Patent US7511643B2 successfully refreshed from Google Patents.
US7511643B2
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Method and apparatus for distributed compressed sensing
Assignee: Rice University
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Filing: 2007-08-08
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Granted: 2009-03-31
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Expires: 2027-08-08
Abstract
Abstract A method for approximating a plurality of digital signals or images using compressed sensing. In a scheme where a common component x c of said plurality of digital signals or images an innovative component x i 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 y c , where y c comprises a vector with only n i entries, where n i is less than m, making a measurement y i for each of said correlated digital signals, where y i comprises a vector with only n i entries, where n i is less than m, and from each said innovation components y i , producing an approximate reconstruction of each m-vector x i using said common component y c and said innovative component y i .
Inventors
- 👤 Richard G. Baraniuk
- 👤 Dror Z. Baron
- 👤 Marco F. Duarte
- 👤 Shriram Sarvotham
- 👤 Michael B. Wakin
- 👤 Mark Davenport
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-09 11:24
CPC Classifications
H; H03; H03M; H03M7/00; H03M7/30; H04; H04N; H04N19/00; H04N19/60; G; G06; G06F; G06F2218/00; G06F2218/22
Claims Analysis
Total Claims: 39
Claim 1
Independent Claim
79 words
A method for reconstructing a plurality of signals, images, or video sequences, comprising the steps of: taking M j measurements of each signal, image or video sequence x j among the plurality of J signals, images, or video sequences; reconstructing the plurality of signals, images or video sequences by seeking possible values for the plurality of signals, images or video sequences that explain the measurements and account for commonality and/or structure shared among the signals, images, or video sequences.
Claim 2
Independent Claim
79 words
A method for reconstructing a plurality of signals, images, or video sequences, comprising the steps of: taking M j measurements of each signal, image or video sequence x j among the plurality of J signals, images, or video sequences; reconstructing the plurality of signals, images or video sequences by seeking possible values for the plurality of signals, images or video sequences that explain the measurements and account for commonality and/or structure shared among the signals, images, or video sequences.
Claim 3
Dependent Claim
28 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 1 , wherein said method reconstructs said signals, images or video sequences approximately.
Claim 4
Dependent Claim
40 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 1 , wherein in said scheme each of the plurality of signals, images or video sequences is measured using the same number M of measurements.
Claim 5
Dependent Claim
65 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 1 , wherein in said scheme for each signal, image or video sequence x j among the plurality of J signals, images or video sequences there exists an N-parameter representation and the M j measurements of x j are obtained by projecting x j onto a plurality of measurement vectors.
Claim 6
Dependent Claim
68 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 1 , wherein in said scheme for each signal, image or video sequence x j among the plurality of J signals, images or video sequences there exists a discrete representation of length N and the M j measurements of x j are obtained by projecting x j onto a plurality of measurement vectors.
Claim 7
Dependent Claim
63 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 1 , wherein in said scheme for each signal, image or video sequence x j among the plurality of J signals, images or video sequences there exists a discrete representation of length N and the number of measurements M j taken of x j is smaller than N.
Claim 8
Dependent Claim
48 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 1 , wherein in said scheme the M j measurements of each of said signals, images or video sequences x j among the plurality of J signals, images or video sequences are encoded.
Claim 9
Dependent Claim
48 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 7 , wherein said scheme the M j measurements of each of said signals, images or video sequences x j among the plurality of J signals, images or video sequences are encoded digitally.
Claim 10
Dependent Claim
55 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 4 , wherein in said scheme the M j measurements of each signal, image or video sequence x j among the plurality of J signals, images or video sequences is measured using different sets of measurement vectors.
Claim 11
Dependent Claim
47 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 3 , wherein in said scheme the M measurements of each of the plurality of signals, images or video sequences are measured using the same plurality of measurement vectors.
