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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-binary Convex Quadratic Optimization and Its Applications in Inference with Sparsity
二元凸 二次优化 稀疏推理
2023/4/14
Sparsity is a naturally occurring characteristic in many real-world applications including signal denoising, outlier detection, and finance. On one hand, sparsity assumption allows people to tackle in...
Tests atternative to higher criticism for high dimensional means under sparsity and column-wise dependence
Large deviation Large p, small n Optimal detection boundary Sparse signal Thresholding Weak dependence
2016/1/25
We consider two alternative tests to the Higher Criticism test of Donoho and Jin (2004) for high dimensional means under the spar-sity of the non-zero means for sub-Gaussian distributed data with unkn...
Adapting to Unknown Sparsity by controlling the False Discovery Rate
Thresholding Wavelet Denoising Minimax Estimation
2015/8/21
We attempt to recover a high-dimensional vector observed in white noise, where
the vector is known to be sparse, but the degree of sparsity is unknown. We consider
three di®erent ways of deˉnin...
Enhancing sparsity by reweighted l1 minimization
1-Minimization ·Iterative reweighting Underdetermined systems of linear equations·Compressive sensing Dantzig selector· Sparsity FOCUSS
2015/8/10
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
Wave atoms and sparsity of oscillatory patterns
Wave atoms Image processing Texture Oscillatory Warping Diffeomorphism
2015/7/14
We introduce “wave atoms” as a variant of 2D wavelet packets obeying the parabolic scaling wavelength ～ (diameter)2. We prove that warped oscillatory functions, a toy model for texture, have a signifi...
Sparsity and Incoherence in Compressive Sampling
`1-minimization basis pursuit restricted orthonormality sparsity singular values of random matrices wavelets discrete Fourier transform
2015/6/17
We consider the problem of reconstructing a sparse signal x0 ∈ Rn from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an orthonormal matrix, we show that...
Enhancing Sparsity by Reweighted ℓ1 Minimization
ℓ 1-minimization iterative reweighting underdetermined systems of linear equations Compressive Sensing the Dantzig selector sparsity FOCUSS
2015/6/17
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constraine...
Mathematics of sparsity (and a few other things)
Underdetermined systems of linear equations compressive sensing matrix completion sparsity low-rank-matrices 1 norm nuclear norm convex programing Gaussian widths
2015/6/17
In the last decade, there has been considerable interest in understanding when it is possible to find structured solutions to underdetermined systems of linear equations. This paper surveys some of th...
Learning Model-Based Sparsity via Projected Gradient Descent
Model-Based Sparsity Projected Gradient Descent
2012/11/22
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization paramete...
Restricted normal cones and sparsity optimization with affine constraints
Compressed sensing constraint qualification Friedrichs angle linear convergence
2012/5/24
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex ...
Conditional Gradient Algorithms for Rank-One Matrix Approximations with a Sparsity Constraint
Sparse Principal Component Analysis PCA Conditional Gradient Algorithms Sparse Eigenvalue Problems
2011/8/26
Abstract: The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine le...
Sparsity and non-Euclidean embeddings
Sparsity non-Euclidean embeddings Functional Analysis
2011/8/25
Abstract: We present a relation between sparsity and non-Euclidean isomorphic embeddings. We introduce a general restricted isomorphism property and show how it enables to construct embeddings of $\el...
SERAPH: Semi-supervised Metric Learning Paradigm with Hyper Sparsity
Semi-supervised Metric Learning Paradigm Hyper Sparsity
2011/6/15
We consider the problem of learning a distance metric from a limited amount of pairwise information as effectively as possible. The proposed SERAPH (SEmi-supervised metRic leArning Paradigm with Hyper...
Non-orthogonal fusion frames and the sparsity of fusion frame operators
Frames Fusion Frames Sparsity Fusion Frame Operator
2011/1/19
Fusion frames have become a major tool in the implemen-tation of distributed systems. The effectiveness of fusion frame appli-cations in distributed systems is reflected in the efficiency of the end f...
Note on sparsity in signal recovery and in matrix identification
Sparse signal recovery compressed sensing Basis Pursuit time-frequency shifts
2008/11/10
We describe a connection between the identi cation problem for matrices with sparse representations in given matrix dictionaries and the problem of sparse signal recovery. This allows the application ...