Study on the method of suppressing surface wave by Curvelet transform
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The Curvelet transform has features such as multi-scale, multi-direction, multi-resolution, etc. It can separate the effective wave and the surface wave in the Curvelet domain by using the characteristics of the frequency, velocity, and direction of the surface wave and the effective wave. Thus it can suppress the surface wave. However, the effect of suppressing the surface wave is affected by the degree of overlapping of the surface wave and the effective wave in the Curvelet domain. In actual seismic data, effective wave and surface wave cannot be completely separated in the Curvelet domain. In this paper, a method of Curvelet threshold iterative based on energy ratio is proposed. First, decomposing the effective wave and the surface wave in the Curvelet domain for many times, then, using different frequency bands and different threshold values to perform multiple information reconstruction, which can effectively separate the effective wave and the surface wave. In this way, a good surface wave suppression effect is achieved.Keywords:
Curvelet
Curvelet
Feature (linguistics)
Backpropagation
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Curvelet transform is the member of multiscale geometric transforms, which provides an best solution to the problems associated with image denoising with wavelets. The wavelet's performance degrades when circular type space-frequency like curve or arc edges or lines are viewed in the image. Curvelet transform has redundant dictionary that can provide sparse representation of signals that have edges along regular curve. The second generation curvelet transform is simpler to understand and use and also faster and less redundant compared to its previous version. Curvelet transform is depicted in various domains and meant for higher dimensions. This paper focused on an better curvelet based denoising technique to improve sonar images.
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Representation
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This paper identifies a novel feature space to address the problem of human face recognition from still images. This is based on the PCA space of the features extracted by a new multiresolution analysis tool called Fast Discrete Curvelet Transform. Curvelet Transform has better directional and edge representation abilities than widely used wavelet transform. Inspired by these attractive attributes of curvelets, we introduce the idea of decomposing images into its curvelet subbands and applying PCA (Principal Component Analysis) on the selected subbands in order to create a representative feature set. Experiments have been designed for both single and multiple training images per subject. A comparative study with wavelet-based and traditional PCA techniques is also presented. High accuracy rate achieved by the proposed method for two well-known databases indicates the potential of this curvelet based feature extraction method.
Curvelet
Feature vector
Feature (linguistics)
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Curvelet
Feature (linguistics)
Backpropagation
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A super-resolution image reconstruction algorithm was proposed using the 2nd generation curvelet to reduce the edge blur caused by traditional algorithms.In the proposed algorithm,the original image is decomposed into j scales using curvelet.The curvelet coefficients in the j scales of the zoomed-in image are obtained by utilizing the proportionality of curvelet bases between adjacent scales,and the curvelet coefficients in the(j+1)th scale are determined by utilizing the spatial template of curvelet coefficients with the largest scale number.All the curvelet coefficients are processed with a nonlinear function to enhance image quality.The zoomed-in image with fine edges is finally created through curvelet reconstruction because of the good directional characteristic of curvelet.Experiments on two benchmarking images shown that,the proposed algorithm could preserve more image features and edge sharpness,and the peak signal to noise ratios(PSNRs) for the two images increased by 2.2 and 0.6 dB,respectively,compared with those obtained with a traditional interpolation algorithm.
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Interpolation
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Summary We present significant improvements in pre-migration seismic velocity estimation through the use of Curvelet transform in prestack noise attenuation. Seismic data is decomposed using the Curvelet transform, which has the capability of separating events having differing frequency, dipping angle and location. Curvelet transforms decompose data as a weighted sum of “Curvelets”, where each Curvelet is localised in both the f-k and t-x domains, and each weight consists of both amplitude and phase. The data are processed in the Curvelet domain by manipulation of these weights. Noise suppression via the Curvelet transform on prestack gathers has contributed to significantly improved pre-migration velocity estimation.
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Surface pressure
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Curvelets are a multiscale system with very high directional sensitivity. A new detection algorithm is herein described which operates on a curvelet decomposition of acoustic imagery. The algorithm detects the presence of cylindrical targets through a statistical mapping of curvelet coefficients. The coefficients are calculated as an inner product between image features and a curvelet basis element. The similarity in appearance between cylindrical targets and curvelet basis elements yield an accurate detection algorithm with a very low false alarm rate.
Curvelet
Basis (linear algebra)
Similarity (geometry)
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The Curvelet is more suitable for image processing than the wavelet and able to represent smooth and edge parts of image with sparsity.Based on the advantages of curvelet,we present a novel method for image restoration and decomposition via curvelet shrinkage.The new model can be seen as generalizations of DaubechiesTeschke's model.By writing the problem in a curvelet framework,we obtain elegant curvelet shrinkage schemes.Various numerical results on denoising,deblurring and decomposition of images are presented and they show that the model is valid.
Curvelet
Deblurring
Shrinkage
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