Algorithms For Image Deblurring Research Articles

Improvement and Assessment of a Blind Image Deblurring Algorithm Based on Independent Component Analysis

The aim of the present paper is to improve an existing blind image deblurring algorithm, based on an independent component learning paradigm, by manifold calculus. The original technique is based on an independent component analysis algorithm applied to a set of pseudo-images obtained by Gabor-filtering a blurred image and is based on an adapt-and-project paradigm. A comparison between the original technique and the improved method shows that independent component learning on the unit hypersphere by a Riemannian-gradient algorithm outperforms the adapt-and-project strategy. A comprehensive set of numerical tests evidenced the strengths and weaknesses of the discussed deblurring technique.

Optimization of Lucy-Richardson Algorithm Using Modified Tikhonov Regularization for Image Deblurring

In this paper, we propose the method to optimize the iteration number of the Lucy-Richardson algorithm for image deblurring. This technique based on the modified Tikhonov regularization which composed of 2 parts which are designed for measuring the image similarity and noise enhancement due to the deblurring process. The regularization parameter will be used to control the desired deblurred image. Several sizes of the Gaussian blur kernel are applied for generating the degraded image in the simulation experiment. The Peak Signal to Noise Ratio (PSNR) metric is used to measure the deblurring performance. The results show that this method can be used to estimate the optimal iteration number and it also gives the PSNR value higher than the default Lucy-Richardson method and regularized filter all sizes of the experimental blur kernel. Moreover, it also tolerance to the deviated blur kernel especially it smaller than exact blur kernel.

A Compressed-Sensing Based Blind Deconvolution Method for Image Deblurring in Dental Cone-Beam Computed Tomography

In cone-beam computed tomography (CBCT), reconstructed images are inherently degraded, restricting its image performance, due mainly to imperfections in the imaging process resulting from detector resolution, noise, X-ray tube's focal spot, and reconstruction procedure as well. Thus, the recovery of CBCT images from their degraded version is essential for improving image quality. In this study, we investigated a compressed-sensing (CS)-based blind deconvolution method to solve the blurring problem in CBCT where both the image to be recovered and the blur kernel (or point-spread function) of the imaging system are simultaneously recursively identified. We implemented the proposed algorithm and performed a systematic simulation and experiment to demonstrate the feasibility of using the algorithm for image deblurring in dental CBCT. In the experiment, we used a commercially available dental CBCT system that consisted of an X-ray tube, which was operated at 90kVp and 5mA, and a CMOS flat-panel detector with a 200-μm pixel size. The image characteristics were quantitatively investigated in terms of the image intensity, the root-mean-square error, the contrast-to-noise ratio, and the noise power spectrum. The results indicate that our proposed method effectively reduced the image blur in dental CBCT, excluding repetitious measurement of the system's blur kernel.

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...

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.

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.

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.

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.

Parameter Estimation for Blind and Non-Blind Deblurring Using Residual Whiteness Measures

Image deblurring (ID) is an ill-posed problem typically addressed by using regularization, or prior knowledge, on the unknown image (and also on the blur operator, in the blind case). ID is often formulated as an optimization problem, where the objective function includes a data term encouraging the estimated image (and blur, in blind ID) to explain the observed data well (typically, the squared norm of a residual) plus a regularizer that penalizes solutions deemed undesirable. The performance of this approach depends critically (among other things) on the relative weight of the regularizer (the regularization parameter) and on the number of iterations of the algorithm used to address the optimization problem. In this paper, we propose new criteria for adjusting the regularization parameter and/or the number of iterations of ID algorithms. The rationale is that if the recovered image (and blur, in blind ID) is well estimated, the residual image is spectrally white; contrarily, a poorly deblurred image typically exhibits structured artifacts (e.g., ringing, oversmoothness), yielding residuals that are not spectrally white. The proposed criterion is particularly well suited to a recent blind ID algorithm that uses continuation, i.e., slowly decreases the regularization parameter along the iterations; in this case, choosing this parameter and deciding when to stop are one and the same thing. Our experiments show that the proposed whiteness-based criteria yield improvements in SNR, on average, only 0.15 dB below those obtained by (clairvoyantly) stopping the algorithm at the best SNR. We also illustrate the proposed criteria on non-blind ID, reporting results that are competitive with state-of-the-art criteria (such as Monte Carlo-based GSURE and projected SURE), which, however, are not applicable for blind ID.

Split Bregman Iteration Algorithm for Image Deblurring Using Fourth-Order Total Bounded Variation Regularization Model

We propose a fourth-order total bounded variation regularization model which could reduce undesirable effects effectively. Based on this model, we introduce an improved split Bregman iteration algorithm to obtain the optimum solution. The convergence property of our algorithm is provided. Numerical experiments show the more excellent visual quality of the proposed model compared with the second-order total bounded variation model which is proposed by Liu and Huang (2010).

