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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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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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The important convolution properties include width, area, differentiation, and integration properties.
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WINNet: Wavelet-Inspired Invertible Network for Image Denoising.

Jun-Jie Huang, Pier Luigi Dragotti

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |June 27, 2022
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    Summary

    We introduce WINNet, a wavelet-inspired invertible network for image denoising. This method combines model-based interpretability with learning-based performance, achieving strong generalization across noise levels.

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    Area of Science:

    • Computer Vision
    • Signal Processing
    • Machine Learning

    Background:

    • Image denoising seeks to recover clean images from noisy observations.
    • Model-based methods offer interpretability and generalization but may lack performance.
    • Learning-based methods excel in performance but often struggle with generalization and interpretability.

    Purpose of the Study:

    • To develop a novel image denoising approach combining the strengths of wavelet-based and learning-based methods.
    • To enhance generalization ability and interpretability in image denoising.

    Main Methods:

    • Proposed a wavelet-inspired invertible network (WINNet) integrating lifting-inspired invertible neural networks (LINNs), sparsity-driven denoising, and noise estimation.
    • LINNs learn a non-linear redundant transform inspired by wavelet lifting schemes for noise removal.
    • A noise estimation network adaptively adjusts thresholds within LINNs.

    Main Results:

    • WINNet demonstrates high interpretability and strong generalization to unseen noise levels.
    • Achieved competitive performance in non-blind/blind image denoising and image deblurring tasks.
    • The network effectively utilizes a redundant multi-scale representation for denoising.

    Conclusions:

    • WINNet successfully merges the interpretability of model-based approaches with the performance of learning-based methods.
    • The proposed architecture offers a robust solution for diverse image denoising challenges.
    • WINNet shows promise for various image restoration applications beyond denoising.