Measurement Matrix Optimization for Compressed Sensing System with Constructed Dictionary via Takenaka-Malmquist...

Area of Science:

• Signal Processing
• Information Theory
• Applied Mathematics

Background:

• Compressed sensing (CS) enables efficient signal acquisition by exploiting signal sparsity.
• Existing CS methods face limitations in achieving optimal sparsity and measurement matrix coherence.
• Takenaka-Malmquist (TM) functions offer adaptability and robustness for signal representation.

Purpose of the Study:

• To enhance compressed sensing system performance.
• To develop a novel sparsifying dictionary using TM functions.
• To optimize the measurement matrix for reduced mutual coherence.

Main Methods:

• Constructed a sparsifying dictionary utilizing Takenaka-Malmquist functions.
• Developed an equiangular tight frame (ETF) based iterative minimization algorithm.
• Modified singular values of the sensing matrix to improve column vector independence.

Main Results:

• The TM-based dictionary resulted in sparser signal representation compared to existing methods.
• The optimized measurement matrix reduced mutual coherence with the dictionary.
• Simulations demonstrated superior signal recovery accuracy for the proposed CS system.

Conclusions:

• The proposed sparsifying dictionary and optimized measurement matrix significantly improve CS performance.
• The integration of TM functions and ETF-based optimization offers a robust approach for compressed sensing.
• This work provides a foundation for more efficient and accurate signal processing applications.