Resolution of the Wavefront Set Using General Continuous Wavelet Transforms
نویسندگان
چکیده
منابع مشابه
Resolution of the Wavefront Set Using Continuous Shearlets
It is known that the Continuous Wavelet Transform of a distribution f decays rapidly near the points where f is smooth, while it decays slowly near the irregular points. This property allows the identification of the singular support of f . However, the Continuous Wavelet Transform is unable to describe the geometry of the set of singularities of f and, in particular, identify the wavefront set...
متن کاملContinuous Curvelet Transform: I. Resolution of the Wavefront Set
We discuss a Continuous Curvelet Transform (CCT), a transform f → Γf (a, b, θ) of functions f(x1, x2) on R , into a transform domain with continuous scale a > 0, location b ∈ R, and orientation θ ∈ [0, 2π). The transform is defined by Γf (a, b, θ) = 〈f, γabθ〉 where the inner products project f onto analyzing elements called curvelets γabθ which are smooth and of rapid decay away from an a by √ ...
متن کاملContinuous Shearlet Frames and Resolution of the Wavefront Set
In recent years directional multiscale transformations like the curveletor shearlet transformation have gained considerable attention. The reason for this is that these transforms are unlike more traditional transforms like wavelets able to efficiently handle data with features along edges. The main result confirming this property for shearlets is contained in [21] where it is shown that for ve...
متن کاملContinuous and Discrete Wavelet Transforms
Rob A. Zuidwijk CWI E-mail: [email protected] Url: http://www.cwi.nl/cwi/projects/wavelets.html November 6, 1997 Abstract In this lecture, the continuous wavelet transform will be discussed and some attention will be given to the discrete wavelet transform. Finally, wavelet transforms on multidimensional data will be considered. The set-up of the lecture is as follows: 1. The continuous wavelet t...
متن کاملContinuous and Discrete Wavelet Transforms
This paper is an expository survey of results on integral representations and discrete sum expansions of functions in L(R) in terms of coherent states. Two types of coherent states are considered: Weyl–Heisenberg coherent states, which arise from translations and modulations of a single function, and affine coherent states, called “wavelets,” which arise as translations and dilations of a singl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2015
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-015-9445-7