Abstract: A data processing system and method for performing a wavelet-like transformation and a corresponding inverse wavelet-like transformation is disclosed. The wavelet-like transformation is performed on input data so as to produce decomposed data. For each set of decomposed data samples of the decomposed data, each decomposed data sample of the set is produced by computing a weighted sum of a predefined set of data samples selected from (A) subsets of the set of input data samples, (B) one or more spatially shifted subsets of the set of input data samples, (C) the sets of decomposed data samples, and (D) one or more spatially shifted sets of the sets of decomposed data samples. The weighted sum is computed using only add and bit shift operations. Similarly, the inverse wavelet-like transformation is performed on decomposed data so as to produce reconstructed data.

Abstract: A data encoder and method utilizes a node list for storing a list of nodes in the data array to be processed, a branch list for storing a list of tree branches in the data array to be processed and a set list for storing a list of data sets. The method begins by initially storing in the node list node identifiers representing a predefined set of nodes in the data array, corresponding to coefficients generated by a last iteration of a data decomposition procedure. Also, it initially stores in the branch list branch identifiers representing tree branches corresponding to a predefined subset of the nodes initially listed in the node list. Each such tree branch has an associated root node and a branch depth value indicating how many node layers intervene between the root node and the nodes of the tree branch closest to the root node. The set list is initially empty, and a parameter called the LayerLimit value is also initialized.

Abstract: A data encoder and method successively analyzes successively smaller blocks of a specified data array. Data blocks are analyzed in a predefined order, and corresponding entries identifying data blocks containing at least one non-zero value are stored in that same order in a list of blocks. Whenever a data block is processed, if the data block is entirely filled with zero data it is so identified in the output data and no further processing of the subblock is required. Otherwise, if the size of the data block is greater than a predefined minimum block size (e.g., 2.times.2), the block is divided into smaller data blocks and those smaller data blocks are put on the list of blocks for further processing. Finally, if the size of a data block that is being processed is the predefined minimum block size, values representing all the data items in that data block are written into the output data.

Abstract: A method and system for compressing and decompressing a sequence of image frames is disclosed. According to the disclosed embodiments of the invention, the compression process includes an intraframe decomposition process (24, 24') performed upon each frame in both the row and column directions, including an m.sup.th order averaging and differencing operation (56, 62). Each frame is then combined with others in an adjacent pair or group of four by way of an interframe decomposition (28). Quantization (30) is then performed, preferably by division of each coefficient by a quantizer (.rho.) associated with the one of the frequency component subbands containing the coefficient. Reconstruction of the compressed frames is accomplished by performing the inverse of the compression process. According to the disclosed embodiments, either the compression or decompression processes and systems performs Cholesky filtering (60, 66; 170, 172), preferably in a recursive manner by way of forward and backward filtering.

Abstract: A data encoder and method successively analyzes successively smaller blocks of a specified data array. Data blocks are analyzed in a predefined order, and corresponding entries identifying data blocks containing at least one non-zero value are stored in that same order in a list of blocks. Whenever a data block is processed, if the data block is entirely filled with zero data it is so identified in the output data and no further processing of the subblock is required. Otherwise, if the size of the data block is greater than a predefined minimum block size (e.g., 2.times.2), the block is divided into smaller data blocks and those smaller data blocks are put on the list of blocks for further processing. Finally, if the size of a data block that is being processed is the predefined minimum block size, values representing all the data items in that data block are written into the output data.

Abstract: An apparatus and a corresponding method for performing compression and reconstruction of documents are disclosed. Compression of the document is performed by applying a scaling function and a wavelet function first in one direction (e.g., rows) and then in another direction (e.g., columns) to digital data representing the document. The scaling and wavelet functions correspond to spline and wavelet functions that are compactly supported over a convolution interval, and which can also be implemented by way of integer operations. Byte-packing may also be applied to the image data, without regard to pixel boundaries, allowing not only binary (two-color) documents to be compressed but also enabling the compression of more complex color documents. The spline-wavelet compression and reconstruction may be performed according to alternative methods, including dual-base wavelets, interpolatory wavelets, and wavelet packets.

Abstract: A method and apparatus for performing video image compression and decompression are disclosed. The video image compression is performed using boundary-spline-wavelet decomposition, in which the wavelets applied to sample locations at the boundaries of image intervals are different from those applied to sample locations within the intervals. As a result, boundary effect artifacts that arise from the use of wavelets requiring support outside of the interval are avoided. The decomposition is performed first for horizontal rows of the image data, and then in a vertical direction upon the results of the first decomposition. Quantization serves to locally round off the higher frequency components of the decomposition, and the decomposition is repeated until the desired compression ratio is obtained. Lossless compression may then be applied to the decomposed image data, and the compressed image is transmitted or stored, depending upon the application.

Abstract: A processor (10) is disclosed which uses a B-spline interpolator (14) to produce a plurality of zero-level spline coefficients c.sup.0 (n). This set of coefficients may be fed to a B-spline generator (16) to produce an approximation of the input signal, and/or may be multiplied by a set of coefficients Bn to produce a set of first-level wavelet coefficients d.sup.-1 (n). The zero-level spline coefficients are also used to create first-level spline coefficients c.sup.-1 (n). The first-level spline and wavelet coefficient c.sup.-1 (n) and d.sup.-1 (n) may be submitted to a respective B-spline generator (22) or B-wavelet generator (24) to produce a first-level spline signal components and a first-level wavelet signal component for extraction of data from the original signal. The signal may in a similar fashion be decomposed to any level of resolution desired. The signal components may then be processed, and an improved signal then reassembled from the last-level spline and the processed wavelet signals.