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Reconstruction of Signal using Interpolation01:10

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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
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Photorealistic Learned Landscapes for Augmented Reality
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Image Restoration by Combined Order Regularization with Optimal Spatial Adaptation.

Sanjay Viswanath, Manu Ghulyani, Simon De Beco

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |May 2, 2020
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel non-convex regularization method for image restoration, adaptively combining Hessian-Schatten and first-order Total Variation norms. The approach demonstrates improved performance in MRI reconstruction and microscopy deconvolution tasks.

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    Area of Science:

    • Image Processing
    • Computational Imaging
    • Applied Mathematics

    Background:

    • Total Variation (TV) and its extensions are widely used in image restoration.
    • Existing methods like Combined Order TV (COTV) and Total Generalized Variation (TGV) explore multi-order derivatives for enhanced performance.
    • There is a need for improved regularization techniques that offer better image reconstruction quality.

    Purpose of the Study:

    • To propose a novel non-convex regularization functional for image restoration.
    • To adaptively combine Hessian-Schatten (HS) norm and first-order TV (TV1) functionals.
    • To improve upon existing convex multi-order regularization methods.

    Main Methods:

    • A novel non-convex regularization functional is proposed, adaptively combining HS norm and TV1 functionals with a spatially varying weight.
    • The adaptive weight is controlled by an additional regularization term, forming a total cost function.
    • A block coordinate descent method is developed for joint minimization with respect to the image and the adaptive weight, including an ADMM algorithm for image minimization.

    Main Results:

    • The proposed method achieves improved performance compared to existing regularization techniques.
    • The method demonstrates effectiveness in image recovery tasks, including MRI reconstruction and microscopy deconvolution.
    • A block coordinate descent method with a convergence proof is established for the minimization process.

    Conclusions:

    • The novel non-convex regularization functional offers a promising advancement in image restoration.
    • Adaptive combination of HS norm and TV1 functionals with spatially varying weights enhances reconstruction quality.
    • The developed computational methods ensure efficient and convergent optimization for image recovery.