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Related Concept Videos

State Space Representation01:27

State Space Representation

504
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...
504
State Space to Transfer Function01:21

State Space to Transfer Function

545
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:
545
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

325
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
325
Transfer Function to State Space01:23

Transfer Function to State Space

735
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 RLC...
735
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

275
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
275
Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

355
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
355

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NDMamba: Dual-Prior State-Space Model for Nighttime Deraining.

Zhirui Liu, Shangquan Sun, Chaopeng Li

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |November 21, 2025
    PubMed
    Summary

    NDMamba, a novel dual-prior-guided state-space model, enhances nighttime image deraining by effectively modeling lighting and rain degradation. This approach balances efficiency and performance, outperforming existing methods on benchmark datasets.

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    Area of Science:

    • Computer Vision
    • Deep Learning
    • Image Processing

    Background:

    • Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) have advanced nighttime image deraining.
    • Current methods lack optimal balance between computational efficiency and restoration performance.
    • Existing models inadequately address low-light characteristics and rain-illumination interactions.

    Purpose of the Study:

    • To propose NDMamba, a dual-prior-guided state-space model for improved nighttime image deraining.
    • To jointly model lighting conditions and rain degradation using a Prior Extraction Module (PEM).
    • To enhance local features and refine deraining through a Prior-Guided Mamba Block (PGMB).

    Main Methods:

    • Developed NDMamba, a state-space model incorporating dual priors for nighttime deraining.
    • Introduced a Prior Extraction Module (PEM) inspired by Retinex theory.
    • Designed a Prior-Guided Mamba Block (PGMB) with Lighting-Adaptive Vision State-Space Module (LVSSM) and Rain Distribution Guidance Module (RDGM).

    Main Results:

    • NDMamba demonstrates superior performance compared to state-of-the-art methods.
    • The model achieves significant improvements on both synthetic and real-world nighttime deraining datasets.
    • Experimental results validate the effectiveness of the proposed dual-prior guidance approach.

    Conclusions:

    • NDMamba effectively addresses limitations in current nighttime image deraining techniques.
    • The proposed model offers a promising solution for high-quality nighttime image restoration.
    • Publicly available code facilitates further research and application in the field.