Search results for "Vanishing moments"
showing 5 items of 5 documents
Sparse Image Representation by Directionlets
2010
Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertical directions. One-dimensional discontinuities in images (edges or contours), which are important elements in visual perception, intersect too many wavelet basis functions and lead to a non-sparse representation. To capture efficiently these elongated structures characterized by geometrical regularity along different directions (not only the horizontal and vertical), a more complex multidirectional (M-DIR) and asymmetric transform is requi…
Periodic Orthogonal Wavelets and Wavelet Packets
2018
In this chapter, we discuss how to derive versatile families of periodic discrete-time orthogonal wavelets and wavelet packets from discrete and discrete-time splines outlined in Chap. 3. These wavelets and wavelet packets, although not having compact supports, are well localized in the time domain. They can have any number of discrete vanishing moments. Their DFT spectra tend to have a rectangular shape when the spline order grows and provide a collection of refined splits of the Nyquist frequency band. The wavelet and wavelet packet transforms are implemented in a fast way using the FFT.
Directionlets: Anisotropic Multidirectional representation with separable filtering
2006
In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based pe…
Space-Frequency Quantization for Image Compression With Directionlets
2007
The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critic…
Local cubic splines on non-uniform grids and real-time computation of wavelet transform
2017
In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are designed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, the splines use either clean or noised arbitrarily-spaced samples. Formulas for the spline’s extrapolation beyond the sampling interval are established. Sharp estimations of the approximation errors are presented. The capability to adapt the grid to the structure of an object and to have minimal requirements to the operating memory are of great advantages for offline processing of s…