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Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to…

Data compression techniques are characterized by four key performance indices which are (i) associated accuracy, (ii) compression ratio, (iii) computational work, and (iv) degree of freedom. The method of data compression developed in this…

Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a…

Today's scientific simulations, for example in the high-performance exascale sector, produce huge amounts of data. Due to limited I/O bandwidth and available storage space, there is the necessity to reduce scientific data of high…

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…

Seismic inversion helps geophysicists build accurate reservoir models for exploration and production purposes. Deep learning-based seismic inversion works by training a neural network to learn a mapping from seismic data to rock properties…

Keypoint detection and matching is a fundamental task in many computer vision problems, from shape reconstruction, to structure from motion, to AR/VR applications and robotics. It is a well-studied problem with remarkable successes such as…

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…

Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…

First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve linear operators and their adjoints, which must be applied…

Traditional compressed sensing considers sampling a 1D signal. For a multidimensional signal, if reshaped into a vector, the required size of the sensing matrix becomes dramatically large, which increases the storage and computational…

This paper addresses the problem of collaborative navigation in an unknown environment, where two robots, referred to in the sequel as the Seeker and the Supporter, traverse the space simultaneously. The Supporter assists the Seeker by…

Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal…

Data compression algorithms typically rely on identifying repeated sequences of symbols from the original data to provide a compact representation of the same information, while maintaining the ability to recover the original data from the…

Dataset Condensation aims to condense a large dataset into a smaller one while maintaining its ability to train a well-performing model, thus reducing the storage cost and training effort in deep learning applications. However, conventional…

We present a powerful and easy-to-implement iterative algorithm for solving large-scale optimization problems that involve $L_1$/total-variation (TV) regularization. The method is based on combining the Alternating Directions Method of…

Compressed sensing enables the reconstruction of high-resolution signals from under-sampled data. While compressive methods simplify data acquisition, they require the solution of difficult recovery problems to make use of the resulting…

Time-lapse seismic monitoring of carbon storage and sequestration is often challenging because the time-lapse signature of the growth of CO2 plumes is weak in amplitude and therefore difficult to detect seismically. This situation is…

Scientific discoveries are increasingly constrained by limited storage space and I/O capacities. For time-series simulations and experiments, their data often need to be decimated over timesteps to accommodate storage and I/O limitations.…