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Multiscale Image Segmentation using WaveletDomain Hidden Markov Models
 IEEE Trans. Image Processing
, 1999
"... We introduce a new image texture segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a treestructured probabilistic graph that captures the statistical properties of the coefficients of the wavelet transform. Since the HMT is particularly well suited ..."
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Cited by 106 (6 self)
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We introduce a new image texture segmentation algorithm, HMTseg, based on wavelets and the hidden Markov tree (HMT) model. The HMT is a treestructured probabilistic graph that captures the statistical properties of the coefficients of the wavelet transform. Since the HMT is particularly well suited to images containing singularities (edges and ridges), it provides a good classifier for distinguishing between textures. Utilizing the inherent tree structure of the wavelet HMT and its fast training and likelihood computation algorithms, we perform multiscale texture classification at a range of different scales. We then fuse these multiscale classifications using a Bayesian probabilistic graph to obtain reliable final segmentations. Since HMTseg works on the wavelet transform of the image, it can directly segment waveletcompressed images without the need for decompression into the space domain. We demonstrate the performance of HMTseg with synthetic, aerial photo, and document image seg...
The Finite Ridgelet Transform for Image Representation
 IEEE Transactions on Image Processing
, 2003
"... The ridgelet transform [6] was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we propose an orthonormal version of the ridgelet transform for discrete and finite size images. Our construction uses the finite ..."
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Cited by 103 (2 self)
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The ridgelet transform [6] was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. In this paper, we propose an orthonormal version of the ridgelet transform for discrete and finite size images. Our construction uses the finite Radon transform (FRAT) [11], [20] as a building block. To overcome the periodization effect of a finite transform, we introduce a novel ordering of the FRAT coefficients. We also analyze the FRAT as a frame operator and derive the exact frame bounds. The resulting finite ridgelet transform (FRIT) is invertible, nonredundant and computed via fast algorithms. Furthermore, this construction leads to a family of directional and orthonormal bases for images. Numerical results show that the FRIT is more effective than the wavelet transform in approximating and denoising images with straight edges.
A Tutorial on Modern Lossy Wavelet Image Compression: Foundations of JPEG 2000
, 2001
"... The JPEG committee has recently released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEG standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based o ..."
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Cited by 91 (0 self)
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The JPEG committee has recently released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEG standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based on the wavelet transform, in contrast to the discrete cosine transform (DCT) used in the original JPEG standard. The significant change in coding methods between the two standards leads one to ask: What prompted the JPEG committee to adopt such a dramatic change? The answer to this question comes from considering the state of image coding at the time the original JPEG standard was being formed. At that time wavelet analysis and wavelet coding were still
A wavelet approach to wideband spectrum sensing for cognitive radios
 in Proc. 1st Int. Conf. on Cognitive Radio Oriented Wireless Networks & Coms. (CROWNCOM), Mykonos
, 2006
"... Abstract — In cognitive radio networks, the first cognitive task preceding any form of dynamic spectrum management is the sensing and identification of spectrum holes in wireless environments. This paper develops a wavelet approach to efficient spectrum sensing of wideband channels. The signal spect ..."
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Cited by 71 (2 self)
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Abstract — In cognitive radio networks, the first cognitive task preceding any form of dynamic spectrum management is the sensing and identification of spectrum holes in wireless environments. This paper develops a wavelet approach to efficient spectrum sensing of wideband channels. The signal spectrum over a wide frequency band is decomposed into elementary building blocks of subbands that are well characterized by local irregularities in frequency. As a powerful mathematical tool for analyzing singularities and edges, the wavelet transform is employed to detect and estimate the local spectral irregular structure, which carries important information on the frequency locations and power spectral densities of the subbands. Along this line, a couple of wideband spectrum sensing techniques are developed based on the local maxima of the wavelet transform modulus and the multiscale wavelet products. The proposed sensing techniques provide an effective radio sensing architecture to identify and locate spectrum holes in the signal spectrum. I.