Claim 12
Dependent Claim
74 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 4 , wherein in said scheme the M j measurements of each signal, image or video sequence x j among a plurality of J signals, images or video sequences comprises a subset of measurements obtained from projections onto the same set of measurement vectors for each signal and another subset of measurements obtained from projections onto different measurement vectors.
Claim 13
Dependent Claim
25 words
A method according to claim 4 wherein said means for measuring measures said plurality of signals, images or video sequences using an incoherent measurement matrix.
Claim 14
Dependent Claim
79 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 4 , wherein in said scheme of obtaining M j measurements of each signal, image or video sequence x j among a plurality of J signals, images or video sequences comprises projecting x j onto at least one of the following types of sequences: random sequences, Bernoulli-distributed sequences, Gaussian-distributed sequences, coding scheme sequences, Fourier sequences, Hadamard sequences, cyclic sequences, Toeplitz sequences, and sparse sequences.
Claim 15
Dependent Claim
52 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 1 , wherein said reconstruction method reconstructs each signal, image or video sequence x j among said plurality of J signals, images or video sequences independently of reconstruction of other signals among said plurality.
Claim 16
Dependent Claim
53 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 1 , wherein in said reconstruction method of seeking possible values for said plurality of signals, images or video sequences that explain the measurements relies on any possible mathematical model for said plurality of signals.
Claim 17
Independent Claim
119 words
A method for reconstructing exactly or approximately a plurality of digital signals, images, or video sequences comprising the steps of: estimating a common component of said plurality of digital signals, images or video sequences; estimating measurements generated by innovations of each of said plurality of digital signals, images or video sequences; constructing approximations of said innovations of each of said plurality of digital signals, images or video sequences; and obtaining an estimate of at least one signal, image or video sequence from said plurality of digital signals, images or video sequences as the sum of said estimate of said common component and estimates of at least one innovation component of said at least one signal, image or video sequence.
Claim 18
Independent Claim
119 words
A method for reconstructing exactly or approximately a plurality of digital signals, images, or video sequences comprising the steps of: estimating a common component of said plurality of digital signals, images or video sequences; estimating measurements generated by innovations of each of said plurality of digital signals, images or video sequences; constructing approximations of said innovations of each of said plurality of digital signals, images or video sequences; and obtaining an estimate of at least one signal, image or video sequence from said plurality of digital signals, images or video sequences as the sum of said estimate of said common component and estimates of at least one innovation component of said at least one signal, image or video sequence.
Claim 19
Dependent Claim
54 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 1 , wherein said reconstruction method relies on a mathematical model where each of said plurality of signals, images or video sequences comprises a linear or approximately linear combination of identical signal elements under different coefficients.
Claim 20
Dependent Claim
54 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 15 , wherein said reconstruction method relies on a mathematical model where each of said plurality of signals, images or video sequences comprises a linear or approximately linear combination of identical signal elements under different coefficients.
Claim 21
Dependent Claim
67 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 1 , wherein said reconstruction method relies on a mathematical model where each of said plurality of signals, images or video sequences comprises a sum of a common signal component and an additional component that comprises a linear or approximately linear combination of identical signal elements under different coefficients.
Claim 22
Dependent Claim
63 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 1 , wherein said reconstruction method relies on mathematical model where each of said plurality of signals, images or video sequences comprises a sum of a common signal component and a set of additional signal components being different for each of the plurality of signals.
Claim 23
Dependent Claim
41 words
A method for reconstructing a video sequence according to claim 20 , wherein said reconstruction method relies on a mathematical model where each of said plurality of different additional signal components represents motion between different image frames of the video sequence.
Claim 24
Dependent Claim
49 words
A method for reconstructing a plurality of signals, images, or video sequences according to claim 1 , wherein said reconstruction method relies on at least one of the following algorithms: l 0 , l 1 , Basis Pursuit with Denoising, LARS, LASSO, Simultaneous Orthogonal Matching Pursuit or Trivial Pursuit.
