Related papers: Digital Shearlet Transforms
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…
Spatial and spectral approaches are two major approaches for image processing tasks such as image classification and object recognition. Among many such algorithms, convolutional neural networks (CNNs) have recently achieved significant…
Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discontinuities such as edges and corners at multiple scales. In this work we address the problem of…
Recently, continuous representation methods emerge as novel paradigms that characterize the intrinsic structures of real-world data through function representations that map positional coordinates to their corresponding values in the…
Image deblurring is a classical computer vision problem that aims to recover a sharp image from a blurred image. To solve this problem, existing methods apply the Encode-Decode architecture to design the complex networks to make a good…
We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case,…
Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed…
Quantum Machine Learning (QML) has emerged as a promising framework for exploring how quantum dynamics may enhance data processing tasks. Here we investigate Quantum Extreme Learning Machines (QELMs), a quantum analogue of classical Extreme…
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…
In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
Machine learning problems involving sparse datasets may benefit from the use of convolutional neural networks if the numbers of samples and features are very large. Such datasets are increasingly more frequently encountered in a variety of…
The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data…
This paper builds on recent developments of adaptive methods for linear transport equations based on certain stable variational formulations of Petrov-Galerkin type. The variational formulations allow us to employ meshes with cells of…
The shape of liquid droplets in air plays an important role in aerodynamic behavior and combustion dynamics of miniaturized propulsion systems such as microsatellites and small drones. Their precise manipulation can yield optimal efficiency…
As the availability of imagery data continues to swell, so do the demands on transmission, storage and processing power. Processing requirements to handle this plethora of data is quickly outpacing the utility of conventional processing…
We present a wavelet-based dual-stream network that addresses color cast and blurry details in underwater images. We handle these artifacts separately by decomposing an input image into multiple frequency bands using discrete wavelet…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
Scattering Transforms (or ScatterNets) introduced by Mallat are a promising start into creating a well-defined feature extractor to use for pattern recognition and image classification tasks. They are of particular interest due to their…