Abstract: Encoding data includes: encoding a residual of a first portion of an array of data to generate a first set of coefficients; decoding the first set of coefficients to generate a decoded representation of the first portion; computing an estimated covariance function for a residual of a second portion of the array of data based on a model that includes a gradient of a plurality of boundary data values located on a boundary of the decoded representation of the first portion; computing a set of transform basis functions from the estimated covariance function; and encoding the residual of the second portion using a first transform that uses the computed set of transform basis functions.

Abstract: Encoding data includes: encoding a residual of a first portion of an array of data to generate a first set of coefficients; decoding the first set of coefficients to generate a decoded representation of the first portion; computing an estimated covariance function for a residual of a second portion of the array of data based on a model that includes a gradient of a plurality of boundary data values located on a boundary of the decoded representation of the first portion; computing a set of transform basis functions from the estimated covariance function; and encoding the residual of the second portion using a first transform that uses the computed set of transform basis functions.

Abstract: Encoding data includes: encoding a first portion of an array of data to generate a first set of coefficients, using a first transform; decoding the first set of coefficients to generate a decoded approximation of the first portion, using the first transform; selecting a second transform from multiple candidate transforms based at least in part on a measure of encoding performance for each candidate transform used to encode the decoded approximation of the first portion; and encoding a second portion of the array of data in proximity to the first portion of the array of data to generate a second set of coefficients using the selected second transform.

Abstract: A method of encoding a sequence of video frames, comprising receiving a sequence of video frames, encoding at least a first portion of the sequence of frames using the first type of transform/subband representation to produce first transform/subband coefficients, encoding at least a second portion of the sequence of frames using the second type of transform/subband representation to produce second transform/subband coefficients; and providing the first and second transform/subband coefficients at an output.

Abstract: Encoding data includes: encoding a first portion of an array of data to generate a first set of coefficients, using a first transform; decoding the first set of coefficients to generate a decoded approximation of the first portion, using the first transform; selecting a second transform from multiple candidate transforms based at least in part on a measure of encoding performance for each candidate transform used to encode the decoded approximation of the first portion; and encoding a second portion of the array of data in proximity to the first portion of the array of data to generate a second set of coefficients using the selected second transform.

Abstract: Encoding data includes: determining multiple patterns for computing one-dimensional transforms over a first array of data elements. Each pattern includes multiple subsets of data elements of the first array. Each subset included in a first pattern has substantially the same number of data elements as each of the other subsets included in the first pattern. Each data element of the first array is included in a single one of the subsets included in the first pattern. At least one subset included in the first pattern consists of data elements that are not in a contiguous sequence along a single dimension. Encoding the data includes: computing, for each pattern, multiple one-dimensional transforms over data elements of respective subsets included in the pattern; selecting a set of transform coefficients from a group of multiple sets of transform coefficients; and encoding the selected set of transform coefficients to represent the first array.

Abstract: Processing images of a scene taken with different focus includes, for each of at least some of the images, determining at least one portion of the image having a predetermined characteristic. A representation of the scene is generated that includes an array of elements, where each of at least some of the elements corresponds to a determined portion of at least one of the images. An element of the array is based on a correspondence between a distance associated with a determined portion of at least one image and a focused distance associated with at least one image. The generated representation is stored or provided as output.

Abstract: Encoding data includes: determining multiple patterns for computing one-dimensional transforms over a first array of data elements. Each pattern includes multiple subsets of data elements of the first array. Each subset included in a first pattern has substantially the same number of data elements as each of the other subsets included in the first pattern. Each data element of the first array is included in a single one of the subsets included in the first pattern. At least one subset included in the first pattern consists of data elements that are not in a contiguous sequence along a single dimension. Encoding the data includes: computing, for each pattern, multiple one-dimensional transforms over data elements of respective subsets included in the pattern; selecting a set of transform coefficients from a group of multiple sets of transform coefficients; and encoding the selected set of transform coefficients to represent the first array.

Abstract: A method of encoding a sequence of video frames, comprising receiving a sequence of video frames, encoding at least a first portion of the sequence of frames using the first type of transform/subband representation to produce first transform/subband coefficients, encoding at least a second portion of the sequence of frames using the second type of transform/subband representation to produce second transform/subband coefficients; and providing the first and second transform/subband coefficients at an output.

Abstract: A method of encoding a sequence of video frames, comprising receiving a sequence of video frames, encoding at least a first portion of the sequence of frames using the first type of transform/subband representation to produce first transform/subband coefficients, encoding at least a second portion of the sequence of frames using the second type of transform/subband representation to produce second transform/subband coefficients; and providing the first and second transform/subband coefficients at an output.

