Deblurring Algorithms Research Articles

Low-rank approach for image nonblind deconvolution with variance estimation

We develop a low-rank approach for image restoration by exploiting the image’s nonlocal self-similarity. We assume that the matrix stacked by the vectors of nonlocal similar patches is of low rank and has sparse singular values. Based on this assumption, we propose a new image deconvolution algorithm that decouples the deblurring and denoising steps. Specifically, in the deblurring step, we involve a regularized inversion of the blur in the Fourier domain, which amplifies and colors the noise and corrupts the image information. Hence, in the denoising step, a singular-value decomposition of similar packed patches is used to efficiently remove the colored noise. Furthermore, we derive an approach to update the estimation of noise variance for setting the threshold parameter at each iteration. Experimental results clearly show that the proposed algorithm outperforms many state-of-the-art deblurring algorithms such as iterative decoupled deblurring BM3D in terms of both improvement in signal-to-noise-ratio and visual perception quality.

Line Integral Alternating Minimization Algorithm for Dual-Energy X-Ray CT Image Reconstruction.

We propose a new algorithm, called line integral alternating minimization (LIAM), for dual-energy X-ray CT image reconstruction. Instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates, LIAM allows for a tunable discrepancy between the basis material projections and the basis sinograms. A parameter is introduced that controls the size of this discrepancy, and with this parameter the new algorithm can continuously go from a two-step approach to the joint estimation approach. LIAM alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm. An edge-preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images. Images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by LIAM while varying the regularization parameters to identify good choices. The results from the dual-energy alternating minimization algorithm applied to the same data were used for comparison. Using a small fraction of the computation time of dual-energy alternating minimization, LIAM achieves better accuracy of the component images in the presence of Poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction.

Acceleration of multiplicative iterative algorithms for image deblurring by duality maps in Banach spaces

An acceleration technique for multiplicative iterative methods, such as Lucy–Richardson and Image Space Reconstruction Algorithm, is presented. The technique is inspired by the Landweber method in Banach spaces and is based on the application of duality maps, which allow to compute the iterations in the dual space. We show the link between the proposed acceleration and the previously known Meinel acceleration, which consists in the introduction of an exponent in the basic iterative formulas. We prove that the new acceleration technique is more stable than the Meinel acceleration. This implies that, in the restoration process, the former is able to get better accuracy and higher speeding-up than the latter. In addition to the main focus of the paper, we propose a generalization of the Landweber method in Banach space, in order to overcome some drawbacks of this recent strategy when compared with classical (Hilbertian) Landweber method. Numerical results show the behavior and the features of the several techniques considered, highlighting the goodness of our proposals.

An Improved Fast Iterative Shrinkage Thresholding Algorithm for Image Deblurring

An improved fast iterative shrinkage thresholding algorithm (IFISTA) for image deblurring is proposed. The IFISTA algorithm uses a positive definite weighting matrix in the gradient function of the minimization problem of the known fast iterative shrinkage thresholding (FISTA) image restoration algorithm. A convergence analysis of the IFISTA algorithm shows that due to the weighting matrix, the IFISTA algorithm has an improved convergence rate and improved restoration capability of the unknown image over that of the FISTA algorithm. The weighting matrix is predetermined and fixed, and hence, like the FISTA algorithm, the IFISTA algorithm requires only one matrix vector product operation in each iteration. As a result, the computational burden per iteration of the IFISTA algorithm remains the same as in the FISTA algorithm. Numerical examples are presented that demonstrate the improved performance of the IFISTA algorithm over that of the FISTA and iterative shrinkage thresholding (ISTA) algorithms in terms...

Image Deblurring via an Adaptive Dictionary Learning Strategy

Recently, sparse representation has been applied to image deblurring. The dictionary is the fundamental part of it and the proper selection of dictionary is very important to achieve super performance. The global learned dictionary might achieve inferior performances since it could not mine the specific information such as the texture and edge which is contained in the blurred image. However, it is a computational burden to train a new dictionary for image deblurring which requires the whole image (or most parts) as input; training the dictionary on only a few patches would result in over-fitting. To address the problem, we instead propose an online adaption strategy to transfer the global learned dictionary to a specific image. In our deblurring algorithm, the sparse coefficients, latent image, blur kernel and the dictionary are updated alternatively. And in every step, the global learned dictionary is updated in an online form via sampling only a few training patches from the target noisy image. Since our adaptive dictionary exploits the specific information, our deblurring algorithm shows superior performance over other state-of-the-art algorithms.

A general framework for regularized, similarity-based image restoration.

