Method and Apparatus for Distributed Compressed Sensing
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Abstract
A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component xc of said plurality of digital signals or images an innovative component xi of each of said plurality of digital signals each are represented as a vector with m entries, the method comprises the steps of making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m, making a measurement yi for each of said correlated digital signals, where yi comprises a vector with only ni entries, where ni is less than m, and from each said innovation components yi, producing an approximate reconstruction of each m-vector xi using said common component yc and said innovative component yi.
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Citations
50 Claims
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1-15. -15. (canceled)
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16. A method for reconstructing a plurality of signals, images, or video sequences, comprising the steps of:
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taking Mj measurements of each signal xj among the plurality of J signals; reconstructing the plurality of signals by seeking possible values for the plurality of signals that explain the measurements. - View Dependent Claims (17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42)
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31. A method for reconstructing exactly or approximately a plurality of digital signals, images, or video sequences comprising the steps of:
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estimating a common component of said plurality of digital signals; estimating measurements generated by innovations of each of said plurality of digital signals; constructing approximations of said innovations of each of said plurality of digital signals; and obtaining an estimate of at least one signal from said plurality of digital signals as the sum of said estimate of said common component and estimates of at least one innovation component of said at least one signal. - View Dependent Claims (49, 50)
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43. A method for detecting the presence or absence of a signal of interest in at least one of a plurality of signals, images, or video sequences, comprising the steps of:
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taking Mj measurements of each signal xj among the plurality of J signals; determining if the measurements are more consistent with the presence or absence of the signal of interest. - View Dependent Claims (44, 45)
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46. A method for estimating the value of a function that depends on one or more of a plurality of signals, images, or video sequences, comprising the steps of:
taking Mj measurements of each signal xj among the plurality of J signals;
determining the value of the function that is most consistent with the measurements.- View Dependent Claims (47, 48)
Specification