Efficient blind image restoration using discrete periodic Radon transform

Author name used in this publication: Daniel P. K. LunAuthor name used in this publication: David Dagan FengCentre for Multimedia Signal Processing, Department of Electronic and Information Engineering2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Blind Image Deblurring Driven by Nonlinear Processing in the Edge Domain

This work addresses the problem of blind image deblurring, that is, of recovering an original image observed through one or more unknown linear channels and corrupted by additive noise. We resort to an iterative algorithm, belonging to the class of Bussgang algorithms, based on alternating a linear and a nonlinear image estimation stage. In detail, we investigate the design of a novel nonlinear processing acting on the Radon transform of the image edges. This choice is motivated by the fact that the Radon transform of the image edges well describes the structural image features and the effect of blur, thus simplifying the nonlinearity design. The effect of the nonlinear processing is to thin the blurred image edges and to drive the overall blind restoration algorithm to a sharp, focused image. The performance of the algorithm is assessed by experimental results pertaining to restoration of blurred natural images

Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Blind Restoration of Motion Blurred Barcode Images using Ridgelet Transform and Radial Basis Function Neural Network

The aim of any image restoration techniques is recovering the original image from a degraded observation. One of the most common degradation phenomena in images is motion blur. In case of blind image restoration accurate estimation of motion blur parameters is required for deblurring of such images. This paper proposed a novel technique for estimating the parameters of motion blur using ridgelet transform. Initially, the energy of ridgelet coefficients is used to estimate the blur angle and then blur length is estimated using a radial biases function neural network. This work is tested on different barcode images with varying parameters of blur. The simulation results show that the proposed method improves the restoration performance

Fast and Scalable Architectures and Algorithms for the Computation of the Forward and Inverse Discrete Periodic Radon Transform with Applications to 2D Convolutions and Cross-Correlations

The Discrete Radon Transform (DRT) is an essential component of a wide range of applications in image processing, e.g. image denoising, image restoration, texture analysis, line detection, encryption, compressive sensing and reconstructing objects from projections in computed tomography and magnetic resonance imaging. A popular method to obtain the DRT, or its inverse, involves the use of the Fast Fourier Transform, with the inherent approximation/rounding errors and increased hardware complexity due the need for floating point arithmetic implementations. An alternative implementation of the DRT is through the use of the Discrete Periodic Radon Transform (DPRT). The DPRT also exhibits discrete properties of the continuous-space Radon Transform, including the Fourier Slice Theorem and the convolution property. Unfortunately, the use of the DPRT has been limited by the need to compute a large number of additions O(N^3) and the need for a large number of memory accesses. This PhD dissertation introduces a fast and scalable approach for computing the forward and inverse DPRT that is based on the use of: (i) a parallel array of fixed-point adder trees, (ii) circular shift registers to remove the need for accessing external memory components when selecting the input data for the adder trees, and (iii) an image block-based approach to DPRT computation that can fit the proposed architecture to available resources, and as a result, for an NxN image (N prime), the proposed approach can compute up to N^2 additions per clock cycle. Compared to previous approaches, the scalable approach provides the fastest known implementations for different amounts of computational resources. For the fastest case, I introduce optimized architectures that can compute the DPRT and its inverse in just 2N +ceil(log2 N)+1 and 2N +3(log2 N)+B+2 clock cycles respectively, where B is the number of bits used to represent each input pixel. In comparison, the prior state of the art method required N^2 +N +1 clock cycles for computing the forward DPRT. For systems with limited resources, the resource usage can be reduced to O(N) with a running time of ceil(N/2)(N + 9) + N + 2 for the forward DPRT and ceil(N/2)(N + 2) + 3ceil(log2 N) + B + 4 for the inverse. The results also have important applications in the computation of fast convolutions and cross-correlations for large and non-separable kernels. For this purpose, I introduce fast algorithms and scalable architectures to compute 2-D Linear convolutions/cross-correlations using the convolution property of the DPRT and fixed point arithmetic to simplify the 2-D problem into a 1-D problem. Also an alternative system is proposed for non-separable kernels with low rank using the LU decomposition. As a result, for implementations with enough resources, for a an image and convolution kernel of size PxP, linear convolutions/cross correlations can be computed in just 6N + 4 log2 N + 17 clock cycles for N = 2P-1. Finally, I also propose parallel algorithms to compute the forward and inverse DPRT using Graphic Processing Units (GPUs) and CPUs with multiple cores. The proposed algorithms are implemented in a GPU Nvidia Maxwell GM204 with 2048 cores@1367MHz, 348KB L1 cache (24KB per multiprocessor), 2048KB L2 cache (512KB per memory controller), 4GB device memory, and compared against a serial implementation on a CPU Intel Xeon E5-2630 with 8 physical cores (16 logical processors via hyper-threading)@3.2GHz, L1 cache 512K (32KB Instruction cache, 32KB data cache, per core), L2 cache 2MB (256KB per core), L3 cache 20MB (Shared among all cores), 32GB of system memory. For the CPU, there is a tenfold speedup using 16 logical cores versus a single-core serial implementation. For the GPU, there is a 715-fold speedup compared to the serial implementation. For real-time applications, for an 1021x1021 image, the forward DPRT takes 11.5ms and 11.4ms for the inverse

