On partial sparse recovery

Abstract

We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the ${\ell }_1$-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to a classical problem in Compressed Sensing where the ${\ell }_1$-norm of the whole solution vector is minimized. We introduce analogues of restricted isometry and null space properties for the recovery of partially sparse vectors and show that these new properties are implied by their original counterparts. We show also how to extend recovery under noisy measurements to the partially sparse case.

References in corpus (2)

• Modified-CS: Modifying Compressive Sensing for Problems with Partially Known Support
• The road to deterministic matrices with the restricted isometry property

Cited by in corpus (6)

• Recursive Recovery of Sparse Signal Sequences from Compressive Measurements: A Review
• Near-optimal phase retrieval of sparse vectors
• Recovery guarantees for polynomial approximation from dependent data with outliers
• Local sparsity and recovery of fusion frames structured signals
• Uniqueness Conditions for A Class of l0-Minimization Problems
• Time Invariant Error Bounds for Modified-CS based Sparse Signal Sequence Recovery