Robust analysis ℓ1-recovery from Gaussian measurements and total variation minimization

Kabavana, M.; Rauhut, H. und Zhang, H. (2015): Robust analysis ℓ1-recovery from Gaussian measurements and total variation minimization. In: European Journal of Applied Mathematics, Vol. 26, No. 6: pp. 917-929

Abstract

Analysis ℓ1-recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the transform domain is generated by a difference operator. In the present paper, we provide a bound on the number of Gaussian measurements required for successful recovery for total variation and for the case that the analysis operator is a frame. The bounds are particularly suitable when the sparsity of the analysis representation of the signal is not very small.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Chair of Mathematics of Information Processing
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0956-7925
• Language: English