Results 11  20
of
74
Fresnelets: new multiresolution wavelet bases for digital holography
 IEEE Trans. Image Process
, 2003
"... Abstract—We propose a construction of new waveletlike bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCDarrays. The starting point is a wavelet basis of P to which we apply a unitary Fresnel transform. The transformed basis fun ..."
Abstract

Cited by 38 (7 self)
 Add to MetaCart
(Show Context)
Abstract—We propose a construction of new waveletlike bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCDarrays. The starting point is a wavelet basis of P to which we apply a unitary Fresnel transform. The transformed basis functions are shiftinvariant on a levelbylevel basis but their multiresolution properties are governed by the special form that the dilation operator takes in the Fresnel domain. We derive a Heisenberglike uncertainty relation that relates the localization of Fresnelets with that of their associated wavelet basis. According to this criterion, the optimal functions for digital hologram processing turn out to be Gabor functions, bringing together two separate aspects of the holography inventor’s work. We give the explicit expression of orthogonal and semiorthogonal Fresnelet bases corresponding to polynomial spline wavelets. This special choice of Fresnelets is motivated by their nearoptimal localization properties and their approximation characteristics. We then present an efficient multiresolution Fresnel transform algorithm, the Fresnelet transform. This algorithm allows for the reconstruction (backpropagation) of complex scalar waves at several userdefined, wavelengthindependent resolutions. Furthermore, when reconstructing numerical holograms, the subband decomposition of the Fresnelet transform naturally separates the image to reconstruct from the unwanted zeroorder and twin image terms. This greatly facilitates their suppression. We show results of experiments carried out on both synthetic (simulated) data sets as well as on digitally acquired holograms. Index Terms—Bsplines, digital holography, Fresnel transform, Fresnelet transform, Fresnelets, wavelets.
Statistical analysis of functional MRI data in the wavelet domain
 IEEE Transactions on Medical Imaging
, 1998
"... Abstract — The use of the wavelet transform is explored for the detection of differences between brain functional magnetic resonance images (fMRI’s) acquired under two different experimental conditions. The method benefits from the fact that a smooth and spatially localized signal can be represented ..."
Abstract

Cited by 30 (5 self)
 Add to MetaCart
(Show Context)
Abstract — The use of the wavelet transform is explored for the detection of differences between brain functional magnetic resonance images (fMRI’s) acquired under two different experimental conditions. The method benefits from the fact that a smooth and spatially localized signal can be represented by a small set of localized wavelet coefficients, while the power of white noise is uniformly spread throughout the wavelet space. Hence, a statistical procedure is developed that uses the imposed decomposition orthogonality to locate waveletspace partitions with large signaltonoise ratio (SNR), and subsequently restricts the testing for significant wavelet coefficients to these partitions. This results in a higher SNR and a smaller number of statistical tests, yielding a lower detection threshold compared to spatialdomain testing and, thus, a higher detection sensitivity without increasing type I errors. The multiresolution approach of the wavelet method is particularly suited to applications where the signal bandwidth and/or the characteristics of an imaging modality cannot be well specified. The proposed method was applied to compare two different fMRI acquisition modalities. Differences of the respective useful signal bandwidths could be clearly demonstrated; the estimated signal, due to the smoothness of the wavelet representation, yielded more compact regions of neuroactivity than standard spatialdomain testing. Index Terms — Functional magnetic resonance imaging, multiresolution analysis, statistical models, wavelet transform. I.
Scalespace derived from Bsplines
 IEEE Trans. Pattern Anal. Machine Intell
, 1998
"... Abstract—It is wellknown that the linear scalespace theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scalespace theory based on Bspline kernels. Our aim is twofold. On one hand, we present a general framework and show how Bsplines provid ..."
Abstract

Cited by 27 (7 self)
 Add to MetaCart
(Show Context)
Abstract—It is wellknown that the linear scalespace theory in computer vision is mainly based on the Gaussian kernel. The purpose of the paper is to propose a scalespace theory based on Bspline kernels. Our aim is twofold. On one hand, we present a general framework and show how Bsplines provide a flexible tool to design various scalespace representations: continuous scalespace, dyadic scalespace frame, and compact scalespace representation. In particular, we focus on the design of continuous scalespace and dyadic scalespace frame representation. A general algorithm is presented for fast implementation of continuous scalespace at rational scales. In the dyadic case, efficient frame algorithms are derived using Bspline techniques to analyze the geometry of an image. Moreover, the image can be synthesized from its multiscale local partial derivatives. Also, the relationship between several scalespace approaches is explored. In particular, the evolution of wavelet theory from traditional scalespace filtering can be well understood in terms of Bsplines. On the other hand, the behavior of edge models, the properties of completeness, causality, and other properties in such a scalespace representation are examined in the framework of Bsplines. It is shown that, besides the good properties inherited from the Gaussian kernel, the Bspline derived scalespace exhibits many advantages for modeling visual mechanism with regard to the efficiency, compactness, orientation feature, and parallel structure. Index Terms—Image modeling, Bspline, wavelet, scalespace, scaling theorem, fingerprint theorem.
Wavelet Correlation Signatures for Color Texture Characterization
 Pattern Recognition
, 1999
"... In the last decade, multiscale techniques for graylevel texture analysis have been intensively used. In this paper, we aim on extending these techniques to color images. Weintroduce wavelet energycorrelation signatures and we derive the transformation of these signatures upon linear color space tr ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
(Show Context)
In the last decade, multiscale techniques for graylevel texture analysis have been intensively used. In this paper, we aim on extending these techniques to color images. Weintroduce wavelet energycorrelation signatures and we derive the transformation of these signatures upon linear color space transformations. Experiments are conducted on a set of 30 natural colored texture images in which color and graylevel texture classi#cation performances are compared. It is demonstrated that the wavelet correlation features contain more information than the intensity or the energy features of each color plane separately. The in#uence of image representation in color space is evaluated. Key words: texture analysis, classi#cation, color spaces, feature extraction, wavelet signatures 1 Introduction For image analysis, color and texture are two of the most important properties, especially when one is dealing with real world images. Classical image analysis schemes only takeinto account the pix...
LeastSquares Image Resizing Using Finite Differences
, 2001
"... We present an optimal splinebased algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projectionbased approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions t ..."
Abstract

