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This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…

We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…

As recent advances in large-scale Text-to-Image (T2I) diffusion models have yielded remarkable high-quality image generation, diverse downstream Image-to-Image (I2I) applications have emerged. Despite the impressive results achieved by…

Implicit neural representations (INRs) have emerged as a promising approach for video storage and processing, showing remarkable versatility across various video tasks. However, existing methods often fail to fully leverage their…

Benefiting from pre-trained text-to-image (T2I) diffusion models, real-world image super-resolution (Real-ISR) methods can synthesize rich and realistic details. However, due to the inherent stochasticity of T2I models, different noise…

This paper focuses on characterizing the fundamental performance limits that can be expected from an ideal decoder given a general model, ie, a general subset of "simple" vectors of interest. First, we extend the so-called notion of…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…

Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…

Image-to-Image (I2I) multi-domain translation models are usually evaluated also using the quality of their semantic interpolation results. However, state-of-the-art models frequently show abrupt changes in the image appearance during…

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…

The performance of objective image quality assessment (IQA) models has been evaluated primarily by comparing model predictions to human quality judgments. Perceptual datasets gathered for this purpose have provided useful benchmarks for…

Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…

Inferring behavior model of a running software system is quite useful for several automated software engineering tasks, such as program comprehension, anomaly detection, and testing. Most existing dynamic model inference techniques are…

While diffusion language models (DLMs) have achieved competitive performance in text generation, improving their reasoning ability with reinforcement learning remains an active research area. Here, we introduce d2, a reasoning framework…

Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test…

For a parameter-unknown linear descriptor system, this paper proposes data-driven methods to testify the system's type and controllability and then to stabilize it. First, a data-based condition is developed to identify whether this unknown…

Denoising diffusion models have emerged as the go-to generative framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution tasks, which remains an under-explored…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Inter prediction is an important module in video coding for temporal redundancy removal, where similar reference blocks are searched from previously coded frames and employed to predict the block to be coded. Although traditional video…