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Fast Second Degree Total Variation Method for Image Compressive Sensing.

Pengfei Liu1, Liang Xiao1, Jun Zhang2

  • 1School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, China.

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Summary
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This study introduces an efficient algorithm for image reconstruction using higher-order total variation (HDTV2) regularization. The novel method enhances image quality and speeds up reconstruction for compressive sensing applications.

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Area of Science:

  • Medical Imaging
  • Computational Imaging
  • Signal Processing

Background:

  • Image compressive sensing (CS) reconstruction is crucial for reducing data acquisition and storage.
  • Existing methods using total variation (TV) regularization have limitations in capturing fine image details.
  • Higher-order total variation (HDTV2) regularization offers potential for improved reconstruction but requires efficient algorithms.

Purpose of the Study:

  • To develop a computationally efficient algorithm for image compressive sensing reconstruction.
  • To leverage second-degree total variation (HDTV2) regularization for enhanced reconstruction quality.
  • To analyze the convergence properties of the proposed reconstruction algorithm.

Main Methods:

  • Derived an equivalent formulation of the HDTV2 functional as a weighted L1-L2 mixed norm of second-degree image derivatives.
  • Introduced an efficient forward-backward splitting (FBS) scheme to solve the HDTV2-based image reconstruction model.
  • Analyzed the convergence of the FBS algorithm using the averaged non-expansive operator theory.

Main Results:

  • The proposed FBS algorithm efficiently solves the HDTV2-based image reconstruction model.
  • Experimental results on medical images show superior performance compared to existing TV and HDTV2 algorithms.
  • Achieved higher peak signal to noise ratio (PSNR) and structural similarity index (SSIM) values.

Conclusions:

  • The developed FBS algorithm provides an efficient and effective solution for HDTV2-based image CS reconstruction.
  • The method demonstrates significant improvements in reconstruction quality and convergence speed.
  • This approach holds promise for advancing medical image analysis and other CS applications.