Any image can be represented as a function defined on a weighted graph, in which the underlying structure of the image is encoded in kernel similarity and associated Laplacian matrices. In this paper, we develop an iterative graph-based framework for image restoration based on a new definition of the normalized graph Laplacian. We propose a cost function, which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph Laplacian. The normalizing coefficients used in the definition of the Laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing. This results in some desired spectral properties for the normalized Laplacian such as being symmetric, positive semidefinite, and returning zero vector when applied to a constant image. Our algorithm comprises of outer and inner iterations, where in each outer iteration, the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations. This procedure improves the performance of the algorithm for image deblurring, where we do not have access to a good initial estimate of the underlying image. In addition, the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations. In addition, the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems, including deblurring, denoising, and sharpening. Experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples.

Efficient Patch-Wise Non-Uniform <newline/>Deblurring for a Single Image

In this paper, we address the problem of estimating a latent sharp image from a single spatially variant blurred image. Non-uniform deblurring methods based on projective motion path models formulate the blur as a linear combination of homographic projections of a clear image. But they are computationally expensive and require large memory due to the calculation and storage of a large number of the projections. Patch-wise non-uniform deblurring algorithms have been proposed to estimate each kernel locally by a uniform deblurring algorithm, which does not require to calculate and store the projections. The key issues of these methods are the accuracy of kernel estimation and the identification of erroneous kernels. To perform accurate kernel estimation, we employ the total variation (TV) regularization to recover a latent image, in which the edges are better enhanced and the ringing artifacts are reduced, rather than Tikhonov regularization that previous algorithms adopt. Thus blur kernels can be estimated more accurately from the latent image and estimated in a closed form while previous methods cannot estimate kernels in closed forms. To identify the erroneous kernels, we develop a novel metric, which is able to measure the similarity between the neighboring kernels. After replacing the erroneous kernels with the well-estimated ones, a clear image is obtained. The experiments show that our approach can achieve better results on the real-world blurry images while using less computation and memory.

A new reweighted l 1 minimization algorithm for image deblurring

In this paper, a new reweighted minimization algorithm for image deblurring is proposed. The algorithm is based on a generalized inverse iteration and linearized Bregman iteration, which is used for the weighted minimization problem . In the computing process, the effective using of signal information can make up the detailed features of image, which may be lost in the deblurring process. Numerical experiments confirm that the new reweighted algorithm for image restoration is effective and competitive to the recent state-of-the-art algorithms.

High-dimensional camera shake removal with given depth map.

Camera motion blur is drastically nonuniform for large depth-range scenes, and the nonuniformity caused by camera translation is depth dependent but not the case for camera rotations. To restore the blurry images of large-depth-range scenes deteriorated by arbitrary camera motion, we build an image blur model considering 6-degrees of freedom (DoF) of camera motion with a given scene depth map. To make this 6D depth-aware model tractable, we propose a novel parametrization strategy to reduce the number of variables and an effective method to estimate high-dimensional camera motion as well. The number of variables is reduced by temporal sampling motion function, which describes the 6-DoF camera motion by sampling the camera trajectory uniformly in time domain. To effectively estimate the high-dimensional camera motion parameters, we construct the probabilistic motion density function (PMDF) to describe the probability distribution of camera poses during exposure, and apply it as a unified constraint to guide the convergence of the iterative deblurring algorithm. Specifically, PMDF is computed through a back projection from 2D local blur kernels to 6D camera motion parameter space and robust voting. We conduct a series of experiments on both synthetic and real captured data, and validate that our method achieves better performance than existing uniform methods and nonuniform methods on large-depth-range scenes.

SU-D-17A-02: Four-Dimensional CBCT Using Conventional CBCT Dataset and Iterative Subtraction Algorithm of a Lung Patient

Purpose: The Iterative Subtraction Algorithm (ISA) method generates retrospectively a pre-selected motion phase cone-beam CT image from the full motion cone-beam CT acquired at standard rotation speed. This work evaluates ISA method with real lung patient data. Methods: The goal of the ISA algorithm is to extract motion and no- motion components form the full reconstruction CBCT. The workflow consists of subtracting from the full CBCT all of the undesired motion phases and obtain a motion de-blurred single-phase CBCT image, followed by iteration of this subtraction process. ISA is realized as follows: 1) The projections are sorted to various phases, and from all phases, a full reconstruction is performed to generate an image CTM. 2) Generate forward projections of CTM at the desired phase projection angles, the subtraction of projection and the forward projection will reconstruct a CTSub1, which diminishes the desired phase component. 3) By adding back the CTSub1 to CTm, no motion CBCT, CTS1, can be computed. 4) CTS1 still contains residual motion component. 5) This residual motion component can be further reduced by iteration. The ISA 4DCBCT technique was implemented using Varian Trilogy accelerator OBI system. To evaluate the method, a lung patient CBCT dataset was used. The reconstruction algorithm is FDK. Results: The single phase CBCT reconstruction generated via ISA successfully isolates the desired motion phase from the full motion CBCT, effectively reducing motion blur. It also shows improved image quality, with reduced streak artifacts with respect to the reconstructions from unprocessed phase-sorted projections only. Conclusion: A CBCT motion de-blurring algorithm, ISA, has been developed and evaluated with lung patient data. The algorithm allows improved visualization of a single phase motion extracted from a standard CBCT dataset. This study has been supported by National Institute of Health through R01CA133539.

