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Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…
With the growing computational power available for high-resolution ensemble simulations in scientific fields such as cosmology and oceanology, storage and computational demands present significant challenges. Current surrogate models fall…
Implicit Neural Representations (INRs) have garnered significant attention for their ability to model complex signals in various domains. Recently, INR-based frameworks have shown promise in neural video compression by embedding video…
Implicit neural representations (INRs) such as NeRF and SIREN encode a signal in neural network parameters and show excellent results for signal reconstruction. Using INRs for downstream tasks, such as classification, is however not…
The Subset Sum Problem is a fundamental NP-complete problem in cryptography and combinatorial optimization, with many real-world applications. The Random Subset Sum Problem (RSSP) is a more applicable version of subset sum, where numbers…
One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the…
While most existing sparse recovery results allow only minimal structure within the measurement scheme, many practical problems possess significant structure. To address this gap, we present a framework for structured measurements that are…
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP)…
A random construction of bipolar sensing matrices based on binary linear codes is introduced and its RIP (Restricted Isometry Property) is analyzed based on an argument on the ensemble average of the weight distribution of binary linear…
Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high…
Dimensionality reduction is a popular approach to tackle high-dimensional data with low-dimensional nature. Subspace Restricted Isometry Property, a newly-proposed concept, has proved to be a useful tool in analyzing the effect of…
This paper tackles the simultaneous optimization of pose and Neural Radiance Fields (NeRF). Departing from the conventional practice of using explicit global representations for camera pose, we propose a novel overparameterized…
This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has been studied extensively through the notion of Restricted…
Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and…
This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…
In this work, we analyze modulated sampling schemes, such as the Nyquist Folding Receiver, which are highly efficient, readily implementable, non-uniform sampling schemes that allows for the blind estimation of a narrow-band signal's…
High-energy, large-scale particle colliders in nuclear and high-energy physics generate data at extraordinary rates, reaching up to $1$ terabyte and several petabytes per second, respectively. The development of real-time, high-throughput…
In artificial neural networks, learning from data is a computationally demanding task in which a large number of connection weights are iteratively tuned through stochastic-gradient-based heuristic processes over a cost-function. It is not…
Snapshot compressed sensing (CS) refers to compressive imaging systems in which multiple frames are mapped into a single measurement frame. Each pixel in the acquired frame is a noisy linear mapping of the corresponding pixels in the frames…
Large-scale dense mapping is vital in robotics, digital twins, and virtual reality. Recently, implicit neural mapping has shown remarkable reconstruction quality. However, incremental large-scale mapping with implicit neural representations…