2,172 research outputs found
Digital Deblurring of CMB Maps II: Asymmetric Point Spread Function
In this second paper in a series dedicated to developing efficient numerical
techniques for the deblurring Cosmic Microwave Background (CMB) maps, we
consider the case of asymmetric point spread functions (PSF). Although
conceptually this problem is not different from the symmetric case, there are
important differences from the computational point of view because it is no
longer possible to use some of the efficient numerical techniques that work
with symmetric PSFs. We present procedures that permit the use of efficient
techniques even when this condition is not met. In particular, two methods are
considered: a procedure based on a Kronecker approximation technique that can
be implemented with the numerical methods used with symmetric PSFs but that has
the limitation of requiring only mildly asymmetric PSFs. The second is a
variant of the classic Tikhonov technique that works even with very asymmetric
PSFs but that requires discarding the edges of the maps. We provide details for
efficient implementations of the algorithms. Their performance is tested on
simulated CMB maps.Comment: 9 pages, 13 Figure
Image restoration by selective short space spectral subtraction
Image restoration by short space spectral subtraction has been applied recursively to a photographic system in an attempt to increase the signal to noise ratio proportionally to the amount of optical density present. The image is smoothed in the frequency domain a small space at a time based on the power spectrum at a given density level. The method is a variable filter that is a function of photographic density
Image Reconstruction and Evaluation: Applications on Micro-Surfaces and Lenna Image Representation
This article develops algorithms for the characterization and the visualization of micro-scale features using a small number of sample points, with the goal of mitigating the measurement shortcomings, which are often destructive or time consuming. The popular measurement techniques that are used in imaging of micro-surfaces include the 3D stylus or interferometric profilometry and Scanning Electron Microscopy (SEM), where both could represent the micro-surface characteristics in terms of 3D dimensional topology and greyscale image, respectively. Such images could be highly dense; therefore, traditional image processing techniques might be computationally expensive. We implement the algorithms in several case studies to rapidly examine the microscopic features of micro-surface of Microelectromechanical System (MEMS), and then we validate the results using a popular greyscale image; i.e., “Lenna” image. The contributions of this research include: First, development of local and global algorithm based on modified Thin Plate Spline (TPS) model to reconstruct high resolution images of the micro-surface’s topography, and its derivatives using low resolution images. Second, development of a bending energy algorithm from our modified TPS model for filtering out image defects. Finally, development of a computationally efficient technique, referred to as Windowing, which combines TPS and Linear Sequential Estimation (LSE) methods, to enhance the visualization of images. The Windowing technique allows rapid image reconstruction based on the reduction of inverse problem
Regularized adaptive long autoregressive spectral analysis
This paper is devoted to adaptive long autoregressive spectral analysis when
(i) very few data are available, (ii) information does exist beforehand
concerning the spectral smoothness and time continuity of the analyzed signals.
The contribution is founded on two papers by Kitagawa and Gersch. The first one
deals with spectral smoothness, in the regularization framework, while the
second one is devoted to time continuity, in the Kalman formalism. The present
paper proposes an original synthesis of the two contributions: a new
regularized criterion is introduced that takes both information into account.
The criterion is efficiently optimized by a Kalman smoother. One of the major
features of the method is that it is entirely unsupervised: the problem of
automatically adjusting the hyperparameters that balance data-based versus
prior-based information is solved by maximum likelihood. The improvement is
quantified in the field of meteorological radar
Photographic Image Restoration
Deblurring capabilities would significantly improve the Flight Science Support Office's ability to monitor the effects of lift-off on the shuttle and landing on the orbiter. A deblurring program was written and implemented to extract information from blurred images containing a straight line or edge and to use that information to deblur the image. The program was successfully applied to an image blurred by improper focussing and two blurred by different amounts of blurring. In all cases, the reconstructed modulation transfer function not only had the same zero contours as the Fourier transform of the blurred image but the associated point spread function also had structure not easily described by simple parameterizations. The difficulties posed by the presence of noise in the blurred image necessitated special consideration. An amplitude modification technique was developed for the zero contours of the modulation transfer function at low to moderate frequencies and a smooth filter was used to suppress high frequency noise
Photographic image enhancement
Deblurring capabilities would significantly improve the scientific return from Space Shuttle crew-acquired images of the Earth and the safety of Space Shuttle missions. Deblurring techniques were developed and demonstrated on two digitized images that were blurred in different ways. The first was blurred by a Gaussian blurring function analogous to that caused by atmospheric turbulence, while the second was blurred by improper focussing. It was demonstrated, in both cases, that the nature of the blurring (Gaussian and Airy) and the appropriate parameters could be obtained from the Fourier transformation of their images. The difficulties posed by the presence of noise necessitated special consideration. It was demonstrated that a modified Wiener frequency filter judiciously constructed to avoid over emphasis of frequency regions dominated by noise resulted in substantially improved images. Several important areas of future research were identified. Two areas of particular promise are the extraction of blurring information directly from the spatial images and improved noise abatement form investigations of select spatial regions and the elimination of spike noise
Bayesian interpretation of periodograms
The usual nonparametric approach to spectral analysis is revisited within the
regularization framework. Both usual and windowed periodograms are obtained as
the squared modulus of the minimizer of regularized least squares criteria.
Then, particular attention is paid to their interpretation within the Bayesian
statistical framework. Finally, the question of unsupervised hyperparameter and
window selection is addressed. It is shown that maximum likelihood solution is
both formally achievable and practically useful
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