Image Completion with Smooth Nonnegative Matrix Factorization

Sadowski, Tomasz; Zdunek, Rafał

doi:10.1007/978-3-319-91262-2_6

Cited by 6 publications

(2 citation statements)

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“…Usual penalties for smoothness involve the total variation norm or the L 2 norm of the second derivative for spline smoothing, [19], [22], [25], [26], [28]. The second strategy consists in representing the factors within specific lower dimensional spaces, using splines, polynomials or kernels [18]- [21], [23], [24], [29]- [31].…”

Section: A Related Workmentioning

confidence: 99%

New penalized criteria for smooth non-negative tensor factorization with missing entries

Durand¹,

Roueff²,

Jicquel³

et al. 2022

Preprint

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Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we focus in understanding how this issue should be dealt with for nonnegative tensor factorization. We investigate several criteria used for non-negative tensor factorization in the case where some entries are missing. In particular we show how smoothness penalties can compensate the presence of missing values in order to ensure the existence of an optimum. This lead us to propose new criteria with efficient numerical optimization algorithms. Numerical experiments are conducted to support our claims.

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Section: A Related Workmentioning

confidence: 99%

New penalized criteria for smooth non-negative tensor factorization with missing entries

Durand¹,

Roueff²,

Jicquel³

et al. 2022

Preprint

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show abstract

“…One of the commonly used methods for extracting low-rank part-based representations from nonnegative matrices is nonnegative matrix factorization (NMF) [28]. It has already found many relevant applications in image analysis, and can also be used for solving image completion problems [29,30]. In this approach, the missing regions are sequentially updated with an NMF-based low-rank approximation of an observed image, which resembles the phenomena of propagating the neighboring information towards the missing regions in the PDE-based inpainting methods.…”

Section: Introductionmentioning

confidence: 99%

Image Completion with Hybrid Interpolation in Tensor Representation

Zdunek¹,

Sadowski²

2020

Applied Sciences

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The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.

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