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image deconvolution to Resolve Astronomical X-Ray Sources in Close Proximity: The NuSTAR images of SXP 15.3 and SXP 305

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ALGORITHMS 2025年第4期18卷 191-191页

作者： Bhattacharya, Sayantan Christodoulou, Dimitris M. Laycock, Silas G. T. Lowell Ctr Space Sci & Technol Lowell MA 01854 USA Tata Inst Fundamental Res Mumbai 400005 India DePaul Univ Dept Math Sci Chicago IL 60614 USA

The broad point spread function of the NuSTAR telescope makes resolving astronomical X-ray sources a challenging task, especially for off-axis observations. This limitation has affected the observations of the high-mass X-ray binary pulsars SXP 15.3 and SXP 305, in which pulsations are detected from nearly overlapping regions without spatially resolving these X-ray sources. To address this issue, we introduce a deconvolution algorithm designed to enhance NuSTAR's spatial resolution for closely spaced X-ray sources. We apply this technique to archival data and simulations of synthetic point sources placed at varying separations and locations, testing the algorithm's efficacy in source detection and differentiation. Our study confirms that on some occasions when SXP 305 is brighter, SXP 15.3 is also resolved, suggesting that some prior non-detections may have resulted from imaging limitations. This deconvolution technique represents a proof of concept test for analyzing crowded fields in the sky with closely spaced X-ray sources in future NuSTAR observations.

关键词： image deconvolution image resolution point spread function (PSF) X-ray astronomy X-ray binary pulsars (XRBs) NuSTAR X-ray telescope

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Hybrid Thresholding for image deconvolution in Expectation Maximization framework

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IMAGING SCIENCE JOURNAL 2025年第2期73卷 227-244页

作者： Pratap Singh, Ravi Kumar Singh, Manoj Banaras Hindu Univ BHU Inst Sci DST Ctr Interdisciplinary Math Sci DST CIMS Varanasi India Banaras Hindu Univ BHU Inst Sci Dept Comp Sci Varanasi 221005 India

In this study, we proposed an image deconvolution method in the expectation maximization (EM) framework. This method involves two steps: (i) E-step: utilizing the fast Fourier transform (FFT) for computationally efficient inversion of the convolution operator and (ii) M-step: employing the discrete wavelet transform (DWT) for estimating the original image from the image obtained in the E-step. In M-step, we proposed a modified L1-clipped penalty resulting in a hybrid thresholding scheme that integrates conventional hard and soft thresholds. This hybrid threshold ameliorates the inherent bias-variance trade-offs associated with traditional hard and soft thresholding schemes. The mathematical expressions for the risk, bias, and variance of the proposed hybrid threshold are derived and the performance is evaluated through simulation. Experimental results show that the proposed method achieves optimal values for variance and bias, thereby minimizing the risk. Moreover, the proposed method outperforms state-of-the-art methods in terms of performance metrics: PSNR, ISNR, and SSIM.

关键词： Expectation-maximization hard thresholding image deconvolution regularization soft thresholding wavelet deblurring risk analysis

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Blind image deconvolution: When Patch-wise Minimal Pixels Prior Meets Fractional-Order Method

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2025年第1期67卷 1-20页

作者： Wu, Tingting Wan, Shaojie Feng, Chenchen Zhang, Hao Zeng, Tieyong Nanjing Univ Posts & Telecommun Sch Sci Nanjing 210023 Peoples R China Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China

Blind image deconvolution is a challenging issue in image processing. In blind image deconvolution, the typical approach involves iteratively estimating both the blur kernel and latent image until convergence to the blur kernel of the observed image is achieved. Recently, several approaches have been attempted to develop a sophisticated regularization to obtain the clean image. However, existing methods often struggle to effectively handle ringing artifacts and local blur. To overcome these limitations, we introduce a fractional-order variational model. This model alleviates the ringing artifacts through the selection of an optimal derivative. Subsequently, to refine the latent image further, we leverage the local prior, namely patch-wise minimal pixels (PMP) prior. Since the PMP prior of clean images blocks is much sparser than that of blurred ones, it is capable of discriminating between clean and blurred image blocks. We illustrate the effective integration of the fractional-order operations and the PMP prior within our proposed approach. Moreover, the convergence of our algorithm has been proved as the values of the objective function monotonically decrease. Extensive experiments on different datasets demonstrate the superiority of the proposed method compared with other methods in terms of reconstruction quality for blind deconvolution.

