Noise Amplification Problem Research Articles

Blind equalisation technique based on an improved constant modulus adaptive algorithm

A blind equalisation technique based on an improved constant modulus adaptive (CMA) algorithm is proposed. This technique can accomplish blind equalisation and carrier phase recovery simultaneously as well as easily switch between blind and decision-directed modes. It also takes advantage of the principle of minimum disturbance to avoid the gradient noise amplification problem and achieve improved stability and robustness with low computational complexity. It can be easily switched over to a decision-directed equalisation scheme whenever the error level is reasonably low to obtain higher convergence speed and lower residual intersymbol interference as well. Computer simulation results have indicated very attractive behaviour of the proposed technique, especially with respect to various noise characteristics and time-varying channels.

A spatial regularization method preserving local photometry for Richardson-Lucy restoration

In this article we give a simple method of spatial regularization deriving from the Richardson-Lucy (RL) algorithm in order to overcome the problem of noise amplification during the image reconstruction process. It is very important in astronomy to regularize images while controlling their photometric behavior. We propose a new reconstruction method preserving both the global and local image photometric properties. A mathematical presentation is described here. This method was applied to an image of Titan -a satellite of Saturn -acquired in near infrared with the adaptive optics system ADONIS installed at the ESO 3.6 m telescope in La Silla (Chile). The local photometric results here are compared using contours normalized at the same intensity levels.

Improvements to the analysis of x-ray photoelectron spectra using a maximum entropy method for deconvolution

X-ray photoelectron spectra are typically broadened by the inclusion of contributions from the exciting X radiation, as well as the spectrometer itself. A procedure for removal of much of this broadening using a version of the maximum entropy method is described. This method uses a nonlinear functional (the spectral “entropy” or information content) to stabilize the noise amplification problem inherent to deconvolution of real data. A less ambiguous solution is therefore obtained compared to previous approaches which use linear estimates. This algorithm avoids the subjective nature of many previous deconvolution methods by assuming that the informational uncertainty is always maximized within the constraint of the data provided. This large scale, nonlinear optimization problem can be solved on a fast personal computer using a sequential quadratic programming algorithm. For spectra with adequately high signal/noise, the linewidths produced approach the limiting core hole lifetime values. The method is applied to study the extended growth of an oxide layer on clean polycrystalline aluminum surfaces following exposure to water vapor. For the early growth stages, the spectral detail is comparable to recent synchrotron-based studies where one or more precursor phases are detected at the interface prior to the nucleation of the extended oxide film. In a related study of the oxidation of gold–aluminum alloy surface films, the evolution of the gold–aluminum near-surface phase could be followed through changes in the Au(4f ) and the Al(2p) spectra. From the latter, the surface oxides grown on the alloy surface are seen to differ distinctly from those on pure aluminum.

Multiresolution image reconstruction using wavelets

To overcome the problem of noise amplification during the image reconstruction process, we present a new method based on wavelet decomposition. After decomposing the raw image to be reconstructed into several wavelet planes and a residual image, we reconstruct each one independently using an iterative Maximum Likelihood algorithm. To control the processs, we stop the reconstruction of each one of the wavelet planes and the residual image at a different number of iterations. The inverse problem is then transformed into a multi-channel reconstruction problem. The method has been applied to a real image of the planet Saturn obtained by the non-refurbished Hubble Space Telescope.