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Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. While deep learning has shown state-of-the-art AD performance, its application in critical systems is hindered…

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…

Deep unfolding networks (DUNs) combine the interpretability of model-based methods with the learning ability of deep networks, yet remain limited for blind image restoration (BIR). Existing DUNs suffer from: (1) \textbf{Degradation-specific…

Deep learning-based methods have shown remarkable success for various image restoration tasks such as denoising and deblurring. The current state-of-the-art networks are relatively deep and utilize (variants of) self attention mechanisms.…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

The training of deep residual neural networks (ResNets) with backpropagation has a memory cost that increases linearly with respect to the depth of the network. A way to circumvent this issue is to use reversible architectures. In this…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

Deep neural networks conventionally employ end-to-end backpropagation for their training process, which lacks biological credibility and triggers a locking dilemma during network parameter updates, leading to significant GPU memory use.…

Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…

Deep learning has become popular in recent years primarily due to the powerful computing device such as GPUs. However, deploying these deep models to end-user devices, smart phones, or embedded systems with limited resources is challenging.…

Deep Neural Networks (DNN) have been widely used to carry out segmentation tasks in both electron and light microscopy. Most DNNs developed for this purpose are based on some variation of the encoder-decoder type U-Net architecture, in…

Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at…

Linear recurrent neural networks, such as State Space Models (SSMs) and Linear Recurrent Units (LRUs), have recently shown state-of-the-art performance on long sequence modelling benchmarks. Despite their success, their empirical…

We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such,…

Single image reflection removal problem aims to divide a reflection-contaminated image into a transmission image and a reflection image. It is a canonical blind source separation problem and is highly ill-posed. In this paper, we present a…

This is a tutorial paper on Recurrent Neural Network (RNN), Long Short-Term Memory Network (LSTM), and their variants. We start with a dynamical system and backpropagation through time for RNN. Then, we discuss the problems of gradient…

While the depth of convolutional neural networks has attracted substantial attention in the deep learning research, the width of these networks has recently received greater interest. The width of networks, defined as the size of the…

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…

Recently, deep learning based methods appeared as a new paradigm for solving inverse problems. These methods empirically show excellent performance but lack of theoretical justification; in particular, no results on the regularization…