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At least 37 records · Page 2

Signal deblurring

Proposed mathematical approaches to processing blurred signals

SIGNAL PROCESSING↗

Maximum entropy method applied to deblurring images on a MasPar MP-1 computer

A statistical inference method based on the principle of maximum entropy is developed for the purpose of enhancing and restoring satellite images. The proposed maximum entropy image restoration method is shown to overcome the difficulties associated with image restoration and provide the smoothest and most appropriate solution consistent with the measured data. An implementation of the method on the MP-1 computer is described, and results of tests on simulated data are presented.

Bonavito, N. L.↗

Image sharpening by holography.

Discussion of the physical and mathematical fundamentals, performance capabilities and potential applications of image deblurring by holography. It is shown that a blurred photograph may be deblurred and a sharpened image extracted from it because the 'blurring' in the original photograph did not irretrievably lose the imaging information, notably in the spatial-frequency regions required for faithful imaging and for high resolution. The principles of optical image deblurring are highly mathematical in nature. One of the most important applications of holographic image deblurring is shown to be the sharpening of electron micrographs of biological specimens beyond the ultimate that can be achieved with even the most powerful instruments available.

Stroke, G. W.↗

Image enhancement by holography.

The speed of the holographic image deblurring method has recently been further enhanced by a new speed in the realization of the powerful holographic image-deblurring filter. The filter makes it possible to carry out the deblurring, in the optical computer used, in times of the order of one second. The experimental achievements using the holographic image-enhancement method are illustrated with examples ranging from out-of-focus or motion-blurred photographs, including 'amateur' photos recorded on Polaroid film, to the sharpening of the best available electron micrographs of viruses. Images recorded with X-rays, notably from rocket-borne photos of the sun, and out-of-focus photographs from cameras in NASA satellites have been similarly deblurred.

Stroke, G. W.↗

Deconvoluting experimental decay energy spectra: The O 26 case

In nuclear reaction experiments, the measured decay energy spectra can give insights into the shell structure of decaying systems. However, extracting the underlying physics from the measurements is challenging due to detector resolution and acceptance effects. The Richardson-Lucy (RL) algorithm, a deblurring method that is commonly used in optics and has proven to be a successful technique for restoring images, was applied to our experimental nuclear physics data. The only inputs to the method are the observed energy spectrum and the detector's response matrix also known as the transfer matrix. We demonstrate that the technique can help access information about the shell structure of particle-unbound systems from the measured decay energy spectrum that is not immediately accessible via traditional approaches such as χ-square fitting. For a similar purpose, we developed a machine learning model that uses a deep neural network (DNN) classifier to identify resonance states from the measured decay energy spectrum. We tested the performance of both methods on simulated data and experimental measurements. Then, we applied both algorithms to the decay energy spectrum of 26 O → 24 O + n + n measured via invariant mass spectroscopy. Here, the resonance states restored using the RL algorithm to deblur the measured decay energy spectrum agree with those found by the DNN classifier. Both deblurring and DNN approaches suggest that the raw decay energy spectrum of 26 O exhibits three peaks at approximately 0.15 MeV, 1.50 MeV, and 5.00 MeV, with half-widths of 0.29 MeV, 0.80 MeV, and 1.85 MeV, respectively.

Spectrometers & spectroscopic techniques↗

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.

Hite, Gerald E.↗

Optical computing.

Applications of the optical computer include an approach for increasing the sharpness of images obtained from the most powerful electron microscopes and fingerprint/credit card identification. The information-handling capability of the various optical computing processes is very great. Modern synthetic-aperture radars scan upward of 100,000 resolvable elements per second. Fields which have assumed major importance on the basis of optical computing principles are optical image deblurring, coherent side-looking synthetic-aperture radar, and correlative pattern recognition. Some examples of the most dramatic image deblurring results are shown.

Stroke, G. W.↗

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.

Hite, Gerald E.↗

CodEx: A Modular Framework for Joint Temporal De-Blurring and Tomographic Reconstruction

In many computed tomography (CT) imaging applications, it is important to rapidly collect data from an object that is moving or changing with time. Tomographic acquisition is generally assumed to be step-and-shoot, where the object is rotated to each desired angle, and a view is taken. However, step-and-shoot acquisition is slow and can waste photons, so in practice fly-scanning is done where the object is continuously rotated while collecting data. However, this can result in motion-blurred views and consequently reconstructions with severe motion artifacts. In this paper, we introduce CodEx, a modular framework for joint de-blurring and tomographic reconstruction that can effectively invert the motion blur introduced in sparse view fly-scanning. The method is a synergistic combination of a novel acquisition method with a novel non-convex Bayesian reconstruction algorithm. CodEx works by encoding the acquisition with a known binary code that the reconstruction algorithm then inverts. Using a well chosen binary code to encode the measurements can improve the accuracy of the inversion process. The CodEx reconstruction method uses the alternating direction method of multipliers (ADMM) to split the inverse problem into iterative deblurring and reconstruction sub-problems, making reconstruction practical to implement. Here we present reconstruction results on both simulated and binned experimental data to demonstrate the effectiveness of our method.

42 ENGINEERING↗

A Hierarchical Gibbs Sampler for Spatially Varying Multi-Regularization Image Reconstructions

This is a presentation for SIAM's (Society for Industrial and Applied Mathematics) conference on computational science and engineering. This presentation describes research on novel techniques to deblur images under a Bayesian framework. The title of the conference is SIAM Conference on Computational Science and Engineering (CSE21). This is a VIRTUAL conference; it was originally scheduled in Fort Worth, TX. The conference dates are March 1-5, 2021. The link to the conference's website is https://www.siam.org/conferences/cm/conference/cse21

97 MATHEMATICS AND COMPUTING↗

Sequential Image Recovery Using Joint Hierarchical Bayesian Learning

Abstract Recovering temporal image sequences (videos) based on indirect, noisy, or incomplete data is an essential yet challenging task. We specifically consider the case where each data set is missing vital information, which prevents the accurate recovery of the individual images. Although some recent (variational) methods have demonstrated high-resolution image recovery based on jointly recovering sequential images, there remain robustness issues due to parameter tuning and restrictions on the type of sequential images. Here, we present a method based on hierarchical Bayesian learning for the joint recovery of sequential images that incorporates prior intra- and inter-image information. Our method restores the missing information in each image by “borrowing” it from the other images. More precisely, we couple sequential images by penalizing their pixel-wise difference. The corresponding penalty terms (one for each pixel and pair of subsequent images) are treated as weakly-informative random variables that favor small pixel-wise differences but allow occasional outliers. As a result, all of the individual reconstructions yield improved accuracy. Our method can be used for various data acquisitions and allows for uncertainty quantification. Some preliminary results indicate its potential use for sequential deblurring and magnetic resonance imaging.

Xiao, Yao↗

Phase-weighted slant stacking for surface wave dispersion measurement

SUMMARY Surface wave retrieval from ambient noise records using seismic interferometry techniques has been widely used for multiscale shear wave velocity (Vs) imaging. One key step during Vs imaging is the generation of dispersion spectra and the extraction of a reliable dispersion curve from the retrieved surface waves. However, the sparse array geometry usually affects the ability for high-frequency (>1 Hz) seismic signals’ acquisition. Dispersion measurements are degraded by array response due to sparse sampling and often present smeared dispersion spectra with sidelobe artefacts. Previous studies usually focus on interferograms’ domain (e.g. cross-correlation function) and attempt to enhance coherent signals before dispersion measurement. We propose an alternative technique to explicitly deblur dispersion spectra through use of a phase-weighted slant-stacking algorithm. Numerical examples demonstrate the strength of the proposed technique to attenuate array responses as well as incoherent noise. Three different field examples prove the flexibility and superiority of the proposed technique: the first data set consists of ambient noise records acquired using a nodal seismometer array; the second data set utilizes distributed acoustic sensing (DAS) and a marine fibre-optic cable to acquire a similar ambient noise data set; the last data set is a vibrator-based active-source surface wave data. The enhanced dispersion measurements provide cleaner and higher-resolution spectra without distortions which will assist both human interpreters as well as ML algorithms in efficiently picking curves for subsequent Vs inversion.

58 GEOSCIENCES↗

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]↗