11,492 research outputs found
A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands
This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups
In this paper we connect the well established discrete frame theory of
generalized shift invariant systems to a continuous frame theory. To do so, we
let , , be a countable family of closed, co-compact
subgroups of a second countable locally compact abelian group and study
systems of the form with generators in and with each
being a countable or an uncountable index set. We refer to systems of this form
as generalized translation invariant (GTI) systems. Many of the familiar
transforms, e.g., the wavelet, shearlet and Gabor transform, both their
discrete and continuous variants, are GTI systems. Under a technical
local integrability condition (-LIC) we characterize when GTI systems
constitute tight and dual frames that yield reproducing formulas for .
This generalizes results on generalized shift invariant systems, where each
is assumed to be countable and each is a uniform lattice in
, to the case of uncountably many generators and (not necessarily discrete)
closed, co-compact subgroups. Furthermore, even in the case of uniform lattices
, our characterizations improve known results since the class of GTI
systems satisfying the -LIC is strictly larger than the class of GTI
systems satisfying the previously used local integrability condition. As an
application of our characterization results, we obtain new characterizations of
translation invariant continuous frames and Gabor frames for . In
addition, we will see that the admissibility conditions for the continuous and
discrete wavelet and Gabor transform in are special cases
of the same general characterizing equations.Comment: Minor changes (v2). To appear in Trans. Amer. Math. So
A Quaternionic Wavelet Transform-based Approach for Object Recognition
Recognizing the objects in complex natural scenes is the challenging task as the object may be occluded, may vary in shape, position and in size. In this paper a method to recognize objects from different categories of images using quaternionic wavelet transform (QWT) is presented. This transform separates the information contained in the image better than a traditional Discrete wavelet transform and provides a multiscale image analysis whose coefficients are 2D analytic, with one near-shift invariant magnitude and three phases. The two phases encode local image shifts and the third one contains texture information. In the domain of object recognition, it is often to classify objects from images that make only limited part of the image. Hence to identify local features and certain region of images, patches are extracted over the interest points detected from the original image using Wavelet based interest point detector. Here QWT magnitude and phase features are computed for every patch. Then these features are trained, tested and classified using SVM classifier in order to have supervised learning model. In order to compare the performance of local feature with global feature, the transform is applied to the entire image and the global features are derived. The performance of QWT is compared with discrete wavelet transform (DWT) and dual tree discrete wavelet transform (DTDWT). Observations revealed that QWT outperforms the DWT and shift invariant DTDWT with lesser equal error rate. The experimental evaluation is done using the complex Graz databases.Defence Science Journal, Vol. 64, No. 4, July 2014, pp. 350-357, DOI:http://dx.doi.org/10.14429/dsj.64.450
Motion Estimation and Compensation in the Redundant Wavelet Domain
Despite being the prefered approach for still-image compression for nearly a decade, wavelet-based coding for video has been slow to emerge, due primarily to the fact that the shift variance of the discrete wavelet transform hinders motion estimation and compensation crucial to modern video coders. Recently it has been recognized that a redundant, or overcomplete, wavelet transform is shift invariant and thus permits motion prediction in the wavelet domain. In this dissertation, other uses for the redundancy of overcomplete wavelet transforms in video coding are explored. First, it is demonstrated that the redundant-wavelet domain facilitates the placement of an irregular triangular mesh to video images, thereby exploiting transform redundancy to implement geometries for motion estimation and compensation more general than the traditional block structure widely employed. As the second contribution of this dissertation, a new form of multihypothesis prediction, redundant wavelet multihypothesis, is presented. This new approach to motion estimation and compensation produces motion predictions that are diverse in transform phase to increase prediction accuracy. Finally, it is demonstrated that the proposed redundant-wavelet strategies complement existing advanced video-coding techniques and produce significant performance improvements in a battery of experimental results
Image Registration Using Redundant Wavelet Transforms
Imagery is collected much faster and in significantly greater quantities today compared to a few years ago. Accurate registration of this imagery is vital for comparing the similarities and differences between multiple images. Since human analysis is tedious and error prone for large data sets, we require an automatic, efficient, robust, and accurate method to register images. Wavelet transforms have proven useful for a variety of signal and image processing tasks, including image registration. In our research, we present a fundamentally new wavelet-based registration algorithm utilizing redundant transforms and a masking process to suppress the adverse effects of noise and improve processing efficiency. The shift-invariant wavelet transform is applied in translation estimation and a new rotation-invariant polar wavelet transform is effectively utilized in rotation estimation. We demonstrate the robustness of these redundant wavelet transforms for the registration of two images (i.e., translating or rotating an input image to a reference image), but extensions to larger data sets are certainly feasible. We compare the registration accuracy of our redundant wavelet transforms to the \u27critically sampled\u27 discrete wavelet transform using the Daubechies (7,9) wavelet to illustrate the power of our algorithm in the presence of significant additive white Gaussian noise and strongly translated or rotated images
Can Region of Interest Coding Improve Overall Perceived Image Quality?
In this paper we review a number of approaches to reducing, or removing, the problem of shift variance in the discrete wavelet transform (DWT). We describe a generalization of the critically sampled DWT and the fully sampled 'algorithme a trous' that provides approximate shift-invariance with an acceptable level of redundancy. The proposed over complete DWT (OCDWT) is critically sub-sampled to a given level of the decomposition, below which it is then fully sampled. The efficacy of the proposed algorithm is illustrated in an edge detection context and directly compared to a number of other shift-invariant transforms in terms of complexity and redundancy
Pose Invariant Face Recognition Using DT-CWT Partitioning and KPCA
In this paper the suitability of Dual Tree Complex Wavelet Transform for pose invariant Face Recognition is studied and a feature extraction frame work is proposed. This proposed framework will aid in design of Face Recognition system to address the challenging issue like Pose Variation. In contrast to the discrete wavelet Transform (DWT) the design of Dual Tree Complex Wavelet Transform is rugged to shift Invariance and poses good directional properties. These features of DT-CWT motivated to study their suitability for Face Feature Extraction, as the features of face are oriented in different directions. In this proposed frame work the Image is decomposed using DT-CWT and the features are extracted from low frequency band using Kernel Principal Component analysis (KPCA). To show the performance, the proposed method is tested on ORL Database. Satisfactory results are obtained using proposed method compared to existing state of art
Stereo image matching using wavelet scale-space representation
A multi-resolution technique for matching a stereo pair of images based on translation invariant discrete multi-wavelet transform is presented. The technique uses the well known coarse to fine strategy, involving the calculation of matching points at the coarsest level with consequent refinement up to the finest level. Vector coefficients of the wavelet transform modulus are used as matching features, where modulus maxima defines the shift invariant high-level features (multiscale edges) with phase pointing to the normal of the feature surface. The technique addresses the estimation of optimal corresponding points and the corresponding 2D disparity maps. Illuminative variation that can exist between the perspective views of the same scene is controlled using scale normalization at each decomposition level by dividing the details space coefficients with approximation space and then using normalized correlation. The problem of ambiguity, explicitly, and occlusion, implicitly, is addressed by using a geometric topological refinement procedure and symbolic tagging.<br /
Discrete Wavelet Transforms
The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications
Shannon Multiresolution Analysis on the Heisenberg Group
We present a notion of frame multiresolution analysis on the Heisenberg
group, abbreviated by FMRA, and study its properties. Using the irreducible
representations of this group, we shall define a sinc-type function which is
our starting point for obtaining the scaling function. Further, we shall give a
concrete example of a wavelet FMRA on the Heisenberg group which is analogous
to the Shannon
MRA on \RR.Comment: 17 page
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