Gradient iteration with -norm constraints

Gradient iterations with ℓ p -norm constrains have been studied recently both in the context of inverse problem and of compressed sensing. Use of ℓ p -norm constrains, p < 2 , is often advocated when a sparse solution is expected. A constrained gradient iteration is usually implemented via a shrinkage operator. In this note, we establish the ℓ 2 -norm convergence of such a constrained gradient iteration when p ∈ ( 1 , 2 ] .