Unbiased risk estimate algorithms for image deconvolution.

本論文工作的主題是圖像反卷積問題。在很多實際應用，例如生物醫學成像，地震學，天文學，遙感和光學成像中，觀測數據經常會出現令人不愉快的退化現象，這種退化一般由模糊效應(例如光學衍射限條件)和噪聲汙染(比如光子計數噪聲和讀出噪聲)造成的，這兩者都是物理儀器自身的條件限制造成的。作為一個標准的線性反問題，圖像反卷積經常被用作恢複觀測到的模糊的有噪點的圖像。我們旨在基于無偏差風險估計准則研究新的反卷積算法。本論文工作主要分為以下兩大部分。首先，我們考慮在加性高斯白噪聲條件下的圖像非盲反卷積問題，即准確的點擴散函數已知。我們的研究准則是最小化均方誤差的無偏差估計，即SURE. SURE- LET方法最初被應用于圖像降噪問題。本論文工作擴展該方法至討論圖像反卷積問題.我們提出了一個新的SURE-LET算法，用于快速有效地實現圖像複原功能。具體而言，我們將反卷積過程參數化表示為有限個基本函數的線性組合，稱作LET方法。反卷積問題最終簡化為求解該線性組合的最優線性系數。由于SURE的二次項本質和線性參數化表示，求解線性系數可由求解線性方程組而得。實驗結果顯示該論文提出的方法在信噪比，圖像的視覺質量和運算時間等方面均優于其他迄今最優秀的算法。論文的第二部分討論圖像盲複原中的點擴散函數估計問題。我們提出了blur-SURE -一個均方誤差修正版的無偏差估計 - 作為點擴散函數估計的最新准則，即點擴散函數由最小化這個新的目標函數獲得。然後我們利用這個估計的點擴散函數，用第一部分所提出的SURE-LET算法進行圖像的非盲複原。我們以一些典型的點擴散函數形式(高斯函數最為典型)為例詳細闡述該blur-SURE理論框架。實驗結果顯示最小化blur-SURE能夠更准確的估計點擴散函數，從而獲得更加優越的反卷積佳能。相比于圖像非盲複原，盲複原所得的圖片的視覺質量損失可忽略不計。本論文所提出的基于無偏差估計的算法可擴展至其他噪聲模型。由于本論文以SURE基礎的方法在理論上並不僅限于卷積問題，該方法可用于解決數據的其他線性失真問題。The subject of this thesis is image deconvolution. In many real applications, e.g. biomedical imaging, seismology, astronomy, remote sensing and optical imaging, undesirable degradations by blurring effect (e.g. optical diffraction-limited condition) and noise corruption (e.g. photon-counting noise and readout noise) are inherent to any physical acquisition device. Image deconvolution, as a standard linear inverse problem, is often applied to recover the images from their blurred and noisy observations. Our interest lies in novel deconvolution algorithms based on unbiased risk estimate. This thesis is organized in two main parts as briefly summarized below.We first consider non-blind image deconvolution with the corruption of additive white Gaussian noise (AWGN), where the point spread function (PSF) is exactly known. Our driving principle is the minimization of an unbiased estimate of mean squared error (MSE) between observed and clean data, known as "Stein's unbiased risk estimate" (SURE). The SURE-LET approach, which was originally developed for denoising, is extended to the deconvolution problem: a new SURE-LET deconvolution algorithm for fast and efficient implementation is proposed. More specifically, we parametrize the deconvolution process as a linear combination of a small number of known basic processings, which we call the linear expansion of thresholds (LET), and then minimize the SURE over the unknown linear coefficients. Due to the quadratic nature of SURE and the linear parametrization, the optimal linear weights of the combination is finally achieved by solving a linear system of equations. Experiments show that the proposed approach outperforms other state-of-the-art methods in terms of PSNR, SSIM, visual quality, as well as computation time.The second part of this thesis is concerned with PSF estimation for blind deconvolution. We propose a "blur-SURE" - an unbiased estimate of a filtered version of MSE - as a novel criterion for estimating the PSF, from the observed image only, i.e. the PSF is identified by minimizing this new objective functional, whose validity has been theoretically verified. The