Recovery of function from noisy Fourier coefficients with respect to the Haar system

Abstract

We consider the classical ill-posed problem of recovering of a function from noisy Fourier coefficients with respect to the Haar system. For the classes of functions given in terms of generalized smoothness, we present a priori and a posteriori regularization parameter choice realizing an order-optimal error bound.

Keywords:

• ill-posed problem
• Fourier series: noisy coefficients
• Tikhonov regularization
• summationmethod
• Haar system

2010 AMS Subject Classifications:

• 42A24
• 42C05
• 42C10
• 65J20

Disclosure statement

No potential conflict of interest was reported by the author.