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Related Concept Videos

State Space Representation01:27

State Space Representation

290
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
290
State Space to Transfer Function01:21

State Space to Transfer Function

307
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
307
Transfer Function to State Space01:23

Transfer Function to State Space

412
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
412

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Related Experiment Video

Updated: Sep 14, 2025

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

642

Pixel adaptive deep-unfolding neural network with state space model for image deraining.

Yao Xiao1, Youshen Xia2

  • 1College of Artificial Intelligence, Anhui University, HeFei, China; College of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing, China.

Neural Networks : the Official Journal of the International Neural Network Society
|July 18, 2025
PubMed
Summary

This study introduces a novel pixel adaptive deep unfolding network for effective image deraining. The method enhances visual quality by improving global structure perception and adaptive step size control, outperforming existing techniques.

Keywords:
Deep-unfolding neural networkImage recoveryRain streaks removalState space model

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Area of Science:

  • Computer Vision
  • Deep Learning
  • Image Processing

Background:

  • Rain streaks degrade image quality and hinder computer vision tasks.
  • Deep unfolding neural networks (DUNs) show promise for image deraining but have limitations.
  • Existing DUNs struggle with global structure perception and adaptive step size control.

Purpose of the Study:

  • To develop an advanced image deraining method addressing limitations of current deep unfolding networks.
  • To enhance the perception of both local and global image structures.
  • To improve the adaptability of deraining methods to diverse input images.

Main Methods:

  • Proposes a pixel adaptive deep unfolding network incorporating state space models (SSMs).
  • Introduces an adaptive pixel-wise gradient descent (APGD) module for flexible step size adjustment.
  • Employs a stage fusion proximal mapping (SFPM) module with a dual-branch architecture (CNNs and SSMs).
  • Utilizes Fourier transform for stage feature fusion to minimize information loss.

Main Results:

  • The proposed method demonstrates superior performance in quantitative metrics and visual quality on public datasets.
  • Achieves effective deraining by enhancing global structure perception and adaptive gradient descent.
  • State space models provide efficient long-range dependency modeling with linear complexity.

Conclusions:

  • The developed pixel adaptive deep unfolding network offers a significant advancement in image deraining.
  • The integration of APGD and SFPM modules effectively overcomes previous limitations in DUNs.
  • The method achieves state-of-the-art results, offering improved visual quality for rainy images.