No abstract

graduated as a mining engineer from Oviedo School of Mines and was awarded a Ph.D. from Oviedo University, Spain. He has held technical and managerial positions in mining and power generation companies in Spain and is currently a senior lecturer at the University of Oviedo.

Compressed sensing involves solving a minimization problem with objective function Ω(x) = x 1 and linear constraints Ax = b. Previous work has explored robustness to errors in A and b under special assumptions. Motivated by these results, we explore robustness to errors in A for a wider class of objective functions Ω and for a more general setting, where the solution may not be unique. Similar results for errors in b are known and easier to prove. More precisely, for a seminorm Ω(x) with a polyhedral unit ball, we prove that the set-valued map S(A) = arg min Ax=b Ω(x) is calm in A whenever A has full rank and the minimum value is positive, where calmness is a kind of local Lipschitz regularity.

No abstract

No abstract