Blind image deblurring using jump regression analysis

Qiu, Peihua; Kang, Yicheng

doi:10.5705/ss.2014.054

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…There are several future research directions for extending our current work. For instance, in some image processing applications, observed images could contain spatial blur (e.g., Kang, 2020; Kang et al, 2018; Qiu & Kang, 2015) in addition to random noise. Our method does not handle blurred images and thus new methods should be developed.…”

Section: Discussionmentioning

confidence: 99%

Statistical quality control using image intelligence: A sparse learning approach

Kang

2022

Naval Research Logistics

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Advances in image acquisition technology have made it convenient and economic to collect large amounts of image data. In manufacturing and service industries, images are increasingly used for quality control purposes because of their ability to quickly provide information about product geometry, surface defects, and nonconforming patterns. In production line monitoring, image data often take the form of image streams in the sense that images from the process are being collected over time. In such applications, a fundamental task is to properly analyze image data streams. This image monitoring problem is challenging for several reasons. First, images often have complicated structures such as edges and singularities, which render many traditional smoothing methods inapplicable. Second, a typical grayscale image contains tens of thousands of pixels, so the data is high-dimensional. It has been shown in the statistical process control (SPC) literature that conventional multivariate control charts have limited power of detecting process shifts when the data dimension is high. In this article, we propose to transform images using a two-dimensional wavelet basis and monitor the wavelet coefficients by sparse learning-based multivariate control charts. By adapting the sparse learning algorithm to our quality control problem, the proposed method is able to detect shifts in the wavelet coefficients in a timely fashion and simultaneously identify those shifted coefficients. Combining this feature with the localization property of the wavelet basis, our method also enables accurate diagnosis of faulty image regions. In addition, the proposed charting statistics have explicit formulas, so they are easy to compute. Theoretical justifications and numerical comparisons with an existing method show that our method works well in applications.

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Section: Discussionmentioning

confidence: 99%

Statistical quality control using image intelligence: A sparse learning approach

Kang

2022

Naval Research Logistics

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“…The method without the parametric assumption on h was published in Qiu (2008). Another follow-up research to make the methods more flexible was published in Qiu and Kang (2015).…”

Section: Peter Was Selected As the Buehler-martin Lecturer By The Schmentioning

confidence: 99%

Peter Hall: My Mentor, Collaborator and Friend

Qiu¹

2018

STAT SINICA

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Peter Hall has left us for about a year. His passing is an irreplaceable loss to our entire statistical community. To me, I lost a long-time mentor, collaborator and friend. In this article, I will share with readers certain episodes in my career during which Peter provided me much precious help, things that I learned from him about research and our research attitude, our research collaborations, and some others. I know that I am only one of many statisticians who ever benefited from Peter's generosity in helping others, especially young researchers. My example could perfectly demonstrate the importance and influence of Peter and his generosity on our growth and career development.

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“…Further generalizations to the case where the observed image also experiences some spatial blur but the pointwise error remains serially uncorrelated are also available, see e.g. Kang and Qiu (2014) and Qiu and Kang (2015). With this background in mind, our model (1.2) effectively amounts to the generalization of the 1-dimensional NJRM to the case of serially correlated errors.…”

Section: Introductionmentioning

confidence: 99%

ACF estimation via difference schemes for a semiparametric model with $m$-dependent errors

Levine¹,

Tecuapetla-Gómez²

2019

Preprint

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We discuss a class of difference-based estimators of the autocovariance function in a semiparametric regression model where the signal consists of the sum of an identifiable smooth function and another function with jumps (change points) and the errors are m-dependent. We establish that the influence of the smooth part of the signal over the bias of our estimators is negligible; this result does not depend on any distributional assumption. Under Gaussianity of the errors, we show that the mean squared error of the proposed estimators does not depend on either the unknown smooth function or on the values of the difference sequence coefficients; our finite sample studies suggest that the latter feature holds true regardless of the Gaussianity assumption. We also allow that both the number of change points and the magnitude of the largest jump grow with the sample size. In this case, we provide conditions on the interplay between the growth rate of these two quantities in order to ensure √ n consistency of our estimators.

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Blind image deblurring using jump regression analysis

Abstract: This supplementary file contains a description of the roof/valley edge detection procedure, proofs of the theoretical results presented in Section 3 of the paper, and some simulation results about the proposed method.

Cited by 8 publications

References 6 publications

Statistical quality control using image intelligence: A sparse learning approach

Statistical quality control using image intelligence: A sparse learning approach

Peter Hall: My Mentor, Collaborator and Friend

ACF estimation via difference schemes for a semiparametric model with $m$-dependent errors

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