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 ...
详细信息
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.
Diagnostic quality medical images consume vast amounts of network time, system bandwidth and disk storage in current computer architectures. There are many ways in which the use of system and network resources may be ...
详细信息
ISBN:
(纸本)0819422134
Diagnostic quality medical images consume vast amounts of network time, system bandwidth and disk storage in current computer architectures. There are many ways in which the use of system and network resources may be optimize without compromising diagnostic image quality. One of these is in the choice of image representation, both for storage and transfer. In this paper, we show how a particularly flexible method of image representation, based on Mallat's algorithm, leads to efficient methods of both lossy image compression and progressive image transmission. We illustrate the application of a progressive transmission scheme to medical images, and provide some examples of image refinement in a multiscale fashion. We show how thumbnail images created by a multiscale orthogonal decomposition can be optimally interpolated, in a minimum square error sense, based on a generalized Moore-Penrose inverse operator. In the final part of this paper, we show that the representation can provide a framework for lossy image compression, with signal/noise ratios far superior to those provided by a standard JPEG algorithm. The approach can also accommodate precision based progressive coding. We show the results of increasing the priority of encoding a selected region of interest in a bit-stream describing a multiresolution image representation.
Volume data such as those acquired by magnetic resonance imaging techniques can be compressed efficiently using the wavelet transform. Wavelet compression methods need to retain both the value and the location of the ...
详细信息
ISBN:
(纸本)0819422134
Volume data such as those acquired by magnetic resonance imaging techniques can be compressed efficiently using the wavelet transform. Wavelet compression methods need to retain both the value and the location of the significant coefficients. We present experimental results demonstrating the use of zerotree encoding methods in wavelet compression can enhance the ability to further compress volume data.
3D data acquisition is increasingly used in positron emission tomography (PET) to collect a larger fraction of the emitted radiation. Major practical difficulties with 3D- PET arise from large sizes of the data sets a...
详细信息
ISBN:
(纸本)0819422134
3D data acquisition is increasingly used in positron emission tomography (PET) to collect a larger fraction of the emitted radiation. Major practical difficulties with 3D- PET arise from large sizes of the data sets and reconstruction times. To take advantage of lossy compression we have developed an algorithm with possibility of compression built into. iT is based on a complete and orthonormal system of 2D wavelets and uses the technique of matched filters. These matched filters are obtained by mapping each 2D wavelet component with the model of the data acquisition geometry. The resulting projection images are convolved with a Ramachandran-Lakshminarayanan filter and multiplied with the projection data. The values of these scalar products in projection space are equal to the contribution of the given 2D wavelet component in the unknown object. This allows for reducing the number of matched filters used by application of a simple thresholding criterion in frequency space.
Multiwavelet transforms are a new class of wavelet transforms that use more than one prototype scaling function and wavelet in the multiresolution analysis/synthesis. The popular Geronimo-Hardin-Massopust multiwavelet...
详细信息
ISBN:
(纸本)0819422134
Multiwavelet transforms are a new class of wavelet transforms that use more than one prototype scaling function and wavelet in the multiresolution analysis/synthesis. The popular Geronimo-Hardin-Massopust multiwavelet basis functions have properties of compact support, orthogonality, and symmetry which cannot be obtained simultaneously in scalar wavelets. The performance of multiwavelets in still image compression is studied using vector quantization of multiwavelet subbands with a multiresolution codebook. The coding gain of multiwavelets is compared with that of other well-known wavelet families using performance measures such as unified coding gain. Implementation aspects of multiwavelet transforms such as pre-filtering/post-filtering and symmetric extension are also considered in the context of image compression.
Though wavelets have been used extensively for image coding, compression,and denoising, they are also gaining popularity in the geophysical sciences as an analysis tool. Capitalizing on the wavelet's relatively ti...