关键词： image deconvolution Blind deconvolution Fractional order Ringing artifacts

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An Efficient Hybrid Threshold for image deconvolution in Expectation Maximization Framework

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2025年第3期44卷 1938-1982页

作者： Singh, Ravi Pratap Singh, Manoj Kumar Banaras Hindu Univ BHU Inst Sci DST Ctr Interdisciplinary Math Sci DST CIMS Varanasi 221005 India Banaras Hindu Univ BHU Inst Sci Dept Comp Sci Varanasi 221005 India

In this paper, we present a computationally efficient hybrid thresholding method for image deconvolution in the expectation maximization (EM) framework. The proposed method alternates between two key steps: an E-step that exploits the fast Fourier transform (FFT) for inversion of the convolution operator and an M-step that uses the discrete wavelet transform (DWT) for denoising. A modified L1-clipped penalty is introduced in the M-step for the computation of the maximum a posteriori (MAP) estimate, leading to a hybrid thresholding scheme, which is a combination of both hard and soft thresholds. Hard thresholding gives high variance, while soft thresholding leads to high bias in the restored image. The proposed hybrid threshold ameliorates the bias and variance trade-offs of the hard and soft thresholding schemes. Also, we performed a detailed mathematical and statistical analysis of the proposed hybrid threshold and computed the risk. The experimental results show that the proposed method attains optimal values for both variance and bias, leading to minimum risk, and also outperforms the state-of-the-art methods by a significant margin in terms of the performance metrics peak signal-to-noise ratio (PSNR) and improved signal-to-noise ratio (ISNR), as well as the visual quality.

关键词： Expectation-maximization Hard thresholding image restoration image deconvolution Wavelet Soft thresholding

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Noise variances and regularization learning gradient descent network for image deconvolution

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JOURNAL OF VISUAL COMMUNICATION AND image REPRESENTATION 2025年 107卷

作者： Kong, Shengjiang Wang, Weiwei Han, Yu Feng, Xiangchu Xidian Univ Sch Math & Stat Xian 710071 Peoples R China Tianshui Normal Univ Sch Math & Stat Tianshui 741001 Peoples R China Shenzhen Univ Coll Math Sci Shenzhen 518060 Peoples R China

Existing image deblurring approaches usually assume uniform Additive White Gaussian Noise (AWGN). However, the noise in real-world images is generally non-uniform AWGN and exhibits variations across different images. This work presents a deep learning framework for image deblurring that addresses nonuniform AWGN. We introduce a novel data fitting term within a regularization framework to better handle noise variations. Using gradient descent algorithm, we learn the inverse covariance of the non-uniform AWGN, the gradient of the regularization term, and the gradient adjusting factor from data. To achieve this, we unroll the gradient descent iteration into an end-to-end trainable network, where, these components are parameterized by convolutional neural networks. The proposed model is called the noise variances and regularization learning gradient descent network (NRL-GDN). Its major advantage is that it can automatically deal with both uniform and non-uniform AWGN. Experimental results on synthetic and real-world images demonstrate its superiority over existing baselines.

关键词： Non-uniform noise Deep convolutional neural network image deconvolution Gradient descent

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image deconvolution in spherical aberration-corrected high-resolution transmission electron microscopy

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ULTRAMICROSCOPY 2006年第6期106卷 539-546页

作者： Tang, C. Y. Chen, J. H. Zandbergen, H. W. Li, F. H. Chinese Acad Sci Inst Phys Beijing Natl Lab Condensed Matter Phys Beijing 100080 Peoples R China Delft Univ Technol Natl Ctr HREM Nanosci Dept NL-2628 CJ Delft Netherlands

The method of image deconvolution developed previously for FEG high-resolution transmission electron microscope (HRTEM) without a spherical aberration (C-s) corrector was for the first time applied to FEG HRTEM with a C-s-corrector. The principle and the procedure of image deconvolution are briefly described. Four qualified [110] images of Si were selected from a through-focus series to perform image deconvolution. The projected potential is successfully derived from all the images, and the obtained "dumbbell" structure maps of Si [110] are in good agreement with the calculated potential map. The criterion of selecting qualified images for performing image deconvolution is indicated. The possibility of applying image deconvolution to defect study and to ab initio crystal structure determination is discussed. (c) 2006 Elsevier B.V. All fights reserved.

