相关论文: On the Sample Complexity of Super-Resolution Radar
Simulating realistic radar data has the potential to significantly accelerate the development of data-driven approaches to radar processing. However, it is fraught with difficulty due to the notoriously complex image formation process. Here…
Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data analysis, has been successfully used in several applications, such as in collaborative filtering to design recommender systems or in computer vision to…
Single-photon Light Detection and Ranging (LiDAR) systems are often equipped with an array of detectors for improved spatial resolution and sensing speed. However, given a fixed amount of flux produced by the laser transmitter across the…
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…
A recent line of work shows that a deep neural network with ReLU nonlinearities arises from a finite sequence of cascaded sparse coding models, the outputs of which, except for the last element in the cascade, are sparse and unobservable.…
Deep Q-learning based algorithms have been applied successfully in many decision making problems, while their theoretical foundations are not as well understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU neural…
The designation of the radar system is to detect the position and velocity of targets around us. The radar transmits a waveform, which is reflected back from the targets, and echo waveform is received. In a commonly used model, the echo is…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Dropout Regularization, serving to reduce variance, is nearly ubiquitous in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks configured with random…
Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…
Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing,…
We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at $L$ using only $L^2$ samples. We obtain the optimal number of samples given by the…
This letter proposes a low-complexity signal detection method for the splitting receiver scheme, which achieves an excellent symbol error rate (SER) performance. Based on the three-dimensional (3D) received signal of the splitting receiver,…
Mueller matrix polarimetry constitutes a nondestructive powerful tool for the analysis of material samples that is used today in an enormous variety of applications. Depolarizing samples exhibit, in general, a complicated physical behavior…