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Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves.…
This paper introduces a novel generative encoder (GE) model for generative imaging and image processing with applications in compressed sensing and imaging, image compression, denoising, inpainting, deblurring, and super-resolution. The GE…
Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of high-dimensional, parametric systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs…
This paper advocates the use of implicit surface representation in autoencoder-based self-supervised 3D representation learning. The most popular and accessible 3D representation, i.e., point clouds, involves discrete samples of the…
A recent line of work has shown promise in using sparse autoencoders (SAEs) to uncover interpretable features in neural network representations. However, the simple linear-nonlinear encoding mechanism in SAEs limits their ability to perform…
Compressive phase retrieval refers to the problem of recovering a structured $n$-dimensional complex-valued vector from its phase-less under-determined linear measurements. The non-linearity of measurements makes designing…
This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
Self-supervised learning has attracted increasing attention as it learns data-driven representation from data without annotations. Vision transformer-based autoencoder (ViT-AE) by He et al. (2021) is a recent self-supervised learning…
The growing volume of high-resolution Whole Slide Images in digital histopathology poses significant storage, transmission, and computational efficiency challenges. Standard compression methods, such as JPEG, reduce file sizes but often…
The volume of remote sensing data is experiencing rapid growth, primarily due to the plethora of space and air platforms equipped with an array of sensors. Due to limited hardware and battery constraints the data is transmitted back to…
Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as the latent space, whose flat geometry, however, is often…
High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…
In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…
Data encoding is a common and central operation in most data analysis tasks. The performance of other models downstream in the computational process highly depends on the quality of data encoding. One of the most powerful ways to encode…
Variational Auto-encoders (VAEs) have been very successful as methods for forming compressed latent representations of complex, often high-dimensional, data. In this paper, we derive an alternative variational lower bound from the one…
Video anomaly detection is often seen as one-class classification (OCC) problem due to the limited availability of anomaly examples. Typically, to tackle this problem, an autoencoder (AE) is trained to reconstruct the input with training…
Principal Component Analysis (PCA) minimizes the reconstruction error given a class of linear models of fixed component dimensionality. Probabilistic PCA adds a probabilistic structure by learning the probability distribution of the PCA…
Latent diffusion models have established a new state-of-the-art in high-resolution visual generation. Integrating Vision Foundation Model priors improves generative efficiency, yet existing latent designs remain largely heuristic. These…
Communication technologies like voice over IP operate under constrained real-time conditions, with voice packets being subject to delays and losses from the network. In such cases, the packet loss concealment (PLC) algorithm reconstructs…
We consider the problem of lossy image compression with deep latent variable models. State-of-the-art methods build on hierarchical variational autoencoders (VAEs) and learn inference networks to predict a compressible latent representation…