Time Invariant Orthonormal Wavelet Representations
"... A simple construction of an orthonormal basis starting with a so called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable ..."
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Cited by 70 (9 self)
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A simple construction of an orthonormal basis starting with a so called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. The conventional way around this problem is to use a redundant decomposition. In this paper, we address the time invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions. We show that it is possible to achieve time invariance and preserve the orthonormality. We subsequently propose an efficient approach to obtain such a decomposition. We demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation.
Multiresolution representations using the autocorrelation functions of compactly supported wavelets
 IEEE Trans. Signal Processing
, 1993
"... CT 06520 0 ..."
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Wavelets, Approximation, and Compression
, 2001
"... this article is to look at recent wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed ..."
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Cited by 67 (6 self)
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this article is to look at recent wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed
A Joint Inter and Intrascale Statistical Model for Bayesian Wavelet Based Image Denoising
 IEEE Trans. Image Proc
, 2002
"... This paper presents a new waveletbased image denoising method, which extends a recently emerged "geometrical" Bayesian framework. The new method combines these criteria for distinguishing supposedly useful coefficient from noise coefficient magnit:q54 tgni evolut47 across scales and spatA ..."
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Cited by 65 (6 self)
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This paper presents a new waveletbased image denoising method, which extends a recently emerged "geometrical" Bayesian framework. The new method combines these criteria for distinguishing supposedly useful coefficient from noise coefficient magnit:q54 tgni evolut47 across scales and spatA5 clust:q5A of large coefficients near image edges. These three crit546 are combined in a Bayesian framework. The spatD5 clust:q5] propert:5 are expressed in a prior model. Thest6[]A:q5D propertAA concerning coefficient magnit[:q andt:55 evolut4[ across scales are expressed in a joint condit:q]6 model. The three main noveltAA with respect to relat[ approaches are:(1)t he int760C7:q]0056: of wavelet coefficient are st0057:q]005 charact:q]55C and different local crit44C for dist]6:q]55C5 useful coefficient from noise are evaluat]6 (2) a joint condit:q]7 model is introduced, and (3) a novel anisot:q]7 Markov Random Field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.
Wavelet Analysis and Its Statistical Applications
, 1999
"... In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be another standard tool of the applied statistician rather than a research novelty. With that in mind, this ..."
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Cited by 61 (13 self)
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In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be another standard tool of the applied statistician rather than a research novelty. With that in mind, this article is intended to give a relatively accessible introduction to standard wavelet analysis and to provide an up to date review of some common uses of wavelet methods in statistical applications. It is primarily orientated towards the general statistical audience who may be involved in analysing data where the use of wavelets might be e ective, rather than to researchers already familiar with the eld. Given that objective, we do not emphasise mathematical generality or rigour in our exposition of wavelets and we restrict our discussion to the more frequently employed wavelet methods in statistics. We provide extensive references where the ideas and concepts discussed can be followed up in...
RegularityPreserving Image Interpolation
 IEEE Transactions on Image Processing
, 1997
"... Common image interpolation methods assume that the underlying signal is continuous and may require that it possess one or more continuous derivatives. These assumptions are not generally true of natural images, most of which have instantaneous luminance transitions at the boundaries between objects. ..."
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Cited by 59 (1 self)
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Common image interpolation methods assume that the underlying signal is continuous and may require that it possess one or more continuous derivatives. These assumptions are not generally true of natural images, most of which have instantaneous luminance transitions at the boundaries between objects. Continuity requirements on the interpolating function produce interpolated images with oversmoothed edges. To avoid this effect, a waveletbased interpolation method that imposes no continuity constraints is introduced. The algorithm estimates the regularity of edges by measuring the decay of wavelet transform coefficients across scales and attempts to preserve the underlying regularity by extrapolating a new subband to be used in image resynthesis. The algorithm produces noticeably sharper edges than traditional techniques and exhibits an average PSNR improvement of 2.5dB over bilinear and bicubic techniques. 1. INTRODUCTION Traditional image interpolation methods rely on assumptions abo...