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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Linear Approximation in Time Domain01:21

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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.
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Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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STanH : Parametric Quantization for Variable Rate Learned Image Compression.

Alberto Presta, Enzo Tartaglione, Attilio Fiandrotti

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |March 3, 2025
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    Summary
    This summary is machine-generated.

    This study introduces STanH, a differentiable quantizer for learned image compression. It enables variable bitrates with a single model, reducing storage and training costs compared to traditional methods.

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    Area of Science:

    • Machine Learning
    • Image Processing
    • Data Compression

    Background:

    • End-to-end learned image compression models typically require training separate encoder-decoder pairs for each target bitrate (λ).
    • This approach leads to significant storage and computational overhead, necessitating multiple models for different compression levels.
    • Optimizing the rate-distortion trade-off (R + λD) is crucial for efficient image compression.

    Purpose of the Study:

    • To develop a novel method for achieving variable rate image compression using a single, adaptable model.
    • To reduce the storage and training complexity associated with traditional learned image compression techniques.
    • To enable flexible control over the rate-distortion trade-off without retraining.

    Main Methods:

    • Proposes STanH, a differentiable quantizer based on a parametric sum of hyperbolic tangents, relaxing the step-wise quantization.
    • Implements STanH as a learnable activation layer within a pre-trained fixed-rate image compression model.
    • Refines the model with the STanH layer to achieve various target bitrates.

    Main Results:

    • The proposed STanH method enables variable rate coding with performance comparable to state-of-the-art methods.
    • Demonstrates significant savings in deployment ease, training time, and storage costs.
    • The differentiable nature of STanH allows for seamless integration and adaptation.

    Conclusions:

    • STanH offers an efficient and flexible solution for learned image compression, addressing the limitations of fixed-rate models.
    • This approach significantly lowers the barrier to deploying learned image compression technologies.
    • The method provides a practical pathway towards high-efficiency, adaptable image compression systems.