A wavelet-based method for solving discrete first-kind Fredholm equations with piecewise constant solutions

• Published in: International journal for numerical methods in engineering Vol. 57; no. 4; pp. 577 - 598
• Main Authors: Sánchez-Ávila, C., Sánchez-Reíllo, R.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 28.05.2003
• Subjects: Algorithms; Approximation; deconvolution problem; discrete ill-posed problems; edge detection; Hilbert space; Holder exponents; Integral equations; Iterative methods; Mathematical analysis; Mathematical models; Regularization; wavelets modulus maxima

The inverse problem of finding piecewise constant solutions to discrete Fredholm integral equations of the first kind arises in many applied fields, e.g. in geophysics. This equation is usually an ill‐posed problem when it is considered in a Hilbert space framework, requiring regularization techniqu...