Nonstationary iterated thresholding algorithms for image deblurring

We propose iterative thresholding algorithms based on theiterated Tikhonov method for image deblurring problems.Our method is similar in idea to the modified linearized Bregman algorithm (MLBA) sois easy to implement. In order to obtain good restorations, MLBA requires an accurate estimate of the regularization parameter $\alpha$ whichis hard to get in real applications.Based on previous results in iterated Tikhonov method, we designtwo nonstationary iterative thresholding algorithms which give nearoptimal results without estimating $\alpha$. One of them is basedon the iterative soft thresholding algorithm and the other is basedon MLBA. We show that the nonstationary methods,if converge, will converge to the same minimizers ofthe stationary variants.Numerical resultsshow that the accuracy and convergence of our nonstationary methods are very robustwith respect to the changes in the parameters and the restorationresults are comparable to those of MLBA with optimal $\alpha$.

Image deblurring with matrix regression and gradient evolution

This paper presents a supervised learning algorithm for image deblurring. The task is addressed into the conceptual framework of matrix regression and gradient evolution. Specifically, given pairs of blurred image patches and their corresponding clear ones, an optimization framework of matrix regression is proposed to learn a matrix mapping. For an image to be deblurred, the learned matrix mapping will be employed to map each of its image patches directly to be a new one with more sharp details. The mapped result is then analyzed in terms of edge profiles, and the image is finally deblurred in way of gradient evolution. The algorithm is fast, and easy to be implemented. Comparative experiments on diverse natural images and the applications to interactive deblurring of real-world out-of-focus images illustrate the validity of our method. ► Develop a supervised learning algorithm for image deblurring. ► Learn matrix mapping to replace conventional kernel estimation. ► Improve image quality with gradient evolution. ► Demonstrate its performance in image quality and computation time. ► Show its applications to interactive image deblurring.

Iterative global and local methods of image restoration

Most of the reconstruction algorithms smooth out the edges of the reconstructed images but iterative total variation regularization and local adaptive methods preserve the edge information without any prior knowledge about the image geometric details. The restoration performance of the proposed algorithms for image deblurring is compared in terms of the mean squared error. Computer simulation results are provided and discussed.

A fast wavelet algorithm for image deblurring

We present a nonlinear fully adaptive wavelet algorithm which can recover a blurred image (n?n) observed in white noise with O(n 2 (logn) 2 ) steps. Our method exploits both the natural representation of the convolution operator in the Fourier domain and the typical characterisation of Besov classes in the wavelet domain. A particular feature of our method includes cycle-spinning band-limited wavelet approximations over all circulant shifts. The speed and the accuracy of the algorithm is illustrated with numerical examples of image deblurring. All figures presented in this paper are reproducible using the WaveD software package.

A parallel implementation of a modified Richardson-Lucy algorithm for image de-blurring

Passive imaging in the millimetre wave region of the spectrum is attractive compared with imaging in the visible and infrared because of its better penetration through cloud and rain. However, the diffraction limited spatial resolution is far worse and computer restoration of millimetre wave images is necessary. The Richardson-Lucy algorithm is frequently used for image restoration because compared with linear algorithms it has reduced sensitivity to error in a priori knowledge, and fewer restoration artefacts. However, it requires many iterations to converge and is very slow compared with linear methods. This paper investigates modifications of the Richardson-Lucy algorithm which speed up the execution of the algorthm. Software techniques investigated include incorporating a speedup parameter, using dual point spread functions and implementation in the Fourier domain. A parallel implementation of the algorithm has also been investigated using a tree topology network of between 1 and 10 transputers. Finally an application of the transputer system to the de-blurring of a millimetre-wave image obtained from a mechanical scanning system is described in the paper.

Adaptive-neighborhood image deblurring

A new technique is presented for the restoration of images degraded by a linear, shift-invariant blurring point-spread function in the presence of additive white Gaussian noise. The algorithm uses overlapping variable-size, variable-shape adaptive neighborhoods (ANs) to define stationary regions in the input image and obtains a spectral estimate of the noise in each AN region. This estimate is then used to obtain a spectral estimate of the original undegraded AN region, which is inverse Fourier transformed to obtain the space-domain deblurred AN region. The regions are then combined to form the final restored image. Mathematical derivation and implementation of the adaptive-neighborhood deblurring (AND) filter is discussed, and experimental results are presented with an analysis of the performance of the AND filter as compared to the fixed-neighborhood sectioned deblurring (FNSD) Wiener and power spectrum equalization filters. It is shown that using the AND algorithm for image deblurring enables the identification of relatively stationary regions. This improves the restoration process and produces results that are superior to those obtained using the FNSD method both visually and in terms of quantitative error measures.