Method and apparatus for compressed sensing
First Claim
1. A method of reconstructing an input signal, the method comprising the steps of:
- (a) forming a first compressed sensing matrix utilizing a first set of time indices corresponding to a first sampling rate, the first sampling rate being less than the Nyquist sampling rate for the input signal;
(b) forming a second compressed sensing matrix utilizing a plurality of frequencies and a second set of time indices corresponding to a second sampling rate, the second sampling rate being less than the Nyquist sampling rate for the input signal;
(c) forming a combined compressed sensing matrix from the first compressed sensing matrix and the second compressed sensing matrix; and
(d) reconstructing at least a portion of the input signal utilizing the combined compressed sensing matrix.
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Abstract
Embodiments of the present invention provide a method and apparatus for compressed sensing. The method generally comprises forming a first compressed sensing matrix utilizing a first set of time indices corresponding to a first sampling rate, forming a second compressed sensing matrix utilizing a plurality of frequencies and a second set of time indices corresponding to a second sampling rate, forming a combined compressed sensing matrix from the first compressed sensing matrix and the second compressed sensing matrix, and reconstructing at least a portion of the input signal utilizing the combined compressed sensing matrix. The first and second sampling rates are each less than the Nyquist sampling rate for the input signal.
74 Citations
37 Claims
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1. A method of reconstructing an input signal, the method comprising the steps of:
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(a) forming a first compressed sensing matrix utilizing a first set of time indices corresponding to a first sampling rate, the first sampling rate being less than the Nyquist sampling rate for the input signal; (b) forming a second compressed sensing matrix utilizing a plurality of frequencies and a second set of time indices corresponding to a second sampling rate, the second sampling rate being less than the Nyquist sampling rate for the input signal; (c) forming a combined compressed sensing matrix from the first compressed sensing matrix and the second compressed sensing matrix; and (d) reconstructing at least a portion of the input signal utilizing the combined compressed sensing matrix. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. An apparatus for reconstructing an input signal, the apparatus comprising:
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a memory operable to store data corresponding to a plurality of frequencies, a first set of time indices corresponding to a first sampling rate, a second set of time indices corresponding to a second sampling rate, the first and second sampling rates each being less than the Nyquist sampling rate for the input signal; and a processor coupled with the memory to receive data therefrom, the processor operable to— form a first compressed sensing matrix utilizing data corresponding to the first set of time indices, form a second compressed sensing matrix utilizing data corresponding to the plurality of frequencies and the second set of time indices, form a combined compressed sensing matrix from the first compressed sensing matrix and the second compressed sensing matrix, and reconstruct at least a portion of the input signal utilizing the combined compressed sensing matrix. - View Dependent Claims (11, 12, 13, 14, 15)
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16. An apparatus for reconstructing an input signal, the apparatus comprising:
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a receiving element operable to receive the input signal; a wideband filter coupled with the receiving element to filter the input signal to a first range of frequencies and provide a wideband output signal corresponding to the filtered input signal; a plurality of narrowband filters coupled with the receiving element, each narrowband filter being operable to filter the input signal to a second range of frequencies, each second range of frequencies being less than the first range of frequencies, the plurality of narrowband filters operable to provide a narrowband output signal corresponding to the sum of the outputs of the narrowband filters; a sampling element coupled with the wideband filter and the narrowband filters to receive the wideband output signal and the narrowband output signal, the sampling element operable to sample the wideband output signal at a first sampling rate and sample the narrowband output signal at a second sampling rate to provide at least one sampled signal, the first and second sampling rates each being less than the Nyquist sampling rate for the input signal; and a processor coupled with the sampling element and operable to— form a first compressed sensing matrix utilizing a first set of time indices corresponding to the first sampling rate, form a second compressed sensing matrix utilizing a plurality of frequencies corresponding to the narrowband filters and a second set of time indices corresponding to the second sampling rate, form a combined compressed sensing matrix from the first compressed sensing matrix and the second compressed sensing matrix, and reconstruct at least a portion of the input signal utilizing the combined compressed sensing matrix. - View Dependent Claims (17, 18, 19, 20, 21, 22, 23, 24)
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25. An apparatus for sampling an input signal, comprising:
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a receiving element operable to receive the input signal; a wideband filter coupled with the receiving element to filter the input signal to a first range of frequencies and provide a wideband output signal corresponding to the filtered input signal; a plurality of narrowband filters coupled with the receiving element, each narrowband filter being operable to filter the input signal to a second range of frequencies, each second range of frequencies being less than the first range of frequencies, the plurality of narrowband filters operable to provide a narrowband output signal corresponding to the sum of the outputs of the narrowband filters; a sampling element coupled with the wideband filter and the narrowband filters to receive the wideband output signal and the narrowband output signal, the sampling element operable to sample the wideband output signal at a first sampling rate and sample the narrowband output signal at a second sampling rate to provide at least one sampled signal; and a processor coupled with the sampling element and operable to process the sampled signal. - View Dependent Claims (26, 27, 28, 29)
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30. A computer program for reconstructing an input signal, the computer program stored on a computer-readable medium for operating a processor and comprising:
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a code segment operable to form a first compressed sensing matrix utilizing a first set of time indices corresponding to a first sampling rate, the first sampling rate being less than the Nyquist sampling rate for the input signal; a code segment operable to form a second compressed sensing matrix utilizing a plurality of frequencies and a second set of time indices corresponding to a second sampling rate, the second sampling rate being less than the Nyquist sampling rate for the input signal; a code segment operable to form a combined compressed sensing matrix from the first compressed sensing matrix and the second compressed sensing matrix; and a code segment operable to reconstruct at least a portion of the input signal utilizing the combined compressed sensing matrix. - View Dependent Claims (31, 32, 33, 34, 35, 36, 37)
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Specification