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The focus of this paper is the application of classical model order reduction techniques, such as Active Subspaces and Proper Orthogonal Decomposition, to Deep Neural Networks. We propose a generic methodology to reduce the number of layers…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties…

Recent works show that reducing the number of layers in a convolutional neural network can enhance efficiency while maintaining the performance of the network. Existing depth compression methods remove redundant non-linear activation…

Deep convolutional neural networks have proven to be well suited for image classification applications. However, if there is distortion in the image, the classification accuracy can be significantly degraded, even with state-of-the-art…

In contrast to the somewhat abstract, group theoretical approach adopted by many papers, our work provides a new and more intuitive derivation of steerable convolutional neural networks in $d$ dimensions. This derivation is based on…

Convolutional neural networks necessitate good algorithms to reduce complexity, and sufficient utilization of parallel processors for acceleration. Within convolutional layers, there are three types of operators: convolution used in forward…

The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper…

Convolutional Neural Networks have revolutionized vision applications. There are image domains and representations, however, that cannot be handled by standard CNNs (e.g., spherical images, superpixels). Such data are usually processed…

Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…

Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…

While most deep learning architectures are built on convolution, alternative foundations like morphology are being explored for purposes like interpretability and its connection to the analysis and processing of geometric structures. The…

Many studies have been conducted so far on image restoration, the problem of restoring a clean image from its distorted version. There are many different types of distortion which affect image quality. Previous studies have focused on…

Shape compactness is a key geometrical property to describe interesting regions in many image segmentation tasks. In this paper, we propose two novel algorithms to solve the introduced image segmentation problem that incorporates a…

Low-dose CT denoising is a challenging task that has been studied by many researchers. Some studies have used deep neural networks to improve the quality of low-dose CT images and achieved fruitful results. In this paper, we propose a deep…

Regularization in convolutional neural networks (CNNs) is usually addressed with dropout layers. However, dropout is sometimes detrimental in the convolutional part of a CNN as it simply sets to zero a percentage of pixels in the feature…

Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heuristic, and the…

Non-Hermitian topological phases can produce some remarkable properties, compared with their Hermitian counterpart, such as the breakdown of conventional bulk-boundary correspondence and the non-Hermitian topological edge mode. Here, we…