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Task-adaptive eigenvector-based projection (EBP) transform for compressed sensing: A case study of spectroscopic

Yinsheng Zhang1,2, Haiyan Wang1, Yongbo Cheng3

  • 1School of Management and E-Business Zhejiang Gongshang University Hangzhou China.

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|May 8, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces an eigenvector-based projection (EBP) transform for compressed sensing (CS). EBP improves signal reconstruction accuracy by leveraging domain-specific knowledge, outperforming traditional transforms like DCT and DFT.

Keywords:
Walsh‐Hadamard transformcompressed sensingdiscrete Fourier transformdiscrete cosine transformeigenvector‐based projectionsparsity

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Area of Science:

  • Signal Processing
  • Data Science
  • Spectroscopy

Background:

  • Compressed sensing (CS) relies on signal sparsity under specific transforms.
  • Non-adaptive transforms (DCT, DFT, WHT) are widely used but limit domain-specific optimization.
  • Leveraging domain knowledge can enhance CS efficiency and reduce sampling requirements.

Purpose of the Study:

  • To introduce a novel task-adaptive eigenvector-based projection (EBP) transform for compressed sensing.
  • To demonstrate the superiority of EBP over non-adaptive transforms in generating sparse representations.
  • To evaluate EBP's performance in a Raman spectroscopic profiling application.

Main Methods:

  • Developed an eigenvector-based projection (EBP) transform.
  • Applied EBP to generate sparse representations in a latent space, analogous to principal component loading.
  • Compared EBP's reconstruction performance against DCT, DFT, and WHT using a Raman spectroscopic dataset.

Main Results:

  • EBP achieved a relative mean square error of 0.00 at a 1% sampling ratio in Raman spectroscopy.
  • Non-adaptive transforms (DCT, DFT, WHT) showed significantly higher errors (0.33, 0.68, 0.32, respectively) under the same conditions.
  • EBP demonstrated superior reconstruction quality and sparsity compared to non-adaptive methods.

Conclusions:

  • The eigenvector-based projection (EBP) transform significantly enhances compressed sensing performance by incorporating domain-specific knowledge.
  • EBP enables substantial reductions in the required sampling ratio, leading to lower measurement costs.
  • EBP offers a powerful approach for improving CS efficiency in specialized applications like spectroscopic profiling.