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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
More filters
Book ChapterDOI
TL;DR: The results show that from both a PSNR and a visual quality, the proposed filter outperforms the other state of the art filters for different image sequences.
Abstract: This paper presents a non-linear technique for noise reduction in video that is suitable for real-time processing The proposed algorithm automatically adapts to detected levels of detail and motion, but also to the noise level, provided it is short-tail noise, such as Gaussian noise It uses a one-level wavelet decomposition, and performs independent processing in four different bands in the wavelet domain The non-decimated transform is used because it leads to better results for image/video denoising than the decimated transform The results show that from both a PSNR and a visual quality, the proposed filter outperforms the other state of the art filters for different image sequences

46 citations

Journal ArticleDOI
TL;DR: It has been shown that the proposed adaptive scheme can detect the singularities both in the domain and near the boundaries and can be utilized for capturing the regions with high gradient both inThe solution and its spatial derivatives.
Abstract: We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast Discrete Wavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the proposed adaptive scheme can detect the singularities both in the domain and near the boundaries. Moreover, the proposed adaptive scheme can be utilized for capturing the regions with high gradient both in the solution and its spatial derivatives. Due to the simplicity of the proposed method, it can be efficiently applied to large scale nearly singular engineering problems.

46 citations

Journal ArticleDOI
TL;DR: This paper deals with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions that satisfy the Littlewood-Paley identity and gives a detailed analysis of the time-frequency localization of these wavelets.
Abstract: In this paper, we deal with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions. These radial basis functions are noted for their effectiveness in terms of “projection”, such as interpolation and least-squares approximation, particularly when the data structure is scattered or the dimension of ℝ s is large. Thus projecting a functionf onto a suitable multiresolution space is relatively easy here. The associated multiresolution spaces approximate sufficiently smooth functions exponentially fast. The non-stationary wavelets satisfy the Littlewood-Paley identity so that perfect reconstruction of wavelet decompositions is achieved. For the univariate case, we give a detailed analysis of the time-frequency localization of these wavelets. Two numerical examples for the detection of singularities with analytic wavelets are provided.

46 citations

Journal ArticleDOI
TL;DR: Wavelet domain thresholding rules are developed, which allow us to identify the coefficients relevant for clutter and to suppress them in order to obtain filtered recon- structions.
Abstract: In this paper, we apply wavelet thresholding for removing automatically ground and intermittent clutter (airplane echoes) from wind profiler radar data. Using the concept of discrete multi-resolution analysis and non-parametric estimation theory, we develop wavelet domain thresholding rules, which allow us to identify the coefficients relevant for clutter and to suppress them in order to obtain filtered reconstructions.

46 citations

Journal ArticleDOI
TL;DR: In this article, an analysis and denoising of cosmic microwave background (CMB) maps using wavelet multiresolution techniques is performed using 12.8×12.8 × 12.2 maps, with the resolution resembling the experimental one expected for future high-resolution space observations.
Abstract: Analysis and denoising of cosmic microwave background (CMB) maps are performed using wavelet multiresolution techniques. The method is tested on 12.8×12.8 deg2 maps, with the resolution resembling the experimental one expected for future high-resolution space observations. Semi-analytic formulae of the variance of wavelet coefficients are given for the Haar and Mexican Hat wavelet bases. Results are presented for the standard cold dark matter (CDM) model. Denoising of simulated maps is carried out by removal of wavelet coefficients dominated by instrumental noise. CMB maps with a signal-to-noise ratio, SN∼1, are denoised with an error improvement factor between 3 and 5. Moreover, we have also tested how well the CMB temperature power spectrum is recovered after denoising. We are able to reconstruct the Cls up to l∼1500 with errors always below 20 per cent in cases with SN1.

46 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202252
202159
202070
201969
201879