2 Fast Wavelet Transform The 2D fast wavelet transform can be represented as a convolution of the image with one-dimensional low-pass h(n) and high-pass g(n) filters (see Figure 1). This procedure results in subband images which provide the global context as well as image details at horizontal, vertical and diagonal directions. Therefore, this tool is suitable for representing numerical charact...

Aiming at the fault diagnosis of rolling element bearings, propose a method for fine bearings based on wavelet transform and one-dimensional convolutional neural network. First use to decompose experimental data; Use resulting low-frequency signal as network input, bearing identification. The experiment uses deep groove ball Case Western Reserve University research object, this identify normal ...

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...

We present an algorithm that compresses two-dimensional data arrays, which are piece-wise smooth in one direction and have oscillating events in the other direction. Seismic, hyper-spectral and fingerprints data have this mixed structure. The transform part of the compression process is an algorithm that combines wavelet and the local cosine transform (LCT) also called an hybrid transform. The ...

In view of the images polluted by mixed noise in actual image processing, in this paper, the hybrid filter algorithm combined by median filtering and wavelet transform is generalized to two-dimensional fractional wavelet domain, verified the effectiveness and advantages of hybrid filtering algorithm combined by median filtering and two-dimensional fractional wavelet transform. And put forward a...

We present a two-dimensional wavelet transform that is invariant to affine distortions of the input signal. Affine distortions include geometric effects such as translation, reflection, uniform and anisotropic scaling, rotation, and shearing of the input signal. Invariance of the wavelet transform to affine distortions is achieved in our work by developing an algorithm that reduces replicas of ...

Many procedures have been developed to characterize a signal by some of the salient features of a speciic transform, whether it is the Fourier, the Gabor, the Wigner or more recently the wavelet transform. Ridges in the modulus of the transform determine regions in the transform domain with a high concentration of energy. For this reason they are regarded as natural candidates for the character...

The Riesz transform is a natural multi-dimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been used to construct complex wavelets and steerable wavelet frames in higher dimensions. The flip side of this approach, however, is that the Riesz transform o...

In order to improve the rate of facial expression recognition. The Gabor wavelet fusion PCA+FLD method is proposed as a new method this paper. Firstly, face image preprocessing, and then carries on the two-dimensional wavelet transform Gabor, first constructed five scale eight directional wavelet filter, through the PCA+FLD method for dimensionality reduction, and finally obtaining an optimum e...