A measurement decoupling based fast algorithm for super-resolving point sources with multi-cluster structure
We consider the problem of resolving closely spaced point sources in one dimension from their Fourier data in a bounded domain. Classical subspace methods (e.g., MUSIC algorithm, Matrix Pencil method, etc.) show great superiority in resolving closely spaced sources, but their computational cost is usually heavy. This is especially the case for point sources with a multi-cluster structure which requires processing large-sized data matrix resulted from highly sampled measurements. To address this issue, we propose a fast algorithm termed D-MUSIC, based on a measurement decoupling strategy. We demonstrate theoretically that for point sources with a known cluster structure, their measurement can be decoupled into local measurements of each of the clusters by solving a system of linear equations that are obtained by using a multipole basis. We further develop a subsampled MUSIC algorithm to detect the cluster structure and utilize it to decouple the global measurement. In the end, the MUSIC algorithm was applied to each local measurement to resolve point sources therein. Compared to the standard MUSIC algorithm, the proposed algorithm has comparable super-resolving capability while having a much lower computational complexity.
Code (0)
등록된 구현이 없습니다.
Tasks
subspace methodsSimilar Papers 제목 키워드 기반
$\boldsymbolγ$-Net: Superresolving SAR Tomographic Inversion via Deep Learning
Synthetic aperture radar tomography (TomoSAR) has been extensively employed in 3-D reconstruction in dense urban areas using high-resolution SAR acquisitions. Compressive sensing (CS)-based algorithms are generally consi…
Compressive SensingComputational EfficiencyDeep LearningSuper-ResolutionAutomated Tuning for Diffusion Inverse Problem Solvers without Generative Prior Retraining
Diffusion/score-based models have recently emerged as powerful generative priors for solving inverse problems, including accelerated MRI reconstruction. While their flexibility allows decoupling the measurement model fro…
MRI ReconstructionHigh-resolution Multi-spectral Imaging with Diffractive Lenses and Learned Reconstruction
Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components t…
DiagnosticRolling Shutter CorrectionVocal Bursts Intensity PredictionFast swap regret minimization and applications to approximate correlated equilibria
We give a simple and computationally efficient algorithm that, for any constant $\varepsilon>0$, obtains $\varepsilon T$-swap regret within only $T = \mathsf{polylog}(n)$ rounds; this is an exponential improvement compar…
FormOptimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factors
We give a proof of the conjecture of Nelson and Nguyen [FOCS 2013] on the optimal dimension and sparsity of oblivious subspace embeddings, up to sub-polylogarithmic factors: For any $n\geq d$ and $ε\geq d^{-O(1)}$, there…