Related papers: 2D Empirical Transforms. Wavelets, Ridgelets and C…

Time series modeling has attracted extensive research efforts; however, achieving both reliable efficiency and interpretability from a unified model still remains a challenging problem. Among the literature, shapelets offer interpretable…

Certain signal classes such as audio signals call for signal representations with the ability to adapt to the signal's properties. In this article we introduce the new concept of quilted frames, which aim at adaptivity in time-frequency…

The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…

In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture…

Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…

This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…

Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…

We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…

Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales…

Shapelets are phase independent subsequences designed for time series classification. We propose three adaptations to the Shapelet Transform (ST) to capture multivariate features in multivariate time series classification. We create a…

We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the…

In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…

Manipulating elastic waves using a transformation approach is challenging due to the complex constitutive relationship. However, for flexural waves, approximated as scalar waves, two straightforward approaches emerge based on geometric…

Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…

Graph Signal Processing generalizes classical signal processing to signal or data indexed by the vertices of a weighted graph. So far, the research efforts have been focused on static graph signals. However numerous applications involve…

In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…

Modern data analytics take advantage of ensemble learning and transfer learning approaches to tackle some of the most relevant issues in data analysis, such as lack of labeled data to use to train the analysis models, sparsity of the…

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…

We propose the multiview wavelets based on voxel patterns of autostereoscopic multiview displays. Direct and inverse continuous wavelet transforms of binary and gray-scale images were performed. The input to the inverse wavelet transform…