This paper extends to two dimensions the frame criterion developed by Daubechies for one-dimensional wavelets, and it computes the frame bounds for the particular case of 2D Gabor wavelets. Completeness criteria for 2D Gabor image representations are important because of their increasing role in many computer vision applications and also in modeling biological vision, since recent neurophysiolo...

In this paper, we introduce several new schemes for calculation of discrete wavelet transforms of images. These schemes reduce the number of steps and, as a consequence, allow to reduce the number of synchronizations on parallel architectures. As an additional useful property, the proposed schemes can reduce also the number of arithmetic operations. The schemes are primarily demonstrated on CDF...

We propose the use of a new implementation of the hyperanalytic wavelet transform, (HWT), in association with a Maximum a Posteriori (MAP) filter named bishrink. The denoising methods based on wavelets are sensitive to the selection of the mother wavelets. Taking into account the drawbacks of the bishrink filter and the sensitivity with the selection of the mother wavelets we propose a denoisin...

This paper has proposed a new baseline deep learning model of more benefits for image classification. Different from the convolutional neural network(CNN) practice where filters are trained by back propagation to represent different patterns an image, we inspired method called PCANet choose filter vectors basis in frequency domain like Fourier coefficients or wavelets without propagation. Resea...

This paper proposes a novel 9/7 wavelet filter bank for texture image coding applications based on lifting a 5/3 filter to a 7/5 filter, and then to a 9/7 filter. Moreover, a one-dimensional optimization problem for the above 9/7 filter family is carried out according to the perfect reconstruction (PR) condition of wavelet transforms and wavelet properties. Finally, the optimal control paramete...

The discrete wavelet transform (DWT) is extended to functions on the discrete circle to create a fast and complete discrete periodic wavelet transform (DPWT) for bounded periodic sequences. This extension also solves the problem of non-invertibility that arises in the application of the DWT to finite-dimensional sequences and provides the proper theoretical setting for previous incomplete solut...

This paper outlines a new perceptual low bit rate audio coding scheme based on adapted wavelet representations. It claims wavelet tree and filter adaptation attending to a perceptual entropy-based method. To achieve such adaptive structure, a periodized wavelet packet transform is performed for each audio frame. After the transform, the encoder employs scalar adaptive quantization, controlled b...

In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as Riemannian manifolds or Lie groups. We rely on the strong connection between wavelets and subdivision schemes to define prediction-correction approach based operate manifold-valued data. The main result concerns decay wavelet coefficients: show our essent...

Shannon wavelets are studied together with their differential properties known as connection coefficients . It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of L2 R functions. The differential properties of Shannon wave...