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1
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Image Compression with Schauder Bases

100%
Ciesielski Z.
Applicationes Mathematicae
|
2001
|
tom 28
|
nr 4
367-390
EN
As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information. For, each of the two bases we present in detail the algorithms for, calculating the basis coefficients and conversely, for, recovering the functions from the coefficients. Next, we use the, fact that both the bases are greedy in suitable Besov norms and, apply thresholding to compress the information carried by the, coefficients. After this operation on the basis coefficients the, corresponding approximation of the image can be obtained. The, principles of these algorithms are known (see e.g. [3]) but the, details seem to be new. Moreover, our philosophy of applying, approximation theory is different. The principal assumption is, that the input data come from some images. Approximation theory, mainly the isomorphisms between Besov function spaces and, suitable sequence spaces given by the Haar and diamond bases, (see [1], [2]), and the greediness of these bases, are used only, to choose a proper norm in the space of images. The norm is, always finite and it is used for thresholding only.
2
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Polynomial and spline estimators of the distribution function with prescribed accuracy

64%
Ciesielski Z., Zieliński R.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 1
1-12
EN
Dvoretzky-Kiefer-Wolfowitz type inequalities for some polynomial and spline estimators of distribution functions are constructed. Moreover, hints on the corresponding algorithms are given as well.
3
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Some remarks on the convergence of functionals on bases

45%
Orlicz W., Ciesielski Z.
Studia Mathematica
|
1957-1958
|
tom 16
|
nr 3
335-352
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Some analytic aspects of probabilistic potential theory

45%
Ciesielski Z., Kac M.
Applicationes Mathematicae
|
1969
|
tom 10
|
nr 1
75-83
5
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Preface, Contents

32%
Ciesielski Z.
Banach Center Publications
|
1989
|
tom 22
|
nr 1
1-8
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