blur-SURE framework is exemplified with a number of parametric forms of the PSF, most typically, the Gaussian kernel. Experiments show that the blur-SURE minimization yields highly accurate estimate of PSF parameters. We then perform non-blind deconvolution using the SURE-LET algorithm proposed in Part I, with the estimated PSF. Experiments show that the estimated PSF results in superior deconvolution performance, with a negligible quality loss, compared to the deconvolution with the exact PSF.One may extend the algorithms based on unbiased risk estimate to other noise model. Since the SURE-based approaches does not restrict themselves to convolution operation, it is possible to extend them to other distortion scenarios.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Xue, Feng.Thesis (Ph.D.)--Chinese University of Hong Kong, 2013.Includes bibliographical references (leaves 119-130).Abstracts also in Chinese.Dedication --- p.iAcknowledgments --- p.iiiAbstract --- p.ixList of Notations --- p.xiContents --- p.xviList of Figures --- p.xxList of Tables --- p.xxiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivations and objectives --- p.1Chapter 1.2 --- Mathematical formulation for problem statement --- p.2Chapter 1.3 --- Survey of non-blind deconvolution approaches --- p.2Chapter 1.3.1 --- Regularization --- p.2Chapter 1.3.2 --- Regularized inversion followed by denoising --- p.4Chapter 1.3.3 --- Bayesian approach --- p.4Chapter 1.3.4 --- Remark --- p.5Chapter 1.4 --- Survey of blind deconvolution approaches --- p.5Chapter 1.4.1 --- Non-parametric blind deconvolution --- p.5Chapter 1.4.2 --- Parametric blind deconvolution --- p.7Chapter 1.5 --- Objective assessment of the deconvolution quality --- p.8Chapter 1.5.1 --- Peak Signal-to-Noise Ratio (PSNR) --- p.8Chapter 1.5.2 --- Structural Similarity Index (SSIM) --- p.8Chapter 1.6 --- Thesis contributions --- p.9Chapter 1.6.1 --- Theoretical contributions --- p.9Chapter 1.6.2 --- Algorithmic contributions --- p.10Chapter 1.7 --- Organization --- p.11Chapter I --- The SURE-LET Approach to Non-blind Deconvolution --- p.13Chapter 2 --- The SURE-LET Framework for Deconvolution --- p.15Chapter 2.1 --- Motivations --- p.15Chapter 2.2 --- Related work --- p.15Chapter 2.3 --- Problem statement --- p.17Chapter 2.4 --- Stein's Unbiased Risk Estimate (SURE) for deconvolution --- p.17Chapter 2.4.1 --- Original SURE --- p.17Chapter 2.4.2 --- Regularized approximation of SURE --- p.18Chapter 2.5 --- The SURE-LET approach --- p.19Chapter 2.6 --- Summary --- p.20Chapter 3 --- Multi-Wiener SURE-LET Approach --- p.23Chapter 3.1 --- Problem statement --- p.23Chapter 3.2 --- Linear deconvolution: multi-Wiener filtering --- p.23Chapter 3.3 --- SURE-LET in orthonormal wavelet representation --- p.24Chapter 3.3.1 --- Mathematical formulation --- p.24Chapter 3.3.2 --- SURE minimization in orthonormal wavelet domain --- p.26Chapter 3.3.3 --- Computational issues --- p.27Chapter 3.4 --- SURE-LET approach for redundant wavelet representation --- p.30Chapter 3.5 --- Computational aspects --- p.32Chapter 3.5.1 --- Periodic boundary extensions --- p.33Chapter 3.5.2 --- Symmetric convolution --- p.36Chapter 3.5.3 --- Half-point symmetric boundary extensions --- p.36Chapter 3.5.4 --- Whole-point symmetric boundary extensions --- p.43Chapter 3.6 --- Results and discussions --- p.46Chapter 3.6.1 --- Experimental setting --- p.46Chapter 3.6.2 --- Influence of the number of Wiener lters --- p.47Chapter 3.6.3 --- Influence of the parameters on the deconvolution performance --- p.48Chapter 3.6.4 --- Influence of the boundary conditions: periodic vs symmetric --- p.52Chapter 3.6.5 --- Comparison with the state-of-the-art --- p.52Chapter 3.6.6 --- Analysis of computational complexity --- p.59Chapter 3.7 --- Conclusion --- p.60Chapter II --- The SURE-based Approach to Blind Deconvolution --- p.63Chapter 4 --- The Blur-SURE Framework to PSF Estimation --- p.65Chapter 4.1 --- Introduction --- p.65Chapter 4.2 --- Problem statement --- p.66Chapter 4.3 --- The blur-SURE framework for general linear model --- p.66Chapter 4.3.1 --- Blur-MSE: a modified version of MSE --- p.66Chapter 4.3.2 --- Blur-MSE minimization --- p.67Chapter 4.3.3 --- Blur-SURE: an unbiased estimate of the blur-MSE --- p.67Chapter 4.4 --- Application of blur-SURE framework for PSF estimation --- p.68Chapter 4.4.1 --- Problem statement in the context of convolution --- p.68Chapter 4.4.2 --- Blur-MSE minimization for PSF estimation --- p.69Chapter 4.4.3 --- Approximation of exact Wiener filtering --- p.70Chapter 4.4.4 --- Blur-SURE minimization for PSF estimation --- p.72Chapter 4.5 --- Concluding remarks --- p.72Chapter 5 --- The Blur-SURE Approach to Parametric PSF Estimation --- p.75Chapter 5.1 --- Introduction --- p.75Chapter 5.1.1 --- Overview of parametric PSF estimation --- p.75Chapter 5.1.2 --- Gaussian PSF as a typical example --- p.75Chapter 5.1.3 --- Outline of this chapter --- p.76Chapter 5.2 --- Parametric estimation: problem formulation --- p.77Chapter 5.3 --- Examples of PSF parameter estimation --- p.77Chapter 5.3.1 --- Gaussian kernel --- p.77Chapter 5.3.2 --- Non-Gaussian PSF with scaling factor s --- p.78Chapter 5.4 --- Minimization via the approximated function λ = λ (s) --- p.79Chapter 5.5 --- Results and discussions --- p.82Chapter 5.5.1 --- Experimental setting --- p.82Chapter 5.5.2 --- Non-Gaussian functions: estimation of scaling factor s --- p.83Chapter 5.5.3 --- Gaussian function: estimation of standard deviation s --- p.84Chapter 5.5.4 --- Comparison of deconvolution performance with the state-of-the-art --- p.84Chapter 5.5.5 --- Application to real images --- p.87Chapter 5.6 --- Conclusion --- p.90Chapter 6 --- The Blur-SURE Approach to Motion Deblurring --- p.93Chapter 6.1 --- Introduction --- p.93Chapter 6.1.1 --- Background of motion deblurring --- p.93Chapter 6.1.2 --- Related work: parametric estimation of motion blur --- p.93Chapter 6.1.3 --- Outline of this chapter --- p.94Chapter 6.2 --- Parametric estimation of motion blur: problem formulation --- p.94Chapter 6.2.1 --- Parametrized form of linear motion blur --- p.94Chapter 