The accuracy of the wavelet approximation at resolution h equals 2-n to a smooth function f is limited by O(hn), where N is the number of vanishing moments of the mother wavelet (psi) . For any positive integer p, we ...
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ISBN:
(纸本)0819422134
The accuracy of the wavelet approximation at resolution h equals 2-n to a smooth function f is limited by O(hn), where N is the number of vanishing moments of the mother wavelet (psi) . For any positive integer p, we derive basis functions which allow us to recover a smooth f from its wavelet coefficients with accuracy O(hp). Related formulas for recovering derivatives of f are also given.
The performance of wavelet compression algorithms is generally judged solely as a function of the compression ratio and the vidual artifacts which are perceivable in the reconstructed image. The problem then becomes o...
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ISBN:
(纸本)0819422134
The performance of wavelet compression algorithms is generally judged solely as a function of the compression ratio and the vidual artifacts which are perceivable in the reconstructed image. The problem then becomes one of obtaining the best compression with fewest visible artifacts--a very subjective measure. Our wavelet compression algorithm uses an information theoretic analysis for the design of the compression maps. We have previously shown that maximizing the information for a given visual communication channel also maximizes the visual quality of the restored image. We utilize this to design quantization maps which maximize information for a given compression ratio. Hence we are able to design quantization maps which maximize the restorability of an image--i.e. the information content, the image quality, and the mean-square difference fidelity--for a given compression ratio.
This paper describes the construction of a new multiresolutional decomposition with applications to image compression. The proposed method designs sparsity-distortion-optimized orthonormal transforms applied in wavele...
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ISBN:
(纸本)9781424479948
This paper describes the construction of a new multiresolutional decomposition with applications to image compression. The proposed method designs sparsity-distortion-optimized orthonormal transforms applied in wavelet domain to arrive at a multiresolutional representation which we term the Sparse Multiresolutional Transform (SMT). Our optimization operates over sub-bands of given orientation and exploits the inter-scale and intra-scale dependencies of wavelet coefficients over image singularities. The resulting SMT is substantially sparser than the wavelet transform and leads to compaction that can be exploited by well-known coefficient coders. Our construction deviates from the literature, which mainly focuses on model-based methods, by offering a data-driven optimization of wavelet representations. Simulation experiments show that the proposed method consistently offers better performance compared to the original wavelet-representation and can reach up to 1dB improvements within state-of-the-art coefficient coders.
This paper proposes a scale correlation-based edge detection scheme. A scale correlation function is defined as the product of detection filter's response at two scales. With the proper choice of detection filters...
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ISBN:
(纸本)0819442666
This paper proposes a scale correlation-based edge detection scheme. A scale correlation function is defined as the product of detection filter's response at two scales. With the proper choice of detection filters such as the first derivative of Gaussian, the scale correlation will magnify the edge structures and suppress the noise. Unlike many of the multiscale techniques that first form the edge maps at several scales and then synthesize them together, in our scheme, edges are determined as the local maxima directly in the correlation function. The detection and localization criteria of the scale correlation are defined. It is shown that with little loss in detection criterion, much improvement is gained on localization criterion. Using scale correlation,the dislocation of neighboring edges is also improved when the width of detection filter is set large to smooth noise.
in wavelets based coding applications, resolution scalability is achieved by retaining the low pass signal subband corresponds to the required resolution and discarding other high pass wavelet subbands. Aliasing is a ...
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ISBN:
(纸本)0780391349
in wavelets based coding applications, resolution scalability is achieved by retaining the low pass signal subband corresponds to the required resolution and discarding other high pass wavelet subbands. Aliasing is a common problem present in such downsampling. In this paper a novel technique for improving the low pass filter for improved downsampling is presented. This method uses an extra update step followed by P+U lifting scheme. The preprocessing update step is chosen as the dual update step associated with the wavelet. The spatially adaptive low pass (SALP) filtering concept is used for the second update step, leading to an overall low pass filter whose size adapts to the underlying signal content. The filter choices for the second update step is recovered at the decoder without any bookkeeping. Results using the 2D 5/3 wavelet with the extra pre-processing update step show improvements over conventional wavelets.
