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This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
The stepped-frequency (SF) waveform is an effective way to achieve high range resolution (HRR) in modern radars. In this paper, we determine some fundamental limits of SF waveforms on ambiguity, stability and accuracy of stable targets…
Interferometric calibration always yields non unique solutions. It is therefore essential to remove these ambiguities before the solutions could be used in any further modeling of the sky, the instrument or propagation effects such as the…
Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve…
The sensitivity limits of space telescopes are imposed by uncalibrated errors in the point spread function, photon-noise, background light, and detector sensitivity. These are typically calibrated with specialized wavefront sensor hardware…
Automatic Gender Recognition (AGR) systems are an increasingly widespread application in the Machine Learning (ML) landscape. While these systems are typically understood as detecting gender, they often classify datapoints based on…
Synthetic Aperture Radar (SAR) imaging systems operate by emitting radar signals from a moving object, such as a satellite, towards the target of interest. Reflected radar echoes are received and later used by image formation algorithms to…
We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…
Radar is a critical perception modality in autonomous driving systems due to its all-weather characteristics and ability to measure range and Doppler velocity. However, the sheer volume of high-dimensional raw radar data saturates the…
Abstraction reasoning is a long-standing challenge in artificial intelligence. Recent studies suggest that many of the deep architectures that have triumphed over other domains failed to work well in abstract reasoning. In this paper, we…
Surgical workflow recognition is vital for automating tasks, supporting decision-making, and training novice surgeons, ultimately improving patient safety and standardizing procedures. However, data corruption can lead to performance…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
Shape optimization approaches to inverse design offer low-dimensional, physically-guided parameterizations of structures by representing them as combinations of shape primitives. However, on discretized rectilinear simulation grids,…
Functional data, representing curves or trajectories, are ubiquitous in fields like biomedicine and motion analysis. A fundamental challenge is phase variability -- temporal misalignments that obscure underlying patterns and degrade model…
Differentiable rendering has received increasing interest for image-based inverse problems. It can benefit traditional optimization-based solutions to inverse problems, but also allows for self-supervision of learning-based approaches for…
This work investigates the problem of tangential velocity estimation in automotive radar systems, addressing the limitations of conventionally considered models. Conventional automotive radars are usually based on far-field models and…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
Quantitative inversion algorithms allow for the reconstruction of electrical properties (such as permittivity, and conductivity) for every point in a scene. However, they are challenging to use on measured datasets due to the need to know…
Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…
Machine learning methods rely on data. However, gathering suitable data can be challenging due to availability constraints, cost, or the need for domain expertise. Expanding datasets with additional sources is a common response to limited…