# Homogeneous Structured Element Pursuit

Finding structured elements from a geometric object, with emphasis on objects containing the origin and hence associated scale ambiguity. (**Update: Jan 25 2020**)

[**S**] indicates my contribution.

### Finding Sparse Vectors in Linear Subspaces

- Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications (2020)
- Dual Principal Component Pursuit: Probability Analysis and Efficient Algorithms (2018)
- Speeding up sum-of-squares for tensor decomposition and planted sparse vectors (2015)
- Dual Principal Component Pursuit (2015)
- Complete Dictionary Recovery over the Sphere (2015)
- Finding a sparse vector in a subspace: Linear sparsity using alternating directions ([
**S**], 2014) - Exact Recovery of Sparsely-Used Dictionaries (2012)
- Blind Source Separation by Sparse Decomposition in a Signal Dictionary (2001)

### Finding Low-rank Matrices in Matrix Subspaces

- Finding a low-rank basis in a matrix subspace (2015)
- Rank-one solutions for homogeneous linear matrix equations over the positive semidefinite cone (2013)
- A simple prior-free method for non-rigid structure-from-motion factorization (2012)

### Finding Sparse Elements in Tensor Subspaces

Disclaimer- This page is meant to serve a hub for references on this problem, and does not represent in any way personal endorsement of papers listed here. So I do not hold any responsibility for quality and technical correctness of each paper listed here. The reader is advised to use this resource with discretion.

If you’d like your paper to be listed here- Just drop me a few lines via email (which can be found on “Welcome” page). If you don’t bother to spend a word, just deposit your paper on arXiv. I get email alert about new animals there every morning, and will be happy to hunt one for this zoo if it seemsfit.