Candes, E. J. (1999). Harmonic analysis of neural networks. Appl. Comput. Harmon. Anal. 6 197-218. Home/Search Document Details and Download
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A Regression Estimation Method Based on Wavelet Frames - Soltani, Canu, Boichu (Correct)
....a frame is a set of complete and non independant functions. The coefficients w i are given by: w i = hf; i i. The set of functions f i (x)g constitutes a dual frame. This latter can be defined in different ways 3 , this means that the decomposition is not unique (see [You80] Dau92] [Can96] for more details) In general we prefer the most economical one 4 . The choice of the wavelets is guided by their ability to analyze functions locally and at different scales. This is due to their spatio frequential localization. To perform the analysis, different dilato translates of the ....
....different scales. This is due to their spatio frequential localization. To perform the analysis, different dilato translates of the wavelet are used. In the context of multidimensional wavelet theory, there exists two ways to define frames: ffl projective frames: the wavelets (called ridgelets in [Can96]) are defined as follows: i (x) a k=2 0 (a k 0 hu l k xi Gamma mt 0 ) 8) Where a 0 1, t 0 2 Rare called elementary dilatation and translation. Vectors u l k are directive unitary vectors, they belong to the unitary sphere of R d , k is the elementary (d Gamma 1) tuple ....
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Emmanuel J. Cand`es. Harmonic analysis of neural networks. Technical report, Department of Statistics, University of Stanford, December 1996.
Monoscale Ridgelets for the Representation of Images with Edges - Candès (1999) Self-citation (Cand) (Correct)
....Ridgelets for the Representation of Images with Edges Emmanuel J. Cand es Department of Statistics Stanford University Stanford, California 94305 4065 In a previous paper [1], the author introduced a new system for representing multivariate functions, namely, the ridgelets. In a following article [3] ridgelets were shown to be optimal for representing functions that are smooth away from hyperplanes, e.g. in two dimensions ridgelets provide optimally sparse ....
....with edges eciently has a statistical corollary : these methods do not remove noise from images with edges eciently. For instance, a thresholding estimator in a nice wavelet basis does not provide good estimation bounds. A more quantitative discussion is provided in section 5. 1. 2 Ridgelets In [1], the author introduced a new discretization of the frequency plane that led to the construction of ridgelet frames. We will brie y explain the ridgelet construction in two dimensions. Suppose that we have a univariate function satisfying an oscillatory condition, namely, Z j ( j 2 ....
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E. J. Candes, Harmonic analysis of neural networks, Appl. Comput. Harmon. Anal., 6, 197-218, 1999.
Recovering Edges in Ill-Posed Inverse Problems: Optimality of .. - Candes, Donoho (2000) (1 citation) Self-citation (Es) (Correct)
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Candes, E. (1999). Harmonic analysis of neural networks. Appl. Comput. Harmon. Anal. 6 197-218.
Curvelets and Curvilinear Integrals - Candes, Donoho (2000) (4 citations) (Correct)
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Candes, E. J. (1999). Harmonic analysis of neural networks. Appl. Comput. Harmon. Anal. 6 197-218.
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