Inverse Methods for Deblurring Pressure-Sensitive Paint Images of Rotating Surfaces

Image blurring is a problem encountered when pressure-sensitive paint is applied to rotating surfaces such as rotorcraft blades. The issue is particularly problematic near the leading and trailing edges of the blade; these are the regions where the impact of blurring is the most significant, yet they also contain the most valuable pressure information. Recent work has developed image-deblurring techniques based on deconvolution of the image with a point-spread function based on the known lifetime decay of pressure-sensitive paint and the rotation speed of the blade. This deblurring technique is effective in recovering information at the blade edges when the amount of blurring is not too high. However, the existing deblurring algorithm assumes rectilinear motion and uniform distribution of luminophore lifetime (i.e., constant pressure distribution). The objective of this work is to relax the rectilinear assumption by allowing for rotational blur and to assess the impact of strong pressure gradients on the resulting deblurred pressure distribution. The new deblurring scheme is evaluated by experiments on a spinning disk with a known pressure field and a corotating, grazing nitrogen jet. The sensitivity of the deblurred results to various input parameters is evaluated, and recommendations for further algorithm development are provided.

A chaotic iterative algorithm based on linearized Bregman iteration for image deblurring

In this paper, we propose a new chaotic iterative algorithm for image deblurring. The algorithm is based on generalized inverse iteration, and linearized Bregman iteration for the basis pursuit problem minu∈Rn{‖u‖1:Au=f}. Numerical experiments show that the chaotic algorithm for image restoration is effective and efficient.

Two soft-thresholding based iterative algorithms for image deblurring

Iterative regularization algorithms, such as the conjugate gradient algorithm for least squares problems (CGLS) and the modified residual norm steepest descent (MRNSD) algorithm, are popular tools for solving large-scale linear systems arising from image deblurring problems. These algorithms, however, are hindered by a semi-convergence behavior, in that the quality of the computed solution first increases and then decreases. In this paper, in order to overcome the semi-convergence behavior, we propose two iterative algorithms based on soft-thresholding for image deblurring problems. One of them combines CGLS with a denoising technique like soft-thresholding at each iteration and another combines MRNSD with soft-thresholding in a similar way. We prove the convergence of MRNSD and soft-thresholding based algorithm. Numerical results show that the proposed algorithms overcome the semi-convergence behavior and the restoration results are slightly better than those of CGLS and MRNSD with their optimal stopping iterations.

A novel gradient attenuation Richardson–Lucy algorithm for image motion deblurring

This paper presents a novel blind image deconvolution algorithm for motion deblurring from a single blurred image. We propose a unified framework for both blur kernel estimation and non-blind image deconvolution by using bilateral filtering (BF) and a new image deconvolution algorithm, called the Gradient Attenuation Richardson–Lucy (GARL) algorithm. In the blur kernel estimation stage, we show that an initial blur kernel, which is used for starting an alternating kernel refinement process, can be obtained from the blurred image with a quadratic regularization approach. In the non-blind image deconvolution stage, we exploit the image gradients and develop the GARL algorithm to alleviate the notorious ringing problem in the Richardson–Lucy-based image restoration approach. Furthermore, the loss of image details due to the suppression of the ringing artifacts around the regions with strong edges is recovered with an incremental detail recovery procedure. The proposed framework is simple yet effective compared to previous statistical approaches. Experimental results on various real data sets are given to demonstrate superior performance of the proposed algorithm over the previous methods.

