Deblurring Saturated Night Image With Function-Form Kernel

Deblurring saturated night images are a challenging problem because such images have low contrast combined with heavy noise and saturated regions. Unlike the deblurring schemes that discard saturated regions when estimating blur kernels, this paper proposes a novel scheme to deduce blur kernels from saturated regions via a novel kernel representation and advanced algorithms. Our key technical contribution is the proposed function-form representation of blur kernels, which regularizes existing matrix-form kernels using three functional components: 1) trajectory; 2) intensity; and 3) expansion. From automatically detected saturated regions, their skeleton, brightness, and width are fitted into the corresponding three functional components of blur kernels. Such regularization significantly improves the quality of kernels deduced from saturated regions. Second, we propose an energy minimizing algorithm to select and assign the deduced function-form kernels to partitioned image regions as the initialization for non-uniform deblurring. Finally, we convert the assigned function-form kernels into matrix form for more detailed estimation in a multi-scale deconvolution. Experimental results show that our scheme outperforms existing schemes on challenging real examples.

No-reference blur assessment of digital pictures based on multifeature classifiers

In this paper, we address the problem of no-reference quality assessment for digital pictures corrupted with blur. We start with the generation of a large real image database containing pictures taken by human users in a variety of situations, and the conduction of subjective tests to generate the ground truth associated to those images. Based upon this ground truth, we select a number of high quality pictures and artificially