A Method of Constructing Measurement Matrix for Compressed Sensing by Chebyshev Chaotic Sequence.

Area of Science:

• Signal Processing
• Applied Mathematics
• Information Theory

Background:

• Compressed sensing requires efficient measurement matrices for signal reconstruction.
• Existing chaotic sequences (Logistic, Tent) offer hardware feasibility but need large sample distances.
• Large sample distances increase resource consumption in measurement matrix construction.

Purpose of the Study:

• To propose a novel method for constructing measurement matrices in compressed sensing.
• To address the limitations of existing chaotic sequence-based matrices, specifically large sample distances.
• To develop a matrix that is efficient and maintains high performance.

Main Methods:

• Utilizing the Chebyshev chaotic sequence for measurement matrix construction.
• Analyzing the restricted isometric property (RIP) satisfaction of the proposed matrix.
• Assuming statistical independence of sampled elements for theoretical analysis.
• Conducting simulations to compare reconstruction performance.

Main Results:

• The Chebyshev chaotic sequence method effectively reduces the required sample distance.
• The proposed measurement matrix satisfies the restricted isometric property (RIP) with high probability.
• Simulation results demonstrate comparable reconstruction performance to existing chaotic matrices.
• The new method offers improved resource efficiency for compressed sensing.

Conclusions:

• The Chebyshev chaotic sequence provides an efficient alternative for measurement matrix construction in compressed sensing.
• The proposed method balances performance and hardware implementation feasibility.
• This approach contributes to more resource-efficient signal reconstruction techniques.