Nearly optimal resolution estimate for the two-dimensional super-resolution and a new algorithm for direction of arrival estimation with uniform rectangular array
In this paper, we develop a new technique to obtain nearly optimal estimates of the computational resolution limits introduced in Appl. Comput. Harmon. Anal. 56 (2022) 402-446; IEEE Trans. Inf. Theory 67(7) (2021) 4812-4827; Inverse Probl. 37(10) (2021) 104001 for two-dimensional super-resolution problems. Our main contributions are fivefold: (i) Our work improves the resolution estimate for number detection and location recovery in two-dimensional super-resolution problems to nearly optimal; (ii) As a consequence, we derive a stability result for a sparsity-promoting algorithm in two-dimensional super-resolution problems (or Direction of Arrival problems (DOA)). The stability result exhibits the optimal performance of sparsity promoting in solving such problems; (iii) Our techniques pave the way for improving the estimate for resolution limits in higher-dimensional super-resolutions to nearly optimal; (iv) Inspired by these new techniques, we propose a new coordinate-combination-based model order detection algorithm for two-dimensional DOA estimation and theoretically demonstrate its optimal performance, and (v) we also propose a new coordinate-combination-based MUSIC algorithm for super-resolving sources in two-dimensional DOA estimation. It has excellent performance and enjoys many advantages compared to the conventional DOA algorithms. The coordinate-combination idea seems to be a promising way for multi-dimensional DOA estimation.
Code (0)
등록된 구현이 없습니다.
Tasks
Direction of Arrival EstimationSuper-ResolutionSimilar Papers 제목 키워드 기반
A mathematical theory of resolution limits for super-resolution of positive sources
A priori information on the positivity of source intensities is ubiquitous in imaging fields and is also important for a multitude of super-resolution and deconvolution algorithms. However, the fundamental resolution lim…
Super-ResolutionConfidence Intervals and Hypothesis Testing for High-Dimensional Regression
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distri…
parameter estimationregressionTwo-sample testingVocal Bursts Intensity PredictionConfidence Intervals and Hypothesis Testing for High-Dimensional Statistical Models
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distri…
Diabetes Predictionparameter estimationTwo-sample testingVocal Bursts Intensity PredictionCollaboratively Learning Linear Models with Structured Missing Data
We study the problem of collaboratively learning least squares estimates for $m$ agents. Each agent observes a different subset of the features$\unicode{x2013}$e.g., containing data collected from sensors of varying reso…
Imputation(Nearly) Optimal Private Linear Regression via Adaptive Clipping
We study the problem of differentially private linear regression where each data point is sampled from a fixed sub-Gaussian style distribution. We propose and analyze a one-pass mini-batch stochastic gradient descent met…
regression