A Library-based Approach to Design of Smooth Orthonormal Wavelets
نویسندگان
چکیده
Recently we addressed the question of using comprehensive libraries of smooth orthonormal wavelets for signalbased wavelet design. Here we present the details of the algorithm for assembling a wavelet library from the continuum of compactly-supported orthonormal wavelets. The algorithm is based on a multi-level minimization, with local variation serving as the smoothness measure and the discrete inner product as the measure used to discriminate between wavelet shapes. An example library is provided.
منابع مشابه
Smooth orthonormal wavelet libraries: design and application
For signal-based design of orthonormal (ON) wavelets, an optimization of a cost function over an N -dimensional angle space is required. However: (1) the N -dim space includes both smooth and non-smooth wavelets; (2) many of the smooth wavelets are similar in shape. A more practical approach for some applications may be to construct a library of smooth ON wavelets in advance—a library that cons...
متن کاملSmooth Wavelet Tight Frames with Zero Moments
This paper considers the design of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. In particular, this paper takes up the design of systems that are analogous to Daubechies orthonormal wavelets—that is, the design of mi...
متن کاملOn Cosine - Modulated Wavelet Orthonormal
Recently multiplicity M, K-regular, orthonormal wavelet bases (that have implications in transform coding applications) have been constructed by several authors 1, 2, 3]. This paper describes and parameterizes the cosine-modulated class of multiplicity M wavelet tight frames (WTFs). In these WTFs (like in the general multiplicity 2 case in 4]), the scaling function uniquely determines the wavel...
متن کاملGeneral Existence Theorems for Orthonormal Wavelets
Methods from noncommutative harmonic analysis are used to develop an abstract theory of orthonormal wavelets. The relationship between the existence of an orthonormal wavelet and the existence of a multi-resolution is clariied, and four theorems guaranteeing the existence of wavelets are proved. As a special case of the fourth theorem, a generalization of known results on the existence of smoot...
متن کاملAlgorithms for designing wavelets to match a specified signal
Algorithms for designing a mother wavelet ( ) such that it matches a signal of interest and such that the family of wavelets 2 ( 2) (2 ) forms an orthonormal Riesz basis of ( ) are developed. The algorithms are based on a closed form solution for finding the scaling function spectrum from the wavelet spectrum. Many applications of signal representation, adaptive coding and pattern recognition r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998