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Construction of Structured Random Measurement Matrices in Semi-Tensor Product Compressed Sensing Based on

Junying Liang1,2, Haipeng Peng1,2, Lixiang Li1,2

  • 1Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.

Sensors (Basel, Switzerland)
|November 11, 2022
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Summary
This summary is machine-generated.

This study introduces structured random matrices, balancing storage and reconstruction accuracy for compressed sensing. These novel matrices show superior performance in reconstructing 1D signals and 2D images.

Keywords:
coherencecompressed sensingembedding operationincidence matricesmeasurement matricessemi-tensor product

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Area of Science:

  • Signal Processing
  • Information Theory
  • Matrix Theory

Background:

  • Random matrices require significant storage and hardware implementation.
  • Deterministic matrices often result in substantial reconstruction errors.
  • Existing methods struggle to balance storage efficiency and reconstruction accuracy.

Purpose of the Study:

  • To develop a novel matrix construction method that balances storage and reconstruction performance.
  • To introduce structured random matrices for compressed sensing applications.
  • To improve the efficiency and accuracy of signal and image reconstruction.

Main Methods:

  • Constructing structured random matrices by embedding combinatorial design incidence matrices with Gram-Schmidt orthonormalized random matrices.
  • Developing a new model for applying these structured random matrices to semi-tensor product compressed sensing.
  • Evaluating reconstruction performance against established matrices through experimental methods.

Main Results:

  • The proposed structured random matrices offer a balance between storage requirements and reconstruction accuracy.
  • Experimental results demonstrate the effectiveness of the new matrices for signal and image reconstruction.
  • The novel matrices outperform several known matrices in specific reconstruction tasks.

Conclusions:

  • Structured random matrices provide an effective solution to the limitations of traditional random and deterministic matrices in compressed sensing.
  • The proposed semi-tensor product compressed sensing model with structured random matrices is efficient for 1D signal and 2D image reconstruction.
  • This work offers a promising direction for developing practical compressed sensing hardware and algorithms.