详细信息
ISBN:
(纸本)0819422134
Though wavelets have been used extensively for image coding, compression,and denoising, they are also gaining popularity in the geophysical sciences as an analysis tool. Capitalizing on the wavelet's relatively tight localization in both the time and frequency domains, the wavelet transform of a data field can yield significant information about the localized frequency content of the underlying process. As an analysis technique, though, standard wavelet transforms suffer from some of the real work constraints that data sets often impose. Primary among these is the fact that the data set is not typically supported on a standard rectangular grid. We investigate the application of a boundary-compensated wavelet transform supported on an arbitrarily-shaped region. applications to satellite-based altimetry of ocean basins are presented.
We developed a method of weighted wavelet packets for separation of small, low contrast signals from large, inhomogeneous background. Our method was applied to the enhancement of microcalcifications on digital mammogr...
详细信息
ISBN:
(纸本)0819422134
We developed a method of weighted wavelet packets for separation of small, low contrast signals from large, inhomogeneous background. Our method was applied to the enhancement of microcalcifications on digital mammograms, which appear as small bright spots superimposed on the background representing the structure of breast tissue, for improvement of the performance of our computer-aided diagnosis scheme for detection of clustered microcalcifications. Our method first approximates signals if interest by a set of wavelets that are extracted from a wavelet packet dictionary by means of the matching pursuit algorithm. The selected set of wavelets is then subjected to a supervised learning process for optimization of the weights assigned to individual time-frequency tiles for enhancement of the microcalcifications and suppression of the background structures. In an analysis of 82 regions of interest extracted from our mammographic database, our new method showed a sensitivity of 92 percent and a specificity of 75 percent. Our new method is shown to perform better than our previous method based on the fixed-weight, orthogonal wavelet transform.
wavelets and multi-rate filter banks are increasingly important tools for various digital imageprocessing (DIP) and image analysis tasks in addition to their traditional applications in one dimensional signal process...
详细信息
wavelets and multi-rate filter banks are increasingly important tools for various digital imageprocessing (DIP) and image analysis tasks in addition to their traditional applications in one dimensional signalprocessing. WaveTool, is an integrated software environment for rapid prototyping of wavelet-based algorithms. It is particularly attractive for signalprocessing because of its rich collection of filter bank choices, online multi-rate filter design, and interactive tree building. This paper presents a general overview of WaveTool with emphasis on its imageprocessing capabilities. Example applications to texture classification, seismic data compression, and image restoration are presented, and the future direction of WaveTool is discussed.
Shift-variance limits the usage of 2D maximally-decimated filter banks in many imageprocessingapplications where shift-invariance is desired. Several approaches have been proposed to overcome this problem for both 1...
详细信息
ISBN:
(纸本)0819422134
Shift-variance limits the usage of 2D maximally-decimated filter banks in many imageprocessingapplications where shift-invariance is desired. Several approaches have been proposed to overcome this problem for both 1D and 2D multirate systems. All of the existing methods are 1D-based algorithms, i.e. dealing with 2D image by separable processing, and thus do not have the advantages that a non- separable 2D system offers. In this paper, a framework for the theory and the design of 2D shift-invariant filter banks with non-separable sampling and/or non-separable filters are presented. There are three major advantages that the proposed 2D shift-invariant filter banks have over the separable 2D systems using the existing methods. First of all, it is a non-separable 2D approach and therefore has the advantages that a 'true' 2D approach offers. Secondly, the resulting 2D filter banks and wavelets have the conventional dyadic structure while possessing better SI property. Finally, the proposed filter bank is independent of input images. Design examples are presented.
A watermark is an invisible mark placed on an image that is designed to identify both the source of an image as well as its intended recipient. The authors present an overview of watermarking techniques and demonstrat...
详细信息
A watermark is an invisible mark placed on an image that is designed to identify both the source of an image as well as its intended recipient. The authors present an overview of watermarking techniques and demonstrate a solution to one of the key problems in image watermarking, namely how to hide robust invisible labels inside grey scale or colour digital images.
暂无评论