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A novel sure based criterion for parametric psf estimation

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A novel sure based criterion for parametric psf estimation

  1. 1. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com A NOVEL SURE-BASED CRITERION FOR PARAMETRIC PSF ESTIMATION By A PROJECT REPORT Submitted to the Department of electronics &communication Engineering in the FACULTY OF ENGINEERING & TECHNOLOGY In partial fulfillment of the requirements for the award of the degree Of MASTER OF TECHNOLOGY IN ELECTRONICS &COMMUNICATION ENGINEERING APRIL 2016
  2. 2. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com CERTIFICATE Certified that this project report titled “A Novel SURE-Based Criterion for Parametric PSF Estimation” is the bonafide work of Mr. _____________Who carried out the research under my supervision Certified further, that to the best of my knowledge the work reported herein does not form part of any other project report or dissertation on the basis of which a degree or award was conferred on an earlier occasion on this or any other candidate. Signature of the Guide Signature of the H.O.D Name Name
  3. 3. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com DECLARATION I hereby declare that the project work entitled “A Novel SURE-Based Criterion for Parametric PSF Estimation” Submitted to BHARATHIDASAN UNIVERSITY in partial fulfillment of the requirement for the award of the Degree of MASTER OF APPLIED ELECTRONICS is a record of original work done by me the guidance of Prof.A.Vinayagam M.Sc., M.Phil., M.E., to the best of my knowledge, the work reported here is not a part of any other thesis or work on the basis of which a degree or award was conferred on an earlier occasion to me or any other candidate. (Student Name) (Reg.No) Place: Date:
  4. 4. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ACKNOWLEDGEMENT I am extremely glad to present my project “A Novel SURE-Based Criterion for Parametric PSF Estimation” which is a part of my curriculum of third semester Master of Science in Computer science. I take this opportunity to express my sincere gratitude to those who helped me in bringing out this project work. I would like to express my Director,Dr. K. ANANDAN, M.A.(Eco.), M.Ed., M.Phil.,(Edn.), PGDCA., CGT., M.A.(Psy.)of who had given me an opportunity to undertake this project. I am highly indebted to Co-OrdinatorProf. Muniappan Department of Physics and thank from my deep heart for her valuable comments I received through my project. I wish to express my deep sense of gratitude to my guide Prof. A.Vinayagam M.Sc., M.Phil., M.E., for her immense help and encouragement for successful completion of this project. I also express my sincere thanks to the all the staff members of Computer science for their kind advice. And last, but not the least, I express my deep gratitude to my parents and friends for their encouragement and support throughout the project.
  5. 5. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ABSTRACT: We propose an unbiased estimate of a filtered version of the mean squared error—the blur-SURE (Stein’s unbiased risk estimate)—as a novel criterion for estimating an unknown point spread function (PSF) from the degraded image only. The PSF is obtained by minimizing this new objective functional over a family of Wiener processings. Based on this estimated blur kernel, we then perform nonblind deconvolution using our recently developed algorithm. The SURE-based framework is exemplified with a number of parametric PSF, involving a scaling factor that controls the blur size. A typical example of such parametrization is the Gaussian kernel. The experimental results demonstrate that minimizing the blur-SURE yields highly accurate estimates of the PSF parameters, which also result in a restoration quality that is very similar to the one obtained with the exact PSF, when plugged into our recent multi-Wiener SURE-LET deconvolution algorithm. The highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on SURE-like estimates.
  6. 6. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com INTRODUCTION: AS A Standard linear inverse problem, image deconvolution has been an important image processing topic for several decades ,In many real applications,e.g., medical imaging uorescence microscopy, astronomical imaging, remote sensing, and photography the point spread fucntion (PSF) may not be easily and accurately obtained. Blind deconvolution amounts to estimating both the original image and the PSF, given the observed data only. In order to address the ill- posedness of the problem, a standard approach consists in enforcing certain regularity conditions (possibly derived from Bayesian priors) on the original image and the PSF, and in formulating the problem as the optimization of a proper objective functional. Recent studies of the standard techniques can be found in and the interested reader may refer to and for a comprehensive review. Other optimization methods are also able to estimate simultaneously both the original image and the PSF (see for example). It is, However, also possible to perform the estimation of the image and the PSF separately; i.e., first estimate the PSF, and then perform non-blind deconvolution to obtain the restored image. Compared to the joint estimation, the separate estimation seems more advantageous in practice, because it allows to apply any developed high-quality non-blind deconvolution algorithm, once the PSF is estimated. In this work, it is this approach that we have chosen and since we have already developed a very efficient non-blind deconvolution algorithm , we are going to focus here on PSF estimation. Note that the accuracy of PSF estimation is very significant for the deconvolution performance: an inaccurately estimated kernel often results in substantial quality loss of the restored image. A. Non-Parametric PSF Estimation If the PSF is represented by the discrete pixel values without any parametric form, the estimation is usually performed by regularization or Bayesian approach, depending on the assumption on the unknown PSF. The common choices of the regularization on the blur kernel include: • Tikhonov 2 -Norm Effective estimation of smooth PSF like Gaussian blur; • TV (Total Variation)-Norm , Suitable for motion blur and out-of-focus blur; • Sparsity Prior, Effective for camera shake and motion blur.
