Method and Apparatus for Distributed Compressed Sensing
First Claim
1. A method for approximating a plurality of digital signals or images using compressed sensing, comprising the steps of:
- in a scheme where a common component xc of said plurality of digital signals or images is represented as a vector with m entries, making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m.
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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.
56 Citations
15 Claims
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1. A method for approximating a plurality of digital signals or images using compressed sensing, comprising the steps of:
in a scheme where a common component xc of said plurality of digital signals or images is represented as a vector with m entries, making a measurement yc, where yc comprises a vector with only ni entries, where ni is less than m. - View Dependent Claims (2, 3)
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4. A method for approximating a plurality of digital signals or images using compressed sensing, 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.
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5. A method for approximating a plurality of digital signals or images using compressed sensing, comprising the steps of:
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in a scheme where an innovative component xi of each of said plurality of digital signals is represented as a vector with m entries each, further comprising the step of;
making a measurement yi for each of said digital signals, where yi comprises a vector with only ni entries, where ni is less than m.
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6. An apparatus for joint measurement of a plurality of signals comprising:
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means for measuring a plurality of correlated signals, said measuring means encoding each signal independently by projecting each said signal onto another incoherent basis;
means for transmitting each said encoded signal from said means for measuring to a signal processor; and
means for recovering said plurality of correlated signals based upon a correlation of said signals. - View Dependent Claims (7, 8, 9)
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10. An apparatus for joint measurement of a plurality of signals comprising:
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means for measuring a plurality of correlated signals, said measuring means encoding each signal independently by projecting each said signal onto another incoherent basis;
means for transmitting each said encoded signal from said means for measuring to a signal processor; and
means for recovering said plurality of correlated signals based upon a correlation of the sparse representations of said signals. - View Dependent Claims (11, 12, 13)
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14. A method for encoding a plurality of signals, comprising:
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measuring said plurality of signals; and
generating a correlation model for each of said plurality of signals;
reconstructing approximations of said plurality of signals using said correlation of said plurality of signals.
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15. A method according to claim 15, wherein said step of generating a correlation model comprises generating a correlation model for a sparse representation of each of said plurality of signals and said step of reconstructing comprises reconstructing approximations of said plurality of signals using said correlation of the sparse representation of said plurality of signals.
Specification