Method and apparatus for distributed compressed sensing

• US 7,271,747 B2
• Filed: 05/10/2006
• Issued: 09/18/2007
• Est. Priority Date: 05/10/2005
• Status: Active Grant

• Current Assignee: Rice University
• Original Assignee: Rice University
• Inventors: Baraniuk, Richard G., Baron, Dror Z., Wakin, Michael B., Duarte, Marco F., Davenport, Mark, Sarvotham, Shriram
• Primary Examiner(s): Jeanglaude; Jean Bruner
• Application Number:
  US11/382,687
• Publication Number:
  US 20070027656A1
• Time in Patent Office: 496 Days
• Field of Search: 341/87, 341/50, 706/20, 375/148, 342/357.12
• US Class Current: 341/87
• CPC Class Codes: G06F 18/213 Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
• CPC Class Codes: G06F 2218/22 Source localisation; Inverse modelling
• CPC Class Codes: H03M 7/30 Compression speech analysis-synthesis for redundancy reduction G10L19/00; for image communication H04N; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
• CPC Class Codes: H04N 19/60 using transform coding

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.

Claims

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 x_c of said plurality of digital signals or images is represented as a vector with m entries, making a measurement y_c, where y_c comprises a vector with only n_i entries, where n_i is less than m; and

wherein in said scheme an innovative component x_i 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 y_i for each of said digital signals, where y_i comprises a vector with only n_i entries, where n_i is less than m.

2. A method for approximating a plurality of digital signals or images using compressed sensing according to claim 1, further comprising the step of:

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.

3. A method for approximating a plurality of digital signals or images using compressed sensing, comprising the steps of:

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.

4. A method for approximating a plurality of digital signals or images using compressed sensing, comprising the steps of:

in a scheme where an innovative component x_i 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 y_i for each of said digital signals, where y_i comprises a vector with only n_i entries, where n_i is less than m.

5. An apparatus for joint measurement of a plurality of signals comprising:

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.

6. An apparatus according to claim 5 wherein said means for measuring comprises a plurality of sensors in any modality.

7. An apparatus according to claim 5 wherein said plurality of sensors comprise at least one selected from the group of:

cameras, acoustic and temperature sensors.

8. An apparatus according to claim 5 wherein said means for measuring measures said plurality of signals using an incoherent measurement matrix.

9. An apparatus for joint measurement of a plurality of signals comprising:

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.

10. An apparatus according to claim 9 wherein said means for measuring comprises a plurality of sensors in any modality.

11. An apparatus according to claim 9 wherein said plurality of sensors comprise at least one selected from the group of:

cameras, acoustic and temperature sensors.

12. An apparatus according to claim 9 wherein said means for measuring measures said plurality of signals using an incoherent measurement matrix.