Claim 25
Dependent Claim
41 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 17 , wherein said reconstruction method relies on a non-iterative greedy algorithm based on matched filtering to identify the said identical signal elements.
Claim 26
Dependent Claim
47 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 19 , wherein said reconstruction method relies on the iterative sequential estimation of the common and additional components of each of said plurality of signals, images or video sequences.
Claim 27
Dependent Claim
47 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 20 , wherein said reconstruction method relies on the iterative sequential estimation of the common and additional components of each of said plurality of signals, images or video sequences.
Claim 28
Dependent Claim
19 words
A method according to claim 1 wherein said means for measuring comprises a plurality of sensors in any modality.
Claim 29
Dependent Claim
25 words
A method according to claim 15 wherein said plurality of sensors comprise at least one selected from the group of: cameras, acoustic and temperature sensors.
Claim 30
Independent Claim
81 words
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: taking M j measurements of each signal x j among the plurality of J signals; and determining if the measurements are more consistent with the presence or absence of the signal of interest, said determining step taking into account commonality and/or structure shared a month the signals, images or video sequences.
Claim 31
Independent Claim
81 words
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: taking M j measurements of each signal x j among the plurality of J signals; and determining if the measurements are more consistent with the presence or absence of the signal of interest, said determining step taking into account commonality and/or structure shared a month the signals, images or video sequences.
Claim 32
Dependent Claim
63 words
A method as in claim 28 , wherein said step of determining if the measurements are more consistent with the presence or absence of the signal of interest comprises using any reconstruction method to obtain an approximation of the signal from which one can more easily test if the measurements are more consistent with the presence or absence of the signal of interest.
Claim 33
Dependent Claim
82 words
A method as in claim 28 , wherein said step of determining if the measurements are more consistent with the presence or absence of the signal of interest comprises using a greedy reconstruction method such as Orthogonal Matching Pursuit or Matching Pursuit, but stopping the algorithm after a small number of iterations, to obtain an approximation of the signal from which one can more easily test if the measurements are more consistent with the presence or absence of the signal of interest.
Claim 34
Independent Claim
82 words
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 M j measurements of each signal, image or video sequence x j among the plurality of J signals, images or video sequences; and determining the value of the function that is most consistent with the measurements, said determining step taking into account commonality and/or structure shared among the signals, images or video sequences.
Claim 35
Independent Claim
82 words
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 M j measurements of each signal, image or video sequence x j among the plurality of J signals, images or video sequences; and determining the value of the function that is most consistent with the measurements, said determining step taking into account commonality and/or structure shared among the signals, images or video sequences.
Claim 36
Dependent Claim
47 words
A method as in claim 31 , wherein said step of determining the value of the function that is most consistent with the measurements comprises using any reconstruction method to obtain an approximation of the signal from which one can then directly estimate the function of interest.
Claim 37
Dependent Claim
66 words
A method as in claim 31 , wherein said step of determining the value of the function that is most consistent with the measurements comprises using a greedy reconstruction method such as Orthogonal Matching Pursuit or Matching Pursuit, but stopping the algorithm after a small number of iterations, to obtain an approximation of the signal from which one can then directly estimate the function of interest.
Claim 38
Dependent Claim
63 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 16 , wherein said estimation of the common component and at least one innovation component uses l 1 norm minimization, where the measurements of the plurality of signals, images or video sequences are constrained to explain all signal components while having minimal l 1 norm.
Claim 39
Dependent Claim
41 words
A method for reconstructing exactly or approximately a plurality of signals, images, or video sequences according to claim 34 , wherein said norm can be weighted differently for each among the single common component and the plurality of J innovation components.
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USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
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| 3.5 Years (Year 4) | 2012-03-30 | 2012-09-29 | 2013-03-31 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2016-03-30 | 2016-09-29 | 2017-03-31 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2020-03-30 | 2020-09-29 | 2021-03-31 | $7700.00 | Window Closed / Lapsed |