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Related Concept Videos

Convolution Properties I01:20

Convolution Properties I

478
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
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Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

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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.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
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Convolution Properties II01:17

Convolution Properties II

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The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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Entropy01:18

Entropy

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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Entropy02:39

Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Updated: Dec 23, 2025

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
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Efficient and Effective Context-Based Convolutional Entropy Modeling for Image Compression.

Mu Li, Kede Ma, Jane You

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |April 20, 2020
    PubMed
    Summary
    This summary is machine-generated.

    Context-based convolutional networks (CCNs) improve image compression by enhancing entropy modeling. These networks offer faster, comparable performance to state-of-the-art methods in both lossless and lossy compression tasks.

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    Area of Science:

    • Computer Vision
    • Information Theory
    • Machine Learning

    Background:

    • Accurate probabilistic modeling of natural images is crucial for efficient image compression.
    • Current end-to-end image compression methods often simplify entropy modeling by assuming statistically factorized latent codes, which can limit performance.
    • This assumption of statistical factorization is generally not accurate for natural images.

    Purpose of the Study:

    • To introduce context-based convolutional networks (CCNs) for more effective and efficient entropy modeling in image compression.
    • To address the limitations of assuming statistically factorized latent codes in existing image compression techniques.
    • To demonstrate the applicability of CCNs in both lossless and lossy image compression scenarios.

    Main Methods:

    • Developed CCNs incorporating 3D zigzag scanning and 3D code dividing techniques to establish coding contexts for parallel entropy decoding.
    • Applied CCNs directly to binarized image representations for lossless compression, estimating Bernoulli distributions.
    • For lossy compression, used three CCNs to estimate parameters of discretized mixture of Gaussian distributions representing categorical distributions of latent codes.
    • Jointly optimized the CCN-based entropy model with analysis and synthesis transforms for rate-distortion performance.

    Main Results:

    • CCNs demonstrated effective entropy modeling for both lossless and lossy image compression.
    • Methods utilizing CCNs achieved compression performance comparable to state-of-the-art techniques.
    • The proposed CCN-based methods were significantly faster than existing state-of-the-art approaches.
    • Experiments were conducted on standard datasets like Kodak and Tecnick.

    Conclusions:

    • CCNs provide a powerful and efficient approach for entropy modeling in image compression.
    • The proposed methods overcome the limitations of traditional statistical factorization assumptions.
    • CCNs offer a promising direction for advancing both lossless and lossy image compression technologies with improved speed and comparable performance.