Related papers: An analytic theory of convolutional neural network…

This thesis studies how the segmentation results, produced by convolutional neural networks (CNN), is different from each other when applied to small biomedical datasets. We use different architectures, parameters and hyper-parameters,…

Pan-sharpening is a fundamental and significant task in the field of remote sensing imagery processing, in which high-resolution spatial details from panchromatic images are employed to enhance the spatial resolution of multi-spectral (MS)…

An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how…

Convolution Neural Networks (CNNs) are widely used in medical image analysis, but their performance degrade when the magnification of testing images differ from the training images. The inability of CNNs to generalize across magnification…

Downsampling operators break the shift invariance of convolutional neural networks (CNNs) and this affects the robustness of features learned by CNNs when dealing with even small pixel-level shift. Through a large-scale correlation analysis…

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural…

We address the problem of semantic correspondence, that is, establishing a dense flow field between images depicting different instances of the same object or scene category. We propose to use images annotated with binary foreground masks…

The inverse problem of electrical resistivity surveys (ERSs) is difficult because of its nonlinear and ill-posed nature. For this task, traditional linear inversion methods still face challenges such as suboptimal approximation and initial…

Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult…

Convolutional Neural Networks (CNNs) filter the input data using spatial convolution operators with compact stencils. Commonly, the convolution operators couple features from all channels, which leads to immense computational cost in the…

Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this encounter, in this study, we assume it is unknown how to solve the imaging problem of Computed…

We study approximation and learning capacities of convolutional neural networks (CNNs) with one-side zero-padding and multiple channels. Our first result proves a new approximation bound for CNNs with certain constraint on the weights. Our…

We developed a convolution neural network (CNN) on semi-regular triangulated meshes whose vertices have 6 neighbours. The key blocks of the proposed CNN, including convolution and down-sampling, are directly defined in a vertex domain. By…

Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…

Recent studies demonstrated the eligibility of convolutional neural networks (CNNs) for solving the image registration problem. CNNs enable faster transformation estimation and greater generalization capability needed for better support…

Convolutional Neural Networks (CNN) have been pivotal to the success of many state-of-the-art classification problems, in a wide variety of domains (for e.g. vision, speech, graphs and medical imaging). A commonality within those domains is…

Recent advancements in Graph Neural Networks (GNNs) have spurred an upsurge of research dedicated to enhancing the explainability of GNNs, particularly in critical domains such as medicine. A promising approach is the self-explaining…

Multivariate time series forecasting is an important yet challenging problem in machine learning. Most existing approaches only forecast the series value of one future moment, ignoring the interactions between predictions of future moments…

In this paper, we provide a theoretical analysis of the inductive biases in convolutional neural networks (CNNs). We start by examining the universality of CNNs, i.e., the ability to approximate any continuous functions. We prove that a…

Inspired by the success of Convolutional Neural Networks (CNNs) for supervised prediction in images, we design the Deconvolutional Generative Model (DGM), a new probabilistic generative model whose inference calculations correspond to those…