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A Novel Complex-Valued Gaussian Measurement Matrix for Image Compressed Sensing.

Yue Wang1, Linlin Xue1, Yuqian Yan1

  • 1School of Information and Electronic Engineering, Zhejiang University of Science and Technology, Hangzhou 310023, China.

Entropy (Basel, Switzerland)
|September 28, 2023
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Summary

Orthogonalizing Gaussian random matrices created a complex-valued matrix that improves compressed sensing image reconstruction. This sparse, complex matrix enhances performance and reduces computational load compared to real-valued matrices.

Keywords:
Gaussian matrixGram–Schmidt orthogonalizationcompressed sensingmeasurement matrixsparse matrix

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Area of Science:

  • Signal Processing
  • Image Reconstruction
  • Compressed Sensing

Background:

  • Compressed sensing (CS) image reconstruction performance is significantly influenced by the measurement matrix.
  • Developing advanced measurement matrices is crucial for improving CS imaging fidelity and efficiency.

Purpose of the Study:

  • To enhance compressed sensing image reconstruction by proposing a novel complex-valued Gaussian measurement matrix.
  • To investigate the impact of orthogonalization and sparsification on the performance of the proposed measurement matrix.

Main Methods:

  • Two distinct Gaussian random matrices were orthogonalized using the Gram-Schmidt process.
  • A complex-valued Gaussian matrix was constructed using the orthogonalized matrices as real and imaginary components.
  • The proposed measurement matrix was sparsified to decrease storage and computational requirements.

Main Results:

  • The orthogonalized complex-valued Gaussian matrix demonstrated superior image reconstruction performance compared to real-valued matrices.
  • Higher peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were achieved with the complex matrix across various compression ratios.
  • Sparsifying the measurement matrix effectively reduced computational complexity.

Conclusions:

  • Orthogonalized complex-valued Gaussian matrices offer significant advantages for compressed sensing image reconstruction.
  • The proposed method provides a viable approach to improve image quality and computational efficiency in CS imaging.
  • Sparsification is an effective strategy for optimizing measurement matrix storage and processing demands.