Approximation and compression of piecewise smooth functions
نویسندگان
چکیده
منابع مشابه
Approximation and Compression of Piecewise Smooth Functions
Wavelet or subband coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate-distortion bounds for wavelet approximation of piecewise smooth functions, in particular the piecewise polynomial case. We contrast these results with rate-distortion bounds achievable using a...
متن کاملOn the compression of two-dimensional piecewise smooth functions
It is well known that wavelets provide good non-linear approximation of one-dimensional (1-D) piecewise smooth functions. However, it has been shown that the use of a basis with good approximation properties does not necessarily lead to a good compression algorithm. The situation in 2-D is much more complicated since wavelets are not good for modeling piecewise smooth signals (where discontinui...
متن کاملApproximating Piecewise-Smooth Functions
We consider the possibility of using locally supported quasi-interpolation operators for the approximation of univariate non-smooth functions. In such a case one usually expects the rate of approximation to be lower than that of smooth functions. It is shown in this paper that prior knowledge of the type of ’singularity’ of the function can be used to regain the full approximation power of the ...
متن کاملPiecewise-smooth Refinable Functions
Univariate piecewise-smooth refinable functions (i.e., compactly supported solutions of the equation φ( 2 ) = ∑N k=0 ckφ(x−k)) are classified completely. Characterization of the structure of refinable splines leads to a simple convergence criterion for the subdivision schemes corresponding to such splines, and to explicit computation of the rate of convergence. This makes it possible to prove a...
متن کاملApproximation and Compression ofPiecewise Smooth
Wavelet or subband coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate-distortion bounds for wavelet approximation of piecewise smooth functions, in particular the piecewise polynomial case. We contrast these results with rate-distortion bounds achievable using a...
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: Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
سال: 1999
ISSN: 1364-503X,1471-2962
DOI: 10.1098/rsta.1999.0449