Related papers: Sample Complexity of the Boolean Multireference Al…
Many combinatorial optimization problems entail a number of hierarchically dependent optimization problems. An often used solution is to associate a suitably large cost with each individual optimization problem, such that the solution of…
We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible: (i) closely located or highly correlated sources…
We propose a metric for the space of multiple sequence alignments that can be used to compare two alignments to each other. In the case where one of the alignments is a reference alignment, the resulting accuracy measure improves upon…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
Boolean networks are dynamical models of disease development in which the activation levels of genes are represented by binary variables. Given a Boolean network, controls represent mutations or medical treatments that fix the activation…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
Multiexponential modeling of relaxation or diffusion MR signal decays is a popular approach for estimating and spatially mapping different microstructural tissue compartments. While this approach can be quite powerful, it is also limited by…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is…
Assume that a source emits a signal in $3$-dimensional space at an unknown time, which is received by at least~$5$ sensors. In almost all cases the emission time and source position can be worked out uniquely from the knowledge of the times…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…
This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples…
We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…
Any data modeling exercise has two main components: parameter estimation and model selection. The latter will be the topic of this lecture note. More concretely we will introduce several Monte-Carlo sampling-based rules for model selection…
The notion of Boolean logic backpropagation was introduced to build neural networks with weights and activations being Boolean numbers. Most of computations can be done with Boolean logic instead of real arithmetic, both during training and…
The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…
The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In…
Previous multimodal sentence representation learning methods have achieved impressive performance. However, most approaches focus on aligning images and text at a coarse level, facing two critical challenges:cross-modal misalignment bias…