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Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling
Liang Chen, Rongrong Lin, Haizhang Zhang
We study the smallest singular value of nonuniform Fourier matrices in two settings: clustered nodes and perturbations of an equispaced grid. By reducing the problem to spectral no…
Computing the Proximal Operator of the -th Power of the -norm for Group Sparsity
Rongrong Lin, Shihai Chen, Han Feng +1
In this note, we comprehensively characterize the proximal operator of the -th power of the -norm (denoted by ) with by exploiting th…
On Choosing Initial Values of Iteratively Reweighted Algorithms for the Piece-wise Exponential Penalty
Rongrong Lin, Shimin Li, Yulan Liu
Computing the proximal operator of the sparsity-promoting piece-wise exponential (PiE) penalty with a given shape parameter , which is treated as a popular nonc…
The Proximal Operator of the Piece-wise Exponential Function and Its Application in Compressed Sensing
Yulan Liu, Yuyang Zhou, Rongrong Lin
This paper characterizes the proximal operator of the piece-wise exponential function with a given shape parameter , which is a popular nonconvex surrog…
An Optimal Convergence Rate for the Gaussian Regularized Shannon Sampling Series
Rongrong Lin
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory conver…