Expanding window compressed sensing for non-uniform compressible signals

Area of Science:

• Signal Processing
• Information Theory
• Data Science

Background:

• Practical compressible signals often exhibit non-uniform support distribution in sparse domains.
• Existing compressed sensing (CS) methods may not optimally handle such non-uniformity.

Purpose of the Study:

• To introduce a novel compressed sensing scheme, expanding window compressed sensing (EW-CS), designed for signals with non-uniform support distribution.
• To enhance the recovery quality and implementation convenience for such signals.

Main Methods:

• Dividing the signal into nested subsets (expanding windows) based on element importance.
• Generating unique measurements for each window using random sensing matrices.
• Ensuring more significant signal elements are captured by a greater number of measurements.

Main Results:

• EW-CS demonstrates superior recovery quality for non-uniform compressible signals compared to ordinary CS.
• The scheme shows improved performance in compressed acquisition of image signals and networked data.
• Theoretical analysis and experimental validation confirm the advantages of EW-CS.

Conclusions:

• EW-CS offers a practical and effective solution for compressed sensing of signals with non-uniform importance.
• The method provides better overall recovery quality and implementation convenience.
• EW-CS outperforms existing ordinary and unequal protection CS schemes in specific applications.