A fast alternating minimization algorithm for total variation deblurring without boundary artifacts

Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang (2008) [32]. The method in a nutshell consists of a discrete Fourier transform-based alternating minimization algorithm with periodic boundary conditions and in which two fast Fourier transforms (FFTs) are required per iteration. In this paper, we propose an alternating minimization algorithm for the continuous version of the total variation image deblurring problem. We establish convergence of the proposed continuous alternating minimization algorithm. The continuous setting is very useful to have a unifying representation of the algorithm, independently of the discrete approximation of the deconvolution problem, in particular concerning the strategies for dealing with boundary artifacts. Indeed, an accurate restoration of blurred and noisy images requires a proper treatment of the boundary. A discrete version of our continuous alternating minimization algorithm is obtained following two different strategies: the imposition of appropriate boundary conditions and the enlargement of the domain. The first one is computationally useful in the case of a symmetric blur, while the second one can be efficiently applied for a nonsymmetric blur. Numerical tests show that our algorithm generates higher quality images in comparable running times with respect to the Fast Total Variation deconvolution algorithm.

An Improved Adaptive Deconvolution Algorithm for Single Image Deblurring

One of the most common defects in digital photography is motion blur caused by camera shake. Shift-invariant motion blur can be modeled as a convolution of the true latent image and a point spread function (PSF) with additive noise. The goal of image deconvolution is to reconstruct a latent image from a degraded image. However, ringing is inevitable artifacts arising in the deconvolution stage. To suppress undesirable artifacts, regularization based methods have been proposed using natural image priors to overcome the ill-posedness of deconvolution problem. When the estimated PSF is erroneous to some extent or the PSF size is large, conventional regularization to reduce ringing would lead to loss of image details. This paper focuses on the nonblind deconvolution by adaptive regularization which preserves image details, while suppressing ringing artifacts. The way is to control the regularization weight adaptively according to the image local characteristics. We adopt elaborated reference maps that indicate the edge strength so that textured and smooth regions can be distinguished. Then we impose an appropriate constraint on the optimization process. The experiments’ results on both synthesized and real images show that our method can restore latent image with much fewer ringing and favors the sharp edges.

Regularized Generalized Inverse Accelerating Linearized Alternating Minimization Algorithm for Frame-Based Poissonian Image Deblurring

Blurred images corrupted by Poisson noise frequently appear in medical and astronomical applications, and variational models based on sparsity priors such as the total variation and the framelet have been devoted to the problem of recovering the Poissonian images. However, developing efficient algorithms for solving the associated optimization problems is still an attractive research area due to the ill-posedness of the blurring operator and the complexity of the data-fidelity term. In this paper, we propose an accelerating linearized alternating minimization algorithm called GILAM for solving the frame-based variational model for Poissonian image deblurring. In the proposed method, a modification of the generalized inverse is introduced to overcome the negative effect of the ill-posed blurring operator, and, further, a discrepancy function is used to adjust the value of the regularization parameter automatically. The global convergence of the proposed algorithms is also investigated. Numerical experiments demonstrate that the proposed algorithms outperform the widely used ADMM (alternating direction method of multipliers) methods, especially in CPU time.

A no-reference metric for evaluating the quality of motion deblurring

Methods to undo the effects of motion blur are the subject of intense research, but evaluating and tuning these algorithms has traditionally required either user input or the availability of ground-truth images. We instead develop a metric for automatically predicting the perceptual quality of images produced by state-of-the-art deblurring algorithms. The metric is learned based on a massive user study, incorporates features that capture common deblurring artifacts, and does not require access to the original images (i.e., is "noreference"). We show that it better matches user-supplied rankings than previous approaches to measuring quality, and that in most cases it outperforms conventional full-reference image-similarity measures. We demonstrate applications of this metric to automatic selection of optimal algorithms and parameters, and to generation of fused images that combine multiple deblurring results.

An alternating iterative algorithm for image deblurring and denoising problems

In this paper, a modified l1 minimization model for image delurring and denoising problems is considered. To solve the proposed l1 minimization model, we present an efficient alternative iterative algorithm in which the fast iterative shrinkge-thresholding method (FISTA) and the well known dual approach for solving the denosing problems are alternately employed. Besides, we prove the convergence of the proposed algorithm. Numerical results demonstrate the efficiency and viability of the proposed algorithm to restore the degraded images.

Nonlocal Total Variation Based Image Deblurring Using Split Bregman Method and Fixed Point Iteration

Nonlocal regularization for image restoration is extensively studied in recent years. However, minimizing a nonlocal regularization problem is far more difficult than a local one and still challenging. In this paper, a novel nonlocal total variation based algorithm for image deblurring is presented. The core idea of this algorithm is to consider the latent image as the fixed point of the nonlocal total variation regularization functional. And a split Bregman method is proposed to solve the minimization problem in each fixed point iteration efficiently. By alternatively reconstructing a sharp image and updating the nonlocal gradient weights, the recovered image becomes more and more sharp. Experimental results on the benchmark problems are presented to show the efficiency and effectiveness of our algorithm.