Compression of signals, images and video for multimedia, communications and other applications
First Claim
1. A method for transmitting compressed image data comprising:
- receiving image data representing an image;
minimizing a space-spatial frequency product of the image data by applying a predetermined Hermite-Gaussian function thereto to generate a minimized mathematical representation of the image data, wherein the minimized space-spatial frequency product of the image data equals ½
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extracting coefficients contained within the generated minimized mathematical representation of the image data;
transmitting the extracted coefficients of the minimized mathematical representation of the image data without any remaining portions of the minimized mathematical representation of the image data from a first location to a second location;
recreating the minimized mathematical representation of the image data comprising the minimized space-spatial frequency product of the image data at the second location responsive to the transmitted extracted coefficients and the predetermined Hermite-Gaussian function stored at the second location; and
generating the image from the recreated minimized mathematical representation of the image data comprising the space-spatial frequency product of the image data.
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Abstract
A system and method for transmitting compressed image data includes an encoder, responsive to received image data representing an image, for minimizing a space-spatial frequency of the image data by applying a predetermined orthogonal function thereto to generate a mathematical representation of the image data and extracting coefficients of the mathematical representation of the image data. A transmitter transmits the coefficients of the image data from a first location to a second location. A receiver receives the transmitted coefficients of the image data at the second location from the first location. A decoder recreates the mathematical representation of the image data at the second location responsive to the received coefficients and the predetermined orthogonal function and generates the image data from the recreated mathematical representation of the image data.
36 Citations
25 Claims
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1. A method for transmitting compressed image data comprising:
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receiving image data representing an image; minimizing a space-spatial frequency product of the image data by applying a predetermined Hermite-Gaussian function thereto to generate a minimized mathematical representation of the image data, wherein the minimized space-spatial frequency product of the image data equals ½
;extracting coefficients contained within the generated minimized mathematical representation of the image data; transmitting the extracted coefficients of the minimized mathematical representation of the image data without any remaining portions of the minimized mathematical representation of the image data from a first location to a second location; recreating the minimized mathematical representation of the image data comprising the minimized space-spatial frequency product of the image data at the second location responsive to the transmitted extracted coefficients and the predetermined Hermite-Gaussian function stored at the second location; and generating the image from the recreated minimized mathematical representation of the image data comprising the space-spatial frequency product of the image data. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
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12. A system for transmitting compressed image data, comprising:
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an encoder, responsive to received image data representing an image, for minimizing a space-spatial frequency product of the image data by applying a predetermined Hermite-Gaussian function thereto to generate a minimized mathematical representation of the image data, wherein the minimized space-spatial frequency product of the image data equals ½
, the encoder further extracting coefficients of the minimized mathematical representation of the image data;a transmitter for transmitting the coefficients of the minimized mathematical representation of the image data without any remaining portions of the minimized mathematical representation of the image data from a first location to a second location; a receiver for receiving the transmitted extracted coefficients of the minimized mathematical representation of the image data at the second location from the first location; and a decoder for recreating the minimized mathematical representation of the image data comprising the minimized space-spatial frequency product of the image data at the second location responsive to the received extracted coefficients and the predetermined Hermite-Gaussian function that is stored at the decoder and generating the image data from the recreated mininmized mathematical representation of the image data comprising the space-spatial frequency product of the image data. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
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23. A method for transmitting compressed video data comprising:
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receiving video data representing a video, the video data representing color data for each pixel making up the video; processing the video data by applying a predetermined hyper-complex quaternion Hermite-Gaussian function thereto to generate a minimized mathematical representation of the video data, wherein the step of processing further comprises; assigning red color data of RGB data to a first component of the hyper-complex quaternion Hermite-Gaussian function; assigning green color data of the RGB data to a second component of the hyper-complex quaternion Hermite-Gaussian function; assigning blue color data of the RGB data to a third component of the hyper-complex quaternion Hermite-Gaussian function; assigning a zero value to a forth component of the hyper-complex quaternion Hermite-Gaussian function; extracting coefficient contained within the generated minimized mathematical representation of the video data; transmitting the extracted coefficients of the minimized mathematical representation of the video data from without any remaining portion of the minimized mathematical representation of the image data from a first location to a second location; recreating the minimized mathematical representation of the video data at the second location responsive to the transmitted extracted coefficients and the three components assigned to the red, green and blue color data of the predetermined hyper-complex quaternian Hermite-Gaussian function stored at the second location; and generating the video from the recreated minimized mathematical representation of the video data.
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24. A method for transmitting compressed image data comprising:
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receiving image data representing an image; processing each pixel of each frame of the image data to determine moments to minimize a space-spatial frequency product of the image data and generate a minimized mathematical representation of the image data responsive to a predetermined Hermite-Gaussian function, wherein the minimized space-spatial frequency product of the image data equals ½
;extracting coefficients from the minimized mathematical representation of the image data; transmitting the extracted coefficients of the minimized mathematical representation of the image data without any remaining portions of the mathematical representation of the image data from a first location to a second location; recreating the minimized mathematical representation of the image data comprising the minimized space-spatial frequency product of the image data at the second location responsive to the transmitted extracted coefficients and the predetermined Hermite-Gaussian function stored at the second location; and generating the image from the recreated minimized mathematical representation of the image data comprising the minimized space-spatial frequency product of the image data. - View Dependent Claims (25)
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Specification