In this work, we consider the problem of blind source separation in the wavelet domain via a Bayesian estimation framework. We use the sparsity and multiresolution properties of the wavelet coefficients to model their...
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ISBN:
(纸本)0819450804
In this work, we consider the problem of blind source separation in the wavelet domain via a Bayesian estimation framework. We use the sparsity and multiresolution properties of the wavelet coefficients to model their distribution by heavy tailed prior probability laws: the generalized exponential family and the Gaussian mixture family. Appropriate MCMC algorithms are developped in each case for the estimation purposes and simulation results are presented for comparison.
In this paper we aim at providing a robust and more compact approach for detecting edges compared to the traditional edge detection algorithms like Roberts, Sobel, Prewitt and evolutionary-inspired Ant Colony Optimiza...
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ISBN:
(纸本)9781467373869
In this paper we aim at providing a robust and more compact approach for detecting edges compared to the traditional edge detection algorithms like Roberts, Sobel, Prewitt and evolutionary-inspired Ant Colony Optimization (ACO) techniques. In this proposed approach, an ACO is used alongside Dual-Tree Complex wavelet Transform (DT-CWT) to detect and emphasize edges that would have been difficult to obtain with directly applying ACO or conventional edge detection algorithms. Initially the image is decomposed using DT-CWT to obtain the oriented wavelets and approximation versions of the original image. ACO is applied to each of the decomposed images and then image is reconstructed to get the processed image with the detected edges. The results obtained reveal superior, more detailed and emphasized edges than directly applying ACO or other conventional techniques. The proposed approach is also capable of identifying edges in slightly varying intensity regions.
wavelet domain image resolution enhancement algorithms assume that the available image is the low-frequency subband of a higher resolution image and high-frequency subbands are not available. Then, these high-frequenc...
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ISBN:
(纸本)9781424407194
wavelet domain image resolution enhancement algorithms assume that the available image is the low-frequency subband of a higher resolution image and high-frequency subbands are not available. Then, these high-frequency coefficients are estimated and the higher resolution image is generated by application of inverse wavelet transform. Some of these techniques have used probabilistic methods and utilisation of HMT (Hidden Markov Tree) was shown to produce promising results. HMT based methods model the wavelet coefficients as Gaussian distributions. However, as Gaussian distributions are symetrical around zero, coefficient signs are generated randomly and have an equal change of being positive or negative. In this paper, significance of having correst coefficient sign information is demonstrated and a post-processing method is proposed to increase the accuracy of the estimated signs.
High-resolution optical mapping is an emerging technique to record the activation and propagation of transmembrane potential on the surface of cardiac tissues. Important electrodynamic information previously not avail...
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ISBN:
(纸本)0819429139
High-resolution optical mapping is an emerging technique to record the activation and propagation of transmembrane potential on the surface of cardiac tissues. Important electrodynamic information previously not available from extracellular electric recording could be extracted from these detailed optical recordings. The noise contamination in the images is a major obstacle that prohibits higher level of information extraction. Because the patterns of interest contain sharp wavefronts and structures that we wish to detect and track in a series of: flames, we seek to perform denoising based on wavelet decomposition approaches. Among the wavelet denoise methods that were tested in this preliminary study, the wavelet packet produced the best results that could be extended to denoise the entire image sequence for multi-dimensional information processing.
We present a novel method to extract subimages from a huge reference image by using integer-type lifting wavelet transforms. Our integer to integer lifting wavelet transform contains controllable free parameters in th...
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ISBN:
(纸本)0819437646
We present a novel method to extract subimages from a huge reference image by using integer-type lifting wavelet transforms. Our integer to integer lifting wavelet transform contains controllable free parameters in the lifting term, which is constructed based on an integer version of Haar wavelet transform. Such free parameters are trained following a vanishing criterion for low frequency components of query images. The trained parameters have characteristics of the query images. We apply a lifting wavelet transform with such parameters to a reference image and check whether they satisfy our vanishing criterion or not, to extract target subimages.
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