Noise revealing in Golub-Kahan bidiagonalization as a mean of regularization in discrete inverse problems
2014
Abstract
We consider a linear inverse problem Ax ~ b, where A is a linear operator with smoothing property and b represents an observation vector polluted by unknown noise. It was shown that high-frequency noise reveals during the Golub-Kahan iterative bidiagonalization in the left bidiagonalization vectors.
We present a method that identifies the iteration with maximal noise revealing and reduces a portion of high-frequency noise in the data by subtracting the corresponding (properly scaled) left bidiagonalization vector from b.