  7. 7. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com B. Parametric PSF Estimation In specific applications, the parametric forms of the PSF can be either theoretically available or practically assumed. In this context, the PSF is completely characterized by a small number of parameters, which dramatically reduces the degrees of freedom of PSF estimation. Typical examples of the parametric model can be found in the applications of linear motion blur. fluorescence microscopy , atmospheric turbulence, and astronomical imaging. For linear motion blur, the blur orientation and length (i.e. the PSF parameters) can be estimated by cepstrum analysis, steerable filter method,or Radon transform. In the case of a Gaussian kernel, the Gaussian variance representing blur size is the only parameter to be estimated. APEX estimated the blur size by fitting the Gaussian blur to the blurred image, utilizing the property of is known, we formulate the estimation of H as the following minimization problem: min H 1 N HfH(y)−H0x 2 where the subscript H in f H emphasizes the dependence, of the processing f on the matrix H. Particularly, in the context of deconvolution, the processing f could be any non-blind deconvolution algorithms (e.g. multi- Wiener SURE-LET, or BM3D, algorithm), depending on the matrix H. Experimentally, we found that given the processing f H, the blur-MSE minimization yields a highly accurate estimate of H0. However, since the ‘arbitrary’ processing f H can be very complicated, our approach, to be described below, is to restrict f to a subclass of processings—typically, Wiener filterings— that also depend on H, and then minimize this blur-MSE (actually, an estimate of this blur-MSE) over H. In this simplified setting, we will be able to demonstrate the link between the result of this minimization and the ground truth PSF. C. SURE-Based Approach A statistical non-Bayesian approach based on the minimization of Stein’s unbiased risk estimate (SURE) ,has been proposed for solving linear inverse problem under additive Gaussian noise assumption. SURE, as an unbiased estimate of the mean squared error (MSE), has been intensively used as a criterion for signal restoration, e.g. image denoising, and non-blind image deconvolution . The key advantage of the SURE-based approach is that it does not require any
  8. 8. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com prior knowledge of the original image. In the present paper, we further extend the SURE-based approach to blind PSF parameter estimation. More specifically, we propose a filtered version of the SURE—“blur-SURE”—as a new criterion for PSF estimation. To exemplify this framework, we consider the parametric forms of PSF, which involve a scaling factor that controls the blur size and estimate. The factor from the degraded image only. A typical example is the Gaussian function. Once the PSF is estimated, we carry out our developed non-blind deconvolution algorithm. D. Paper Organization Section II proposes a novel criterion for PSF estimation: the blur-MSE—a filtered version of the MSE—incorporating a simple Wiener filtering. In Section III, we present the blur-SURE—an unbiased estimate of the blur-MSE defined in Section II, and formulate the PSF estimation as a blur-SURE minimization. Section IV exemplifies the blur-SURE framework with several types of PSF, and proposes an efficient minimization algorithm. Section V reports and discusses the experimental results. Throughout this paper, we use boldface lowercase letters, e.g. x ∈ R N, to denote N-dimensional real vectors, where N is typically the number of pixels in an image. The n-th element of x is written as x n. The linear (matrices) and non-linear transformationsR N →R M are denoted by boldface uppercase letters, e.g. H ∈ R M×N. HT ∈ R N×M denotes the transpose of matrix H. Also note that we use the subscript (·) 0 to denote the true (“ground truth”) quantity of (·); for example, matrix H0 is the true quantity of H.
  9. 9. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com CONCLUSION: In this paper, we proposed a parametric PSF estimation method based on a new criterion—the “blur-SURE”.We have shown that in conjunction with Wiener filtering,the minimization of the blur-SURE yields highly accurate PSF estimations. The blur-SURE framework is exemplified by several parametric forms of PSF. For fast implementation,we also proposed an efficient algorithm for performing the blur-SURE minimization. The results obtained show that, pipelining this novel PSF estimation method with our non-blind multi-Wiener SURE-LET deconvolution algorithm, results in a blind deconvolution algorithm which outperforms other approaches numerically, visually, and in terms of computational efficiency. The examples of blur kernels listed in this paper are only a small subset of possible models. It is worth emphasizing that the blur-SURE minimization itself does not specify any particular parametric form for the PSF. In addition, it should be noted that the blur-SURE criterion is not limited to 2D signals: it can be extended painlessly to 3D (or any other dimension). It is not limited either to additive Gaussian noise: the blur-SURE expression can also be adapted to any noise type for which an unbiased risk estimate can be devised ,Hence, despite its apparent phase limitation, we believe that this criterion has a huge potential in the development of specific algorithms for various applications; e.g. fluorescence microscopy.
  10. 10. OUR OFFICES @CHENNAI/ TRICHY / KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: +91 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com REFERENCES: [1] H. Liao and M. K. Ng, “Blind deconvolution using generalized crossvalidation approach to regularization parameter estimation,” IEEE Trans.Image Process., vol. 20, no. 3, pp. 670–680, Mar. 2011. [2] M. S. C. Almeida and L. B. Almeida, “Blind and semi-blind deblurring of natural images,” IEEE Trans. Image Process., vol. 19, no. 1, pp. 36–52, Jan. 2010. [3] S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Variational Bayesian blind deconvolution using a total variation prior,” IEEE Trans. Image Process., vol. 18, no. 1, pp. 12–26, Jan. 2009. [4] J. Bolte, P. L. Combettes, and J.-C. Pesquet, “Alternating proximal algorithm for blind image recovery,” in Proc. 17th IEEE Int. Conf. Image Process., Hong Kong, Sep. 2010, pp. 1673–1676. [5] T. Bishop, S. Babacan, B. Amizic, A. Katsaggelos, T. F. Chan, and R. Molina, “Blind image deconvolution: Problem formulation and existing approaches,” 2007. [6] F. Xue, F. Luisier, and T. Blu, “Multi-Wiener SURE-LET deconvolution,” IEEE Trans. Image Process., vol. 22, no. 5, pp. 1954–1968,May 2013. [7] Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graph., vol. 27, no. 3, Aug. 2008, Art. ID 73. [8] L. Chen and K.-H. Yap, “A soft double regularization approach to parametric blind image deconvolution,” IEEE Trans. Image Process., vol. 14, no. 5, pp. 624–633, May 2005.

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