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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...
ENDMEMBER EXTRACTION OF HIGHLY MIXED DATA USING L1 SPARSITY-CONSTRAINED MULTILAYER NONNEGATIVE MATRIX FACTORIZATION
Hyperspectral Imagery Nonnegative Matrix Factorization Multilayer Nonnegative Matrix Factorization Sparsity Constraint Endmember Extraction
2018/5/11
Due to the limited spatial resolution of remote hyperspectral sensors, pixels are usually highly mixed in the hyperspectral images. Endmember extraction refers to the process identifying the pure endm...
2017SPIE小波和稀疏光学专题会议（Wavelets and Sparsity XVII）。
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 ...
Gradually Atom Pruning for Sparse Reconstruction and Extension to Correlated Sparsity
Smoothed l0 l1 minimization compressed sensing reconstruction algorithm correlated sparsity
2012/4/23
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of no...
On the Role of Diversity in Sparsity Estimation
Role of Diversity Sparsity Estimation Information Theory
2011/9/22
Abstract: A major challenge in sparsity pattern estimation is that small modes are difficult to detect in the presence of noise. This problem is alleviated if one can observe samples from multiple rea...
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...