6.2.2 --- The blur-SURE framework to motion blur estimation --- p.94Chapter 6.3 --- An example of the blur-SURE approach to motion blur estimation --- p.95Chapter 6.4 --- Implementation issues --- p.96Chapter 6.4.1 --- Estimation of motion direction --- p.97Chapter 6.4.2 --- Estimation of blur length --- p.97Chapter 6.4.3 --- Short summary --- p.98Chapter 6.5 --- Results and discussions --- p.98Chapter 6.5.1 --- Experimental setting --- p.98Chapter 6.5.2 --- Estimations of blur direction and length --- p.99Chapter 6.5.3 --- Motion deblurring: the synthetic experiments --- p.99Chapter 6.5.4 --- Motion deblurring: the real experiment --- p.101Chapter 6.6 --- Conclusion --- p.103Chapter 7 --- Epilogue --- p.107Chapter 7.1 --- Summary --- p.107Chapter 7.2 --- Perspectives --- p.108Chapter A --- Proof --- p.109Chapter A.1 --- Proof of Theorem 2.1 --- p.109Chapter A.2 --- Proof of Eq.(2.6) in Section 2.4.2 --- p.110Chapter A.3 --- Proof of Eq.(3.5) in Section 3.3.1 --- p.110Chapter A.4 --- Proof of Theorem 3.6 --- p.112Chapter A.5 --- Proof of Theorem 3.12 --- p.112Chapter A.6 --- Derivation of noise variance in 2-D case (Section 3.5.4) --- p.114Chapter A.7 --- Proof of Theorem 4.1 --- p.116Chapter A.8 --- Proof of Theorem 4.2 --- p.11

Data comparison schemes for Pattern Recognition in Digital Images using Fractals

Pattern recognition in digital images is a common problem with application in remote sensing, electron microscopy, medical imaging, seismic imaging and astrophysics for example. Although this subject has been researched for over twenty years there is still no general solution which can be compared with the human cognitive system in which a pattern can be recognised subject to arbitrary orientation and scale. The application of Artificial Neural Networks can in principle provide a very general solution providing suitable training schemes are implemented. However, this approach raises some major issues in practice. First, the CPU time required to train an ANN for a grey level or colour image can be very large especially if the object has a complex structure with no clear geometrical features such as those that arise in remote sensing applications. Secondly, both the core and file space memory required to represent large images and their associated data tasks leads to a number of problems in which the use of virtual memory is paramount. The primary goal of this research has been to assess methods of image data compression for pattern recognition using a range of different compression methods. In particular, this research has resulted in the design and implementation of a new algorithm for general pattern recognition based on the use of fractal image compression. This approach has for the first time allowed the pattern recognition problem to be solved in a way that is invariant of rotation and scale. It allows both ANNs and correlation to be used subject to appropriate pre-and post-processing techniques for digital image processing on aspect for which a dedicated programmer's work bench has been developed using X-Designer