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.
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TL;DR: A new wavelet method for the fast estimation of continuous Karhunen-Loeve eigenfunctions is developed by projecting the ensemble functions onto orthogonal or biorthogonal interpolating function spaces and the covariance matrix may be sparsified by a multiresolution decomposition.
Abstract: This paper develops a new wavelet method for the fast estimation of continuous Karhunen-Loeve eigenfunctions. The method of snapshots is modified by projecting the ensemble functions onto orthogonal or biorthogonal interpolating function spaces. Under well-behaved piecewise smooth polynomial ensemble functions, the size of the covariance matrix produced is greatly reduced, without sacrificing much accuracy. Moreover, the covariance matrix C/spl tilde/ may be easily decomposed such that C/spl tilde/ = A/sup T/ A, and thus, the more stable singular value decomposition (SVD) algorithm may be applied. An interpolating scheme that reduces the computation of projecting the ensemble functions onto the biorthogonal subspace to a single sample is also developed. Furthermore, by projecting the ensemble functions onto wavelet spaces, the covariance matrix may be sparsified by a multiresolution decomposition. Error bounds for the eigenvalues between the sparsified and nonsparsified covariance matrix are also derived.
23 citations
01 Feb 2007
TL;DR: A novel retina feature, named wavelet energy feature (WEF) is defined in this paper, employing wavelet, which is a powerful tool of multi-resolution analysis, which can reflect theWavelet energy distribution of the vessels with different thickness and width in several directions at different wavelet decomposition levels (scales), so its ability to discriminate retinas is very strong.
Abstract: Retina is a new biometric method to recognize a person. The fact that blood vessels have vessels with different thickness and width motivate us to analyze the retina using multi-resolution analysis method. A novel retina feature, named wavelet energy feature (WEF) is defined in this paper, employing wavelet, which is a powerful tool of multi-resolution analysis. WEF can reflect the wavelet energy distribution of the vessels with different thickness and width in several directions at different wavelet decomposition levels (scales), so its ability to discriminate retinas is very strong. Easiness to compute is another virtue of WEF. Using semiconductors and various environmental temperatures in electronic imaging systems cause noisy images, so in this article noisy retinal images are used in recognition. In existence of 5 db to 20 db noise, the proposed method can achieve %100 recognition rates.
23 citations
08 Nov 2010
TL;DR: The drawback of conventional LBP operators in describing some textures that has the same small structures but differential large structures is investigated and a multi-structure local binary pattern operator is achieved by executing the LBP method on different layers of image pyramid.
Abstract: Recently, the local binary pattern (LBP) has been widely used in texture classification. The conventional LBP methods only describe micro structures of texture images, such as edges, corners, spots and so on, although many of them show a good performance on texture classification. This situation still could not be changed, even though the multiresolution analysis technique is used in methods of local binary pattern. In this paper, we investigate the drawback of conventional LBP operators in describing some textures that has the same small structures but differential large structures. And a multi-structure local binary pattern operator is achieved by executing the LBP method on different layers of image pyramid. The proposed method is simple yet efficient to extract not only the micro structures but also the macro structures of texture images. We demonstrate the performance of our method on the task of rotation invariant texture classification. The experimental results on Outex database show advantages of the proposed method.
23 citations
TL;DR: A novel, scalable, and progressive MP-based region-of-interest image-coding scheme is presented that is capable of providing a trade off between rate, distortion, and complexity and can be adapted to the computational power of the image encoder.
Abstract: Matching pursuit (MP) is a multiresolution signal analysis method and can be used to render a selected region of an image with a specific quality. A novel, scalable, and progressive MP-based region-of-interest image-coding scheme is presented. The method is capable of providing a trade off between rate, distortion, and complexity. The method also provides an interactive way of information refinement for regions of an image with higher receiver's priority. By selecting a proper subset of the huge initial MP dictionary, using the method described in this paper, the complexity burden of MP analysis can be adapted to the computational power of the image encoder
23 citations
TL;DR: In this paper, a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions is presented, which can be carried out in any number of dimensions and for a big variety of dilation matrices.
Abstract: In this article we present a nonseparable multiresolution structure based on frames which is defined by radial frame scaling functions. The Fourier transform of these functions is the indicator (characteristic) function of a measurable set. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a big variety of dilation matrices.
23 citations