Method and apparatus for distributed compressed sensing

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.

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.

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.