Abstract: Encoding data includes: determining multiple patterns for computing one-dimensional transforms over a first array of data elements. Each pattern includes multiple subsets of data elements of the first array. Each subset included in a first pattern has substantially the same number of data elements as each of the other subsets included in the first pattern. Each data element of the first array is included in a single one of the subsets included in the first pattern. At least one subset included in the first pattern consists of data elements that are not in a contiguous sequence along a single dimension. Encoding the data includes: computing, for each pattern, multiple one-dimensional transforms over data elements of respective subsets included in the pattern selecting a set of transform coefficients from a group of multiple sets of transform coefficients; and encoding the selected set of transform coefficients to represent the first array.

Abstract: Encoding data includes: computing a first set of coefficients based on a plurality of transforms each computed over a different portion of an array of data, a second set of coefficients based on a plurality of transforms each computed over a different portion of the array of data, and a third set of coefficients based on a transform computed over the array of data; choosing a set of coefficients to represent the array of data from a group of multiple sets of coefficients, the group including the first set of coefficients, the second set of coefficients, and the third set of coefficients; and encoding the chosen coefficients and one or more parameters related to the chosen coefficients.

Abstract: Encoding data includes: computing a first set of coefficients based on a plurality of transforms each computed over a different portion of an array of data, and a second set of coefficients based on a transform computed over the array of data; choosing a set of coefficients to represent the array of data from a group of multiple sets of coefficients, the group including the first set of coefficients and the second set of coefficients; and encoding the chosen coefficients and one or more parameters related to the chosen coefficients.

Abstract: Processing images of a scene taken with different focus includes, for each of at least some of the images, determining at least one portion of the image having a predetermined characteristic. A representation of the scene is generated that includes an array of elements, where each of at least some of the elements corresponds to a determined portion of at least one of the images. An element of the array is based on a correspondence between a distance associated with a determined portion of at least one image and a focused distance associated with at least one image. The generated representation is stored or provided as output.

Abstract: Encoding data includes: computing a first set of coefficients based on a plurality of transforms each computed over a different portion of an array of data, a second set of coefficients based on a plurality of transforms each computed over a different portion of the array of data, and a third set of coefficients based on a transform computed over the array of data; choosing a set of coefficients to represent the array of data from a group of multiple sets of coefficients, the group including the first set of coefficients, the second set of coefficients, and the third set of coefficients; and encoding the chosen coefficients and one or more parameters related to the chosen coefficients.

Abstract: Encoding data includes: computing a first set of coefficients based on a plurality of transforms each computed over a different portion of an array of data, and a second set of coefficients based on a transform computed over the array of data; choosing a set of coefficients to represent the array of data from a group of multiple sets of coefficients, the group including the first set of coefficients and the second set of coefficients; and encoding the chosen coefficients and one or more parameters related to the chosen coefficients.

Abstract: Processing images of a scene taken with different focus includes, for each of at least some of the images, determining at least one portion of the image having a predetermined characteristic. A representation of the scene is generated that includes an array of elements, where each of at least some of the elements corresponds to a determined portion of at least one of the images. An element of the array is based on a correspondence between a distance associated with a determined portion of at least one image and a focused distance associated with at least one image. The generated representation is stored or provided as output.

Abstract: Variable-rate encoding of a signal by processing the signal to determine the data rate demand over a time period for multiple values of an encoding parameter, such as a quantization parameter which affects the encoded data rate, and selecting a value for the encoding parameter with which to encode a segment of the time period. Determining the data rate demands of a set of image sequences and selecting a subset of the sequences based on the data rate demands, for example, to satisfy a storage volume constraint, and then encoding each of the selected subset of sequences for transmission or storage.

Abstract: The performance of digital communication over a noisy communication channel is improved. An encoder combines bit modulation with error control encoding to allow the decoder to use the redundancy in the error control codes to detect uncorrectable bit errors. This method improves the efficiency of the communication system since fewer bits are required for error control, leaving more bits available for data. In the context of a speech coding system, speech quality is improved without sacrificing robustness to bit errors. A bit prioritization method further improves performance over noisy channels. Individual bits in a set of quantizer values are arranged according to their sensitivity to bit errors. Error control codes having higher levels of redundancy are used to protect the most sensitive (highest priority) bits, while lower levels of redundancy are used to protest less sensitive bits.

Abstract: An audio type signal is encoded. The signal is first divided into bands. For each band, a yardstick signal element is selected. The yardstick may be the signal element having the largest magnitude in the band, the second largest, closest to the median magnitude, or having some other selected magnitude. This magnitude is used for various purposes, including assigning bits to the different bands, and for establishing reconstruction levels within a band. The magnitude of non yardstick signal elements is also quantized. The encoded signal is also decoded. Apparatus for both encoding and decoding are also disclosed. The location of the yardstick element within its band may also be recorded and encoded, and used for efficiently allocating bits to non-yardstick signal elements. Split bands may be established, such that each split band includes a yardstick signal element and each full band includes a major and a minor yardstick signal element.