Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
A Chambolle, RA De Vore, NY Lee… - IEEE Transactions on …, 1998 - ieeexplore.ieee.org
This paper examines the relationship between wavelet-based image processing algorithms
and variational problems. Algorithms are derived as exact or approximate minimizers of …
and variational problems. Algorithms are derived as exact or approximate minimizers of …
[图书][B] A mathematical introduction to wavelets
P Wojtaszczyk - 1997 - books.google.com
This book presents a mathematical introduction to the theory of orthogonal wavelets and
their uses in analyzing functions and function spaces, both in one and in several variables …
their uses in analyzing functions and function spaces, both in one and in several variables …
Image compression through wavelet transform coding
A novel theory is introduced for analyzing image compression methods that are based on
compression of wavelet decompositions. This theory precisely relates (a) the rate of decay in …
compression of wavelet decompositions. This theory precisely relates (a) the rate of decay in …
[PDF][PDF] Fast wavelet techniques for near-optimal image processing
In recent years many authors have introduced certain nonlinear algorithms for data
compression, noise removal, and image reconstruction. These methods include wavelet and …
compression, noise removal, and image reconstruction. These methods include wavelet and …
The averaging lemma
Averaging lemmas deduce smoothness of velocity averages, such as\[\bar f (x):=\int
_\Omega f (x, v) dv,\quad\Omega\subset\mathbb {R}^ d,\] from properties of $ f $. A canonical …
_\Omega f (x, v) dv,\quad\Omega\subset\mathbb {R}^ d,\] from properties of $ f $. A canonical …
Nonlinear piecewise polynomial approximation beyond Besov spaces
B Karaivanov, P Petrushev - Applied and computational harmonic analysis, 2003 - Elsevier
We study nonlinear n-term approximation in L p (R 2)(0< p<∞) from Courant elements or
(discontinuous) piecewise polynomials generated by multilevel nested triangulations of R 2 …
(discontinuous) piecewise polynomials generated by multilevel nested triangulations of R 2 …
Approximation of smoothness classes by deep rectifier networks
We consider approximation rates of sparsely connected deep rectified linear unit (ReLU)
and rectified power unit (RePU) neural networks for functions in Besov spaces B^q(L^p) in …
and rectified power unit (RePU) neural networks for functions in Besov spaces B^q(L^p) in …
Refinable shift-invariant spaces: from splines to wavelets
RQ Jia - SERIES IN APPROXIMATIONS AND …, 1995 - World Scientific
We survey some recent results concerning refinable shiftinvariant spaces. These spaces
form a natural framework for the study of splines and wavelets. The following four topics will …
form a natural framework for the study of splines and wavelets. The following four topics will …
Characterizations of function spaces on the sphere using frames
F Dai - Transactions of the American Mathematical Society, 2007 - ams.org
In this paper we introduce a polynomial frame on the unit sphere $\mathbb {S}^{d-1} $ of
$\mathbb {R}^ d $, for which every distribution has a wavelet-type decomposition. More …
$\mathbb {R}^ d $, for which every distribution has a wavelet-type decomposition. More …
[HTML][HTML] Multivariate n-term rational and piecewise polynomial approximation
P Petrushev - Journal of Approximation Theory, 2003 - Elsevier
We study nonlinear approximation in L p (R d)(0< p<∞, d> 1) from (a) n-term rational
functions, and (b) piecewise polynomials generated by different anisotropic dyadic partitions …
functions, and (b) piecewise polynomials generated by different anisotropic dyadic partitions …