Related papers: Redundant Wavelets on Graphs and High Dimensional …

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…

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 describe a new wavelet transform, for use on hierarchies or binary rooted trees. The theoretical framework of this approach to data analysis is described. Case studies are used to further exemplify this approach. A first set of…

In deep networks, the lost data details significantly degrade the performances of image segmentation. In this paper, we propose to apply Discrete Wavelet Transform (DWT) to extract the data details during feature map down-sampling, and…

Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image in the transform domain, using a set of scalar…

In this paper, we propose a new two-dimensional directional discrete wavelet transform that can decompose an image into 12 multiscale directional edge components. The proposed transform is designed in a fully discrete setting and thus is…

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…

To reduce cost in storing, processing and visualizing a large-scale point cloud, we consider a randomized resampling strategy to select a representative subset of points while preserving application-dependent features. The proposed strategy…

Today, image denoising by thresholding of wavelet coefficients is a commonly used tool for 2D image enhancement. Since the data product of spectroscopic imaging surveys has two spatial and one spectral dimension, the techniques for…

Graph filters and their inverses have been widely used in denoising, smoothing, sampling, interpolating and learning. Implementation of an inverse filtering procedure on spatially distributed networks (SDNs) is a remarkable challenge, as…

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…

Wavelets are well known for data compression, yet have rarely been applied to the compression of neural networks. This paper shows how the fast wavelet transform can be used to compress linear layers in neural networks. Linear layers still…

The tradeoff between receptive field size and efficiency is a crucial issue in low level vision. Plain convolutional networks (CNNs) generally enlarge the receptive field at the expense of computational cost. Recently, dilated filtering has…

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass…

In this paper, we propose two contributions to neural network based denoising. First, we propose applying separate convolutional layers to each sub-band of discrete wavelet transform (DWT) as opposed to the common usage of DWT which…

In this paper, we consider an inverse problem in graph learning domain -- ``given the graph representations smoothed by Graph Convolutional Network (GCN), how can we reconstruct the input graph signal?" We propose Graph Deconvolutional…

Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms (e.g., graph Fourier or…

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…

Deep convolutional neural networks (CNNs) are used for image denoising via automatically mining accurate structure information. However, most of existing CNNs depend on enlarging depth of designed networks to obtain better denoising…

A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…