Restoration algorithm

Therefore, the adaptive properties of the above system include the PDD restoration algorithms from empirieal data. 

Software base complexes are used for this purpose, which realize analytical restoration algorithms and various procedures of tomograms processing Program complexes ensure the control of a measuring process and dialoguing with the operator. 

Under these prior conditions, the restoring algorithm given by Eqs. (59) and (60) becomes very close to one previously used by Frieden (1972). That one was also a maximum-entropy restoring algorithm in the presence of additive noise. We present some results of the latter method applied to spectral data. 

J. A. Conchello and E. W. Hansen, Enhanced 3-D reconstruction from confocal scarming microscope images. I. Deterministic and maximum likelihood reconstructions, Appl. Opt. v., 1990, 29, 3795-3804 see also J. Markham and J.-A. Conchello, Fast maximum- likelihood image-restoration algorithms for three dimensional fluorescence microscopy. J. Opt. Soc. Am. A, V. 18, (2001) p. 1062. 

Image restoration algorithm Point spread function... 

The obvious image restoration algorithm is the so-called inverse filter. Given that... 

Fig. 2. Deep K, ixnage of the field of FSC10214+4724 obtained on the W.M. Kedc telescope. On the left the foil 38"x38" field is shown. The FWHM of stellar images in this image is 0.6" and the faintest objects seen in the image have K, 22 mag. On the right the central 10" x 10" around the infrared source is diown in an enlargement where the Ridiardson-Lucy image restoration algorithm has been applied to enhance low levd features.

The adaptive estimation of the pseudo-inverse parameters a n) consists of the blocks C and E (Fig. 1) if the transformed noise ( ) has unknown properties. Bloek C performes the restoration of the posterior PDD function w a,n) from the data a (n) + (n). It includes methods and algorithms for the PDD function restoration from empirical data [8] which are based on empirical averaging. Beeause the noise is assumed to be a stationary process with zero mean value and the image parameters are constant, the PDD function w(a,n) converges, at least, to the real distribution. The posterior PDD funetion is used to built a back loop to block B and as a direct input for the estimator E. For the given estimation criteria f(a,d) an optimal estimation a (n) can be found from the expression... 

Low and High frequency can be restored by use of a deconvolution algorithm that enhances the resolution. We operate an improvement of the spectral bandwidth by Papoulis deconvolution based essentially on a non-linear adaptive extrapolation of the Fourier domain. 

To restore resolution, we proposed a signal processing method based on Papoulis deconvolution. We implemented this algorithm and tried to operate an improvement from an aluminum rod smaller than the wavelength. 

Lanteri, H., Roche, M., and Aime, C., 2002, Penalized maximum likelihood image restoration with positivity constraints multiplicative algorithms. Inverse Problems 18, 1397... 

To date, the prior knowledge built into deconvolution algorithms has mainly been deterministic in nature, such as by use of positivity or boundedness. But a unified approach to estimating spectra should accommodate all possible physical and statistical prior knowledge about formation of the spectra. In particular, the approach should be physical, based on the Bose-Einstein nature of photons. Such an approach will be presented here. One general restoring principle will be derived, from which particular estimators... 

Using spectral image data provided by Jansson et al (1970), we restored a portion of the Q branch of the v3 band of CH4. Results are shown in Fig. 4. Note the smoothness of the output, no doubt enforced by the prior conviction of a flat object. But, despite this smoothness, the right-hand line has been split into two components. These same data were also restored by Jansson, using his bound-constrained algorithm (see Chapters 4, 6, and 7... 

Finally, in Fig. 6(d) we asked what the effect would be of inputting for Qm the true object but displaced to the left by one point. This would test the sensitivity of the tactic to registration error. Results show that the output is indeed sensitive to such error. If a high-gradient Qm is used, it had better be in the correct registration. (The restoration for z = 2 is not shown because the algorithm would not converge under these contradictory conditions.)... 

When using the fast-Fourier-transform algorithm to calculate the DFT, inverse filtering can be very fast indeed. By keeping the most noise-free inverse-filtered spectral components, and adding to these an additional band of restored spectral components, it is usually found that only a small number of components are needed to produce a result that closely approximates the original function. This is an additional reason for the efficiency of the method developed in this research. 

Even though restoration in two distinct spectral bands leads to very fast algorithms, it is still not optimum because of the residual error in the low-frequency band of spectral components used as a region of support. Perhaps the requirement that the inverse-filtered low-frequency spectrum (or, equivalently, its corresponding spatial function) be held constant for the restoration... 

---