Cited by 24 (2 self)
 Add to MetaCart
We present an optimal splinebased algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projectionbased approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are Bsplines of any degree . A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor . For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signaltonoise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of Bsplines and their derivatives.
Ten Good Reasons For Using Spline Wavelets
 Proc. SPIE vol. 3169, Wavelet Applications in Signal and Image Processing V
, 1997
"... The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (BattleLemari), semiorthogonal (e.g., Bspline), shiftorthogonal, and biorthogonal (CohenDaubechiesFeauveau) . Unlike most other wavelet bases ..."
Abstract

Cited by 23 (5 self)
 Add to MetaCart
(Show Context)
The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (BattleLemari), semiorthogonal (e.g., Bspline), shiftorthogonal, and biorthogonal (CohenDaubechiesFeauveau) . Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates their manipulation. They allow for a progressive transition between the two extreme cases of a multiresolution: Haar's piecewise constant representation (spline of degree zero) versus Shannon's bandlimited model (which corresponds to a spline of infinite order). Spline wavelets are extremely regular and usually symmetric or antisymmetric. They can be designed to have compact support and to achieve optimal timefrequency localization (Bspline wavelets). The underlying scaling functions are the Bsplines, which are the shortest and most regular scaling functions of order L. Finally, splines have the best approximation properties among all known wavelets of a given order L. In other words, they are the best for approximating smooth functions.
Wavelets, Fractals, and Radial Basis Functions
 IEEE TRANS. SIGNAL PROCESSING
, 2002
"... Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that t ..."
Abstract

Cited by 20 (6 self)
 Add to MetaCart
(Show Context)
Wavelets and radial basis functions (RBFs) lead to two distinct ways of representing signals in terms of shifted basis functions. RBFs, unlike wavelets, are nonlocal and do not involve any scaling, which makes them applicable to nonuniform grids. Despite these fundamental differences, we show that the two types of representation are closely linked together ... through fractals. First, we identify and characterize the whole class of selfsimilar radial basis functions that can be localized to yield conventional multiresolution wavelet bases. Conversely, we prove that for any compactly supported scaling function 9(0c), there exists a onesided central basis function p+ (x) that spans the same multireso lution subspaces. The central property is that the multiresolution bases are generated by simple translation of p+ without any dilation. We also present an explicit timedomain representation of a scaling function as a sum of harmonic splines. The leading term in the decomposition corresponds to the fractional splines: a recent, continuousorder generalization of the polynomial splines.
Zheludev Construction of biorthogonal discrete wavelet transforms using interpolatory splines
"... We present a new family of biorthogonal wavelet and wavelet packet transforms for discrete periodic signals and a related library of biorthogonal periodic symmetric waveforms. The construction is based on the superconvergence property of the interpolatory polynomial splines of even degrees. The cons ..."
Abstract

Cited by 17 (15 self)
 Add to MetaCart
(Show Context)
We present a new family of biorthogonal wavelet and wavelet packet transforms for discrete periodic signals and a related library of biorthogonal periodic symmetric waveforms. The construction is based on the superconvergence property of the interpolatory polynomial splines of even degrees. The construction of the transforms is performed in a “lifting ” manner that allows more efficient implementation and provides tools for custom design of the filters and wavelets. As is common in lifting schemes, the computations can be carried out “in place ” and the inverse transform is performed in a reverse order. The difference with the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform. Our algorithm allows a stable construction of filters with many vanishing moments. The computational complexity of the algorithm is comparable with the complexity of the standard wavelet transform. Our scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. In addition, these filters yield perfect frequency resolution. © 2002 Elsevier Science 1.
Visualization of multidimensional shape and texture features in laser range data using complex valued Gabor wavelets
 Proc. of SPIE Vol. 5559 411 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 02/19/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx
, 1995
"... ..."