transform process, first and second transform halves are merged using combinational processing into a merged transformed data whole in the transform domain. In either case, time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole.

Abstract: A generalized radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain enabling recursive merges and splits in transform domain data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. In the split transform process, whole transformed data is split using combinational processing into first and second transformed data halves in the transform domain as a true split. In the merge transform process, first and second transform halves are merged using combinational processing into a merged transformed data whole in the transform domain. In either case, time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole.

Abstract: Fast Fourier Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain for enabling recursive merges and splits in transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. In the split transform process, whole transformed data is split using combinational processing into first and second transformed data halves in the transform domain as a true split. In the merge transform process, first and second transform halves are merged using combinational processing into a merged transformed data whole in the transform domain. In either case, time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole.

Abstract: Fast Hartley Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain for enabling recursive merges and splits in transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. In the split transform process, whole transformed data is split using combinational processing into first and second transformed data halves in the transform domain as a true split. In the merge transform process, first and second transform halves are merged using combinational processing into a merged transformed data whole in the transform domain. In either case, time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole.

Abstract: Discrete Karhunen-Loeve Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain for enabling recursive merges and splits in transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. In the split transform process, whole transformed data is split using combinational processing into first and second transformed data halves in the transform domain as a true split. In the merge transform process, first and second transform halves are merged using combinational processing into a merged transformed data whole in the transform domain. In either case, time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole.