A quantitative evaluation of various iterative deconvolution algorithms

Automatic simultaneous measurement of phase velocity and thickness in composite plates using iterative deconvolution

“…Iterative deconvolution [28,[35][36][37][38][39][40] assumes that if received signal is the sum of the step responses at each reflector, reflections can be separated subtracting a reference signal properly placed and weighted. In our case, iterative deconvolution is performed as follows:…”

“…Remainder is negated before correlation to take into account the inversion caused by reflection in back surface. There are several choices for the reference signal [28,36,[40][41][42]: the mean of all the first reflections after aligning them to a reference point, a reflection from a polished and flat reflecting surface of the same material, a reflection from an ideal reflector (usually aluminum) and finally just the water-path signal from the through-transmission experiment. We have chosen this latter because it does not need any additional calculation neither new signal acquisition.…”

An algorithm for removing charging effects from X-ray photoelectron spectra of nanoscaled non-conductive materials

“…This approach is most effective for conductive materials or specially prepared "model" samples, and the main problem consists in separating the signal from the noise. A number of mathematical techniques were developed for these purposes, such as convolution of the original spectrum with the source function or an instrumental function [2,3], Fourier filtering of the original spectrum [4][5][6][7], and using algorithms that consider the full frequency range of the original signal, such as the maximum entropy method [4,[8][9][10]. These algorithms are often used to enhance the spectral resolution of the experimental photoelectron spectra obtained from the clean surfaces of model samples: single crystals [4,8,9,11], polycrystalline metal foils [5,6], thin films [10], or ultraviolet photoelectron spectra obtained from the gas phase [5,7].…”

Deconvolution of X-Ray Backscatter Diffraction Data for NDE of Corrosion

“…The iterations proceeded according to the formula 'Jk+l ='Jk + reg -h®'Jk) (11) where 'jk+1 and'jk are the (k+ l)th and k'th iteration results, respectively, and r is a "selected" constant which determines the step size for iteration. Various modifications to (11) have been reported [8,9], among which are a "truncation" modification, and Jansson's method. Both of these take the same general form as (11) except that r is no longer constant, but a function of the k'th iteration value, i.e., r = rrJ*).…”

“…This solution is called the pseudo-inverse. (5) (6) (7) (8) (9) In the case of the Wiener filter the power spectra for signal and noise should be known a priori, but in practice we may not know them exactly. It may then be convenient to write the transfer function for the Wiener filter as (10) where SNR is an estimated (constant) signal to noise ratio, then examine the outcome for various choices of the constant and select the one that seems to give the best performance.…”