A new system, called dual ridgelet frame, is introduced. The construction of the dual ridgelet frame starts with a dual frame constructed using a biorthogonal wavelet basis in the Radon domain, and, then, the image of...
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A new system, called dual ridgelet frame, is introduced. The construction of the dual ridgelet frame starts with a dual frame constructed using a biorthogonal wavelet basis in the Radon domain, and, then, the image of the resulting dual frame under an isometric map from the Radon domain to the L/sup 2/(R/sup 2/) spatial domain is a dual frame again, and we call it a dual ridgelet frame. The dual ridgelet frame can be thought of as an extension of the notion of orthonormal ridgelet. It provides a more flexible and effective tool for image analysis and processingapplications. The high performance of the dual ridgelet frame for image denoising is demonstrated experimentally.
Several approaches have been proposed to improve the compaction performance of the wavelet transform by taking into account the singularities present in the image and their 2D directionalities. This improvement is val...
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Several approaches have been proposed to improve the compaction performance of the wavelet transform by taking into account the singularities present in the image and their 2D directionalities. This improvement is valid both for compression and de-noising applications. Here, we investigate an edge adaptive wavelet transform which has a better rate-distortion characteristic than the classical wavelet transform. The proposed approach can be viewed roughly as a combination of image segmentation and shape adaptive wavelet transform. The algorithm consists of two steps. In the first step we locate edges by using a sigma filter. In the second step we apply the modified wavelet transform on the separated parts of the image. We provide performance results in terms of rate-distortion curves for both 1D and relatively simple 2D signals.
Discrete wavelet transform (DWT) became a powerful method for signalprocessing in the last decade. One of the most important applications of this tool is compression, for the bi-dimensional signals JPEG 2000 being an...
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Discrete wavelet transform (DWT) became a powerful method for signalprocessing in the last decade. One of the most important applications of this tool is compression, for the bi-dimensional signals JPEG 2000 being an example. Although the new standard offers better results than the old one, new innovating ideas can improve even the JPEG 2000. One idea is to use complex wavelet transforms, transforms that offers more directions, instead of classical DWT. This paper comes to show the superiority of complex wavelet transforms in image compression, testing a new transform developed by N.G. Kingsbury. For this, the embedded zero-tree wavelet (EZW) algorithm proposed by Shapiro was used to compress images at some different bit rates
Directional information is an important and unique feature of multidimensional signals. As a result of a separable extension from 1D bases, the multidimensional wavelet transform has very limited directionality. Furth...
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Directional information is an important and unique feature of multidimensional signals. As a result of a separable extension from 1D bases, the multidimensional wavelet transform has very limited directionality. Furthermore, different directions are mixed in certain wavelet subbands. In this paper, we propose a new transform that fixes this frequency mixing problem by using a simple "add-on" to the wavelet transform. In the 2D case, it provides one lowpass subband and six directional highpass subbands at each scale. Just like the wavelet transform, the proposed transform is nonredundant, and can be easily extended to higher dimensions. Though nonseparable in essence, the proposed transform has an efficient implementation based on 1D operations only.
images are often corrupted as a result of various factors that can occur during acquisition and transmission processes. image denoising is aimed at removing or reducing noise, so that a good-quality image can be obtai...
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images are often corrupted as a result of various factors that can occur during acquisition and transmission processes. image denoising is aimed at removing or reducing noise, so that a good-quality image can be obtained for various applications. The paper presents a neural network based denoising method implemented in the wavelet transform domain. A noisy image is first wavelet transformed into four subbands, then a trained layered neural network is applied to each subband to generate noise-removed wavelet coefficients from their noisy ones. The denoised image is thereafter obtained through the inverse transform on the noise-removed wavelet coefficients. Simulation results demonstrate that this method is very efficient in removing noise. Compared with other methods performed in the wavelet domain, it requires no a priori knowledge about the noise and needs only one level of signal decomposition to obtain very good denoising results.
The wavelet transform is a very powerful tool for image coding for which the quality of the compression is depending on the choice of the filter banks associated to the wavelet. These filters can be characterized by t...
The wavelet transform is a very powerful tool for image coding for which the quality of the compression is depending on the choice of the filter banks associated to the wavelet. These filters can be characterized by two indices: a spatial index related to their significant support and a frequency index related to their aliasing. This work explores the connection between a quality criteria and these two indices for a given image family. Two useful applications are presented: in the first one a neural network allows us to deduce the best filter bank for a given image. In the second one a quality criterion for a new image is estimated knowing the filter bank.
Spherical maps occur in a range of applications for instance in geophysics or in astrophysics with the study of the cosmic microwave background (CMB) radiation field, where observations are over the whole sky. Analyzi...
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Spherical maps occur in a range of applications for instance in geophysics or in astrophysics with the study of the cosmic microwave background (CMB) radiation field, where observations are over the whole sky. Analyzing these images requires specific tools. This paper describes a new multiscale decomposition for data on the sphere, namely the curvelet transform on the sphere. The curvelet transform, in its first step, requires the use of an isotropic wavelet transform. Therefore, our new curvelet transform also includes a new wavelet transform on the sphere which has properties similar to those of the a trous isotropic wavelet transform.
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