关键词： C-s-corrected microscope image deconvolution high-resolution electron microscopy Si

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image deconvolution using a micro genetic algorithm

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OPTICS COMMUNICATIONS 1997年第1-3期140卷 6-10页

作者： Johnson, EG Abushagur, MAG UNIV ALABAMA DEPT ELECT & COMP ENGNHUNTSVILLEAL 35899

image deconvolution is addressed using a modified Genetic Algorithm for the error minimization, Numerical examples are presented to demonstrate the algorithm's robustness. Specifically, noise levels and various regions of support are investigated to verify the approach to the blind deconvolution problem of two positively constrained images. Good results were obtained using the algorithm in recovering images from their convolutions without any a priori information, other than the maximum bounds on their regions of support. (C) 1997 Elsevier Science B.V.

关键词： image deconvolution image processing image filtering design optimization

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image deconvolution using wavelet-based regularization

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JOURNAL OF ELECTRONIC IMAGING 2002年第1期11卷 5-10页

作者： Shen, LX Natl Univ Singapore Dept Math Singapore 117543 Singapore

In this paper, we propose a wavelet-based regularization algorithm for image deconvolution problems whose blurring filter is a low pass filter of an M-band wavelet. The perfect reconstruction formula of this M-band wavelet is used to establish our wavelet-based regularization algorithm. The simulations show that our proposed algorithm for image deconvolution performs better than that of the Wiener filter and some other wavelet-based deconvolution algorithms in terms of the improvement in signal-to-noise ratio, (C) 2002 SPIE and IST.

关键词： Wavelets deconvolution Linear filtering Signal to noise ratio Reconstruction algorithms Filtering (signal processing) image deconvolution Cameras image filtering Optical filters

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image deconvolution for defected crystals in field-emission high-resolution electron microscopy

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ULTRAMICROSCOPY 1997年第1-2期70卷 1-11页

作者： He, WZ Li, FH Chen, H Kawasaki, K Oikawa, T Chinese Acad Sci Inst Phys Beijing 100080 Peoples R China Chinese Acad Sci Ctr Condensed Matter Phys Beijing 100080 Peoples R China Jeol Ltd Tokyo 196 Japan

It is demonstrated that for images taken with a field-emission high-resolution electron microscope the image deconvolution based on the weak-phase object approximation is available for restoring the crystal defects with the resolution close to the information resolution limit. The image deconvolution is firstly carried out for simulated [110] images of perfect and defect Si crystal structure models with different thickness. The deconvoluted images reveal the atomic pairs as black dumbbells and show the correct atomic configuration including that at the twin boundary and near the 60 degrees dislocation core for the crystal thickness at least up to 76 Angstrom. An experimental [110] image of SiGe/Si has been restored to reveal an extended stacking fault sandwiched between two partial dislocations at the atomic level.

关键词： high-resolution electron microscopy image deconvolution crystal defect Si SiGe/Si

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image deconvolution in digital autoradiography: A preliminary study

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MEDICAL PHYSICS 2008年第2期35卷 522-530页

作者： Zhang, Mutian Chen, Qing Li, Xiao-Feng O'Donoghue, Joseph Ruan, Shutian Zanzonico, Pat Ling, C. Clifton Humm, John L. Mem Sloan Kettering Canc Ctr Dept Med Phys New York NY 10065 USA Columbia Univ Grad Sch Arts & Sci New York NY 10027 USA Mem Sloan Kettering Canc Ctr Nucl Med Serv Dept Radiol New York NY 10065 USA

Digital autoradiography (DAR) is a powerful method to determine quantitatively the "small-scale" (i.e., submillimeter) distribution of a radiotracer within a tissue section. However, the limited spatial resolution of the DAR image, due to blurring by the point spread function (PSF), can result in a poor correlation with tissue histology and immunohistochemistry. The authors attempt to overcome this limitation by recovering the radiotracer distribution by image deconvolution using the Richardson-Lucy algorithm and a measured PSF obtained from a small radioactive source on hydrophobic microscope slide. Simulation studies have shown that the deconvolution algorithm reliably recovers the pixel values corresponding to the radioactivity distributions. As an example, the proposed image restoration approach has been tested with DAR images of different radiolabeled markers on tumor sections obtained from clinical and preclinical animal model studies. Digital autoradiograms following deconvolution show improved sharpness and contrast relative to the unprocessed autoradiograms. (C) 2008 American Association of Physicists in Medicine.

关键词： digital autoradiography image deconvolution imaging plate point spread function Richardson-Lucy algorithm

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