Topic
Multiresolution analysis
About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, it was shown that the existence of a pair of biorthogonal compactly supported vector-valued wavelet scaling functions guarantees that there is also a corresponding pair of scalar wavelet scalar scalar scaling functions.
Abstract: In this paper, we introduce the biorthogonal vector-valued wavelets. We prove that, like in the scalar wavelet case, the existence of a pair of biorthogonal compactly supported vector-valued scaling functions guarantees the existence of a pair of biorthogonal compactly supported vector-valued wavelet functions. An algorithm for constructing a pair of biorthogonal compactly supported vector-valued wavelet functions is presented by means of vector-valued multiresolution analysis and matrix theory. The notion of biorthogonal vector-valued wavelet packets is introduced, and their properties are investigated by virtue of time–frequency analysis and algebra theory. Three biorthogonality formulas concerning the wavelet packets are established. Relation to some physical theories such as E -infinity Cantorian space–time theory is also discussed.
78 citations
TL;DR: In this article, the authors study properties such as regularity, convergence, and stability of a normal multiresolution analysis of a curve and show that these properties critically depend on the underlying subdivision scheme.
Abstract: A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal multiresolution analysis. In particular, we show that these properties critically depend on the underlying subdivision scheme and that, in general, the convergence of normal multiresolution approximations equals the convergence of the underlying subdivision scheme.
78 citations
TL;DR: It is shown that the hyperspectral image can be restored using a few sparse components and that WSRRR not only effectively removes noise but also maintains more fine features compared to other methods used.
Abstract: In this paper, a method called wavelet-based sparse reduced-rank regression (WSRRR) is proposed for hyperspectral image restoration. The method is based on minimizing a sparse regularization problem subject to an orthogonality constraint. A cyclic descent-type algorithm is derived for solving the minimization problem. For selecting the tuning parameters, we propose a method based on Stein's unbiased risk estimation. It is shown that the hyperspectral image can be restored using a few sparse components. The method is evaluated using signal-to-noise ratio and spectral angle distance for a simulated noisy data set and by classification accuracies for a real data set. Two different classifiers, namely, support vector machines and random forest, are used in this paper. The method is compared to other restoration methods, and it is shown that WSRRR outperforms them for the simulated noisy data set. It is also shown in the experiments on a real data set that WSRRR not only effectively removes noise but also maintains more fine features compared to other methods used. WSRRR also gives higher classification accuracies.
78 citations
TL;DR: A novel multiresolution fully convolutional network for automatically removing moiré patterns from photos, which achieves the state-of-the-art performance on this data set in comparison to existing learning architectures for image restoration problems.
Abstract: Digital cameras and mobile phones enable us to conveniently record precious moments. While digital image quality is constantly being improved, taking high-quality photos of digital screens still remains challenging because the photos are often contaminated with moire patterns, a result of the interference between the pixel grids of the camera sensor and the device screen. Moire patterns can severely damage the visual quality of photos. However, few studies have aimed to solve this problem. In this paper, we introduce a novel multiresolution fully convolutional network for automatically removing moire patterns from photos. Since a moire pattern spans over a wide range of frequencies, our proposed network performs a nonlinear multiresolution analysis of the input image before computing how to cancel moire artefacts within every frequency band. We also create a large-scale benchmark dataset with 100,000+ image pairs for investigating and evaluating moire pattern removal algorithms. Our network achieves state-of-the-art performance on this dataset in comparison to existing learning architectures for image restoration problems.
77 citations
TL;DR: A wavelet-based approach to linear inverse problems in image processing where both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem.
Abstract: We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results. >
77 citations