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An overview of low-rank matrix recovery from incomplete observations
Low-rank matrices play a fundamental role in modeling and computational methods for
signal processing and machine learning. In many applications where low-rank matrices …
signal processing and machine learning. In many applications where low-rank matrices …
Transformers as support vector machines
Since its inception in" Attention Is All You Need", transformer architecture has led to
revolutionary advancements in NLP. The attention layer within the transformer admits a …
revolutionary advancements in NLP. The attention layer within the transformer admits a …
Global convergence of ADMM in nonconvex nonsmooth optimization
In this paper, we analyze the convergence of the alternating direction method of multipliers
(ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, ϕ (x_0 …
(ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, ϕ (x_0 …
Measure what should be measured: progress and challenges in compressive sensing
T Strohmer - IEEE Signal Processing Letters, 2012 - ieeexplore.ieee.org
Is compressive sensing overrated? Or can it live up to our expectations? What will come
after compressive sensing and sparsity? And what has Galileo Galilei got to do with it …
after compressive sensing and sparsity? And what has Galileo Galilei got to do with it …
Iterative reweighted algorithms for matrix rank minimization
The problem of minimizing the rank of a matrix subject to affine constraints has applications
in several areas including machine learning, and is known to be NP-hard. A tractable …
in several areas including machine learning, and is known to be NP-hard. A tractable …
Sparse representation of a polytope and recovery of sparse signals and low-rank matrices
This paper considers compressed sensing and affine rank minimization in both noiseless
and noisy cases and establishes sharp restricted isometry conditions for sparse signal and …
and noisy cases and establishes sharp restricted isometry conditions for sparse signal and …
Low-rank matrix recovery via iteratively reweighted least squares minimization
We present and analyze an efficient implementation of an iteratively reweighted least
squares algorithm for recovering a matrix from a small number of linear measurements. The …
squares algorithm for recovering a matrix from a small number of linear measurements. The …
t-Schatten- Norm for Low-Rank Tensor Recovery
In this paper, we propose a new definition of tensor Schatten-norm (t-Schatten-norm) based
on t-SVD, and prove that this norm has similar properties to matrix Schatten-norm. More …
on t-SVD, and prove that this norm has similar properties to matrix Schatten-norm. More …
A high-resolution DOA estimation method with a family of nonconvex penalties
The low-rank matrix reconstruction (LRMR) approach is widely used in direction-of-arrival
(DOA) estimation. As the rank norm penalty in an LRMR is NP-hard to compute, the nuclear …
(DOA) estimation. As the rank norm penalty in an LRMR is NP-hard to compute, the nuclear …
Augmented and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm
This paper studies the long-existing idea of adding a nice smooth function to “smooth” a
nondifferentiable objective function in the context of sparse optimization, in particular, the …
nondifferentiable objective function in the context of sparse optimization, in particular, the …