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At least 19 records

Deblurring

In most instances, traditional EEG methodology provides insufficient spatial detail to identify relationships between brain electrical events and structures and functions visualized by magnetic resonance imaging or positron emission tomography. This article describes a method called Deblurring for increasing the spatial detail of the EEG and for fusing neurophysiologic and neuroanatomic data. Deblurring estimates potentials near the outer convexity of the cortex using a realistic finite element model of the structure of a subject's head determined from their magnetic resonance images. Deblurring is not a source localization technique and thus makes no assumptions about the number or type of generator sources. The validity of Deblurring has been initially tested by comparing deblurred data with potentials measured with subdural grid recordings. Results suggest that deblurred topographic maps, registered with a subject's magnetic resonance imaging and rendered in three dimensions, provide better spatial detail than has heretofore been obtained with scalp EEG recordings. Example results are presented from research studies of somatosensory stimulation, movement, language, attention and working memory. Deblurred ictal EEG data are also presented, indicating that this technique may have future clinical application as an aid to seizure localization and surgical planning.

Non-NASA Center↗

Deblurring galaxy images with Tikhonov regularization on magnitude domain

Abstract We propose a regularization-based deblurring method that works efficiently for galaxy images. The spatial resolution of a ground-based telescope is generally limited by seeing conditions and is much worse than space-based telescopes. This circumstance has generated considerable research interest in the restoration of spatial resolution. Since image deblurring is a typical inverse problem and often ill-posed, solutions tend to be unstable. To obtain a stable solution, much research has adopted regularization-based methods for image deblurring, but the regularization term is not necessarily appropriate for galaxy images. Although galaxies have an exponential or Sérsic profile, the conventional regularization assumes the image profiles to behave linearly in space. The significant deviation between the assumption and real situations leads to blurring of the images and smoothing out the detailed structures. Clearly, regularization on logarithmic domain, i.e., magnitude domain, should provide a more appropriate assumption, which we explore in this study. We formulate a problem of deblurring galaxy images by an objective function with a Tikhonov regularization term on a magnitude domain. We introduce an iterative algorithm minimizing the objective function with a primal–dual splitting method. We investigate the feasibility of the proposed method using simulation and observation images. In the simulation, we blur galaxy images with a realistic point spread function and add both Gaussian and Poisson noise. For the evaluation with the observed images, we use galaxy images taken by the Subaru HSC-SSP. Both of these evaluations show that our method successfully recovers the spatial resolution of the deblurred images and significantly outperforms the conventional methods. The code is publicly available from the GitHub 〈https://github.com/kzmurata-astro/PSFdeconv_amag〉.

Murata, Kazumi↗

Bayesian Spatially Varying Multi-Regularization Image Deblurring

Many scientific experiments such as those found in astronomy, geology, microbiology, and X-ray radiography require the use of high-energy instruments to capture images. Since blur and noise are inevitably present in any imaging system, the images must be \deblurred" to extract the full information content. Mathematically, image deblurring is an ill-posed inverse problem that requires regularization. The regularization, in turn, has a large effect on the deblurred image: different regularization strengths, and types, lead to drastically different reconstructions. Moreover, many images contain a mixture of smooth and sharp features which suggests the use of multi-regularization, i.e., varying the type of regularization (e.g. Tikhonov or total variation) across the image. We address these issues by formulating the image deblurring problem within a hierarchical Bayesian framework in which we spatially adapt the strength of the regularization and also vary the regularization type across the image. In this way, the image itself, along with corresponding regularization strength at each pixel, are described jointly by a posterior distribution which we can sample by Markov chain Monte Carlo (MCMC) methods. We illustrate our techniques on simplified test problems and apply them to high-energy X-ray images taken at the Nevada National Security Site. Numerical tests show that our new method is robustly applicable and increases the quality of the image reconstruction when compared to other (Bayesian) methods.

97 MATHEMATICS AND COMPUTING↗

Non-Blind Deblurring for Fluorescence: A Deformable Latent Space Approach with Kernel Parameterization

We report N\non-blind deblurring (NBD) is a modeling method of the image deblurring problem in computer vision, where the blurring kernel is known or can be externally estimated. In this paper, we attempt to solve a parametric NBD problem, inspired by the simultaneous acquisition of ptychography and fluorescent imaging (FI). Ptychography is an imaging method that favors larger probes, i.e. convolutional kernels, while FI relies on a small probe for high resolution. Also, the kernel can be solved during ptychographic reconstruction. With Ptycho-FI using the same larger kernel, we can perform NBD on the blurred fluorescent images to achieve high-resolution FI, and thus speed up the experiments. To this end, we design a deep latent space deformation network that is directly parameterized by the kernel. The network consists of three components: encoder, deformer, and decoder, where the deformer is specifically meant to rectify the latent space representations of blurred images to a standard latent space, regardless of the kernel. The deformation network is trained with a two-stage training scheme. We conduct extensive experiments to confirm that our parametric model can adapt to drastically different blurring kernels and perform robust deblurring.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Deblurring for nuclei: 3D characteristics of heavy-ion collisions

Observables from nuclear and high-energy experiments can be degraded by detector performance and/or methodology in extracting the observables, such as of the final-state characteristics of heavy-ion collisions in relation to a coarsely estimated reaction-plane direction. We propose the use of deblurring methods, such as in optics, to correct for observable degradation. Our main focus is the restoration of triple-differential particle distributions in heavy-ion collisions. We demonstrate that these could be extracted from collision measurements following the Richardson-Lucy deblurring method from optics. We illustrate basic features of the restoration methodology in a schematic model assuming either ideal or more realistic particle detection. Here, the inferred three-dimensional (3D) distributions for collisions may be easier to interpret in terms of collision dynamics and sought properties of bulk matter than the currently employed Fourier coefficients, that combine information from different azimuthal angles relative to the reaction plane.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Source function from two-particle correlation function through entropy-regularized Richardson-Lucy deblurring

Source functions are obtained from p – p and d – α correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the p – p and d – α correlation functions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

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.↗