An adaptive LSQR algorithm for computing discontinuous solutions in deconvolution problems

Ill-posed problems described by first-kind Fredholm equations appear in many interesting practical cases in engineering or mathematical physics, such as the inverse problem of signal deconvolution, and require regularization techniques to get adequate solutions ([C. Sánchez-Ávila, A.R. Figueiras-Vidal, J. Comp. Appl. Math. 72 (1996) 21–39] and [A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, A.G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems, Kluwer Academic Publishers, Dordrecht, 1995]).