Sparse recovery with integrality constraints

Sparse Recovery With Integrality Constraints

In this paper, we investigate conditions for the unique recoverability of sparse integer-valued signals from few linear measurements. Both the objective of minimizing the number of nonzero components, the so-called l0-norm, as well as its popular substitute, the l1-norm, are covered. Furthermore, integer constraints and possible bounds on the variables are investigated. Our results show that th...

Total Dual Integrality of Matching Forest Constraints

Sparse Recovery with Very Sparse Compressed Counting

Compressed1 sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently [11] developed the methodology of using (dense) Compressed Counting for recovering nonnegative Ksparse signals. In this paper, we adopt very sparse Compressed Counting for nonnegative signal recovery. Our design matrix is sampled from a maximally-skewed α-stable distribution (0 < α < 1), and ...

Sparse Coding with Invariance Constraints

We suggest a new approach to optimize the learning of sparse features under the constraints of explicit transformation symmetries imposed on the set of feature vectors. Given a set of basis feature vectors and invariance transformations, from each basis feature a family of transformed features is generated. We then optimize the basis features for optimal sparse reconstruction of the input patte...

Weighted sparse recovery with expanders

We derived the first sparse recovery guarantees for weighted l1 minimization with sparse random matrices and the class of weighted sparse signals, using a weighted versions of the null space property to derive these guarantees. These sparse matrices from expender graphs can be applied very fast and have other better computational complexities than their dense counterparts. In addition we show t...