Gradient iteration with ℓp-norm constraints

Gradient iterations with ℓp-norm constrains have been studied recently both in the context of inverse problem and of compressed sensing. Use of ℓp-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 ℓ2-norm convergence of such a constrained gradient iteration when p∈(1,2].