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Patient scans from MRI often suffer from noise, which hampers the diagnostic capability of such images. As a method to mitigate such artifact, denoising is largely studied both within the medical imaging community and beyond the community…

In this article, we show existence of minimizers in the loss landscape for residual artificial neural networks (ANNs) with multi-dimensional input layer and one hidden layer with ReLU activation. Our work contrasts earlier results in [D.…

This work investigates use of equivariant neural networks as efficient and high-performance frameworks for image reconstruction and denoising in nuclear medicine. Our work aims to tackle limitations of conventional Convolutional Neural…

Ultra-low-field (ULF, <0.1 T) magnetic resonance imaging (MRI) systems offer advantages in cost, portability, and accessibility, but their current utility is still limited by low signal-to-noise ratio (SNR). Deep learning (DL)-based…

Recent studies on learning-based image denoising have achieved promising performance on various noise reduction tasks. Most of these deep denoisers are trained either under the supervision of clean references, or unsupervised on synthetic…

Recently, denoising methods based on supervised learning have exhibited promising performance. However, their reliance on external datasets containing noisy-clean image pairs restricts their applicability. To address this limitation,…

Visual illusions teach us that what we see is not always what it is represented in the physical world. Its special nature make them a fascinating tool to test and validate any new vision model proposed. In general, current vision models are…

We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…

Denoising has to do with estimating a signal $x_0$ from its noisy observations $y=x_0+z$. In this paper, we focus on the "structured denoising problem", where the signal $x_0$ possesses a certain structure and $z$ has independent normally…

Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…

Networks are widely used in many fields for their powerful ability to provide vivid representations of relationships between variables. However, many of them may be corrupted by experimental noise or inappropriate network inference methods…

Learning image representations that capture rich semantic relationships remains a significant challenge. Existing approaches are either contrastive, lacking robust theoretical guarantees, or struggle to effectively represent the partial…

Neural networks are popular and useful in many fields, but they have the problem of giving high confidence responses for examples that are away from the training data. This makes the neural networks very confident in their prediction while…

Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…

Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…

Deep Neural Networks have shown great promise on a variety of downstream applications; but their ability to adapt and generalize to new data and tasks remains a challenge. However, the ability to perform few or zero-shot adaptation to novel…

Deep neural networks represent the gold standard for image classification. However, they usually need large amounts of data to reach superior performance. In this work, we focus on image classification problems with a few labeled examples…

All techniques for denoising involve a notion of a true (noise-free) image, and a hypothesis space. The hypothesis space may reconstruct the image directly as a grayscale valued function, or indirectly by its Fourier or wavelet spectrum.…

Normalization techniques have only recently begun to be exploited in supervised learning tasks. Batch normalization exploits mini-batch statistics to normalize the activations. This was shown to speed up training and result in better…

Neural implicit representations have emerged as a powerful paradigm for 3D reconstruction. However, despite their success, existing methods fail to capture fine geometric details and thin structures, especially in scenarios where only…