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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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Convolution computations can be simplified by utilizing their inherent properties.
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The important convolution properties include width, area, differentiation, and integration properties.
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Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
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Related Experiment Video

Updated: Jan 11, 2026

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
03:31

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications

Published on: December 15, 2023

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An accurate pixel-Level explainable approach for CNNs and its application.

Haitao Zhang1, Jing Wang1, Ziyue Wang1

  • 1School of Information Science & Engineering, Lanzhou University, No. 222, Tianshui South Road, Chengguan District, Lanzhou, 730000, Gansu, China.

Neural Networks : the Official Journal of the International Neural Network Society
|November 13, 2025
PubMed
Summary

This study introduces a novel pixel-level explainable approach for Convolutional Neural Networks (CNNs), achieving 100% accuracy in interpreting image classification. This method also enhances the adversarial robustness of CNN models.

Keywords:
Artificial intelligenceCNNExplainable AIImage processingRobustnessSymbolic execution

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Area of Science:

  • Computer Vision
  • Artificial Intelligence
  • Machine Learning

Background:

  • Convolutional Neural Networks (CNNs) are prevalent in image classification.
  • Interpreting the decision-making process of trained CNN models remains a challenge.
  • Existing explainable methods often lack sufficient interpretation accuracy.

Purpose of the Study:

  • To develop a novel pixel-level explainable approach for CNNs.
  • To address the limitations of insufficient interpretation accuracy in current methods.
  • To design a scheme for enhancing the adversarial robustness of CNN models.

Main Methods:

  • A novel pixel-level explainable approach was developed and tested.
  • Experiments were conducted on PyTorch team published CNN models.
  • A scheme to enhance adversarial robustness was designed based on the explainable approach.

Main Results:

  • The presented approach achieved 100% accuracy in interpreting the pixel-level classification basis of input images.
  • The designed scheme effectively improved the adversarial robustness of CNN models.
  • The technique demonstrated transferability across different CNN model structures.

Conclusions:

  • The novel pixel-level explainable approach significantly improves interpretation accuracy for CNNs.
  • The developed method offers an effective strategy for enhancing CNN adversarial robustness.
  • This approach provides a valuable tool for understanding and securing CNN models.