Point spread function deconvolution

It is still possible to enhance the resolution also when the point-spread function is unknown. For instance, the resolution is improved by subtracting the second-derivative g x) from the measured signal g x). Thus the signal is restored by ag x) - (7 - a)g Xx) with 0 < a < 1. This llgorithm is called pseudo-deconvolution. Because the second-derivative of any bell-shaped peak is negative between the two inflection points (second-derivative is zero) and positive elsewhere, the subtraction makes the top higher and narrows the wings, which results in a better resolution (see Fig. 40.30). Pseudo-deconvolution methods can correct for sym-... 

A small dot sample of DPPH was measured first to obtain the point spread function (PSF) or a system function. The blurred image of an actual sample is deconvoluted with PSF to obtain a better resolution depending on the S/N ratio.1 Although it took hours to get an image with a good resolution with cw-ESR, measurements are automatically made with a computer-controlled X-Y-Z stage. 

At the most basic level, the data can be visualized (rendered) as an image volume viewed at varying angles and manually compressed or stretched to fit. Alternatively, a more mathematical approach can be taken if the optical aberrations can be measured. In 3D fluorescence microscopy, this measurement is known as the point spread function (psf), and a process of deconvolution can be used to correct any aberrations with a known psf. Once corrected, the data can be rendered for viewing and measurement with confidence. 

In image processing, blind deconvolution is a technique used to correct blurred images when the system Point Spread Function (PSF) is unknown or poorly known. The PSF is then estimated from the image. This technique has been used for decades (Ayers and Dainty 1988 Levin et al. 2009) and in this section a blind deconvolution iterative algorithm is applied to spectro-spatial data to study its applicability. 

This family of algorithms may be used for non-specialist purposes, or when the point spread function is unknown. It takes twice as long as the MLE per iteration but can produce better results than the use of a theoretical PSF, especially if unpredicted aberrations are present. Nevertheless, we always recommend that the acquisition system be characterized and calibrated (see above on PSF determination), to minimize aberrations before acquisition, because the better the acquisition, the better the result of the deconvolution is likely to be, regardless of the algorithm used. 

The technique of image restoration (or deconvolution ) can now be simply put given the measured, noisy, image Im(x, y) and the point-spread function b(x, y), estimate the true image i(x, y). 

We use the simultaneously measured point spread function to perform a Richardson-Lucy deconvolution of the galaxy image. Usually five or so iterations are optimum. To monitor the progress we throw in a bright point source on top of the galaxy (but not on its center) and require that no moats develop. 

Deconvolution can be used to reduce the effeas of defocus and so reduce the width of the point spread function in the axial or depth direction. ... 

What meaning do these two-point resolution criteria have in describing the deconvolution process, that is, resolution before and after deconvolution Although width criteria may be applied to derive suitable before-after ratios, the Rayleigh criterion raises an interesting question. Because the diffraction pattern is an inherent property of the observing instrument, would it not be best to reserve this criterion to describe optical performance The effective spread function after deconvolution is not sine squared anyway. 

Have we solved the problem Is this all there is to deconvolution Let us look a little closer at the three-point example by examining Eq. (5). Suppose that the first spread-function value s x is small relative to the other values of s, as is typical. The value i0 would also then be small. We are dealing with data acquired from the real world, and no observation can be without error. Suppose that the observation of im is subject to the error nm. We may then write our object estimate... 

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