Enhancement of STM images and estimation of atomic positions based on maximum entropy deconvolution

Some trends in microscope image processing

“…(a) the approximation of missing cone data in 3D electron tomography (Barth et al, 1988;Lawrence et al, 1989) (b) the enhancement of scanning tunnelling microscopy and the estimation of atomic positions (Böhmig et al, 1994) (c) the reconstruction of compositional depth profiles from electron probe microanalysis data (Smith et al, 1995) (d) focus tuning in exit-wavefunction reconstruction in high resolution electron microscopy the deconvolution of high resolution transmission electron microscope images (Pennicook et al, 1992;Fu et al, 1994;Chen et al, 1999) (e) the a posteriori correction of uneven illumination (shading) in optical microscopy (Likar et al, 1999) In the future, we will probably witness the generalization of the maximum entropy principle, i.e. the minimization of the Kullback-Leibler cross-entropy, applied to microscope image processing problems.…”

Novel response function resolves by image deconvolution more details of surface nanomorphology

“…Instead of using fast-Fourier transforms (FFTs), the maximum entropy method (MEM) may be applied to deconvolution [40,46]. MEM presumes that the image is generated by a convolution between the surface structure and the instrumental response where the original signal, X (t), is influenced by noise in the form of statistical fluctuations [43].…”

“…MEM presumes that the image is generated by a convolution between the surface structure and the instrumental response where the original signal, X (t), is influenced by noise in the form of statistical fluctuations [43]. Since the apparatus response function is unknown, a Gaussian response function is arbitrarily chosen [43,46]. By applying MEM to deconvolute images of atomic resolution, it was found that only the central core of the peaks of atomic positions were retained and all noise features were completely eliminated, leaving no structural information between peaks [43,46].…”

“…Since the apparatus response function is unknown, a Gaussian response function is arbitrarily chosen [43,46]. By applying MEM to deconvolute images of atomic resolution, it was found that only the central core of the peaks of atomic positions were retained and all noise features were completely eliminated, leaving no structural information between peaks [43,46]. The effect of MEM is thus observed as an almost perfect deblurring of the images with the smoothness to the image features retained, however [43].…”

“…The effect of MEM is thus observed as an almost perfect deblurring of the images with the smoothness to the image features retained, however [43]. Even by using an elongated Gaussian as the MEM response function, a cut-off value is required for distances in the neighbourhood of atomic position, in order to isolate the peaks of atoms [46]. Therefore, the correct choice of the cut-off value becomes an issue for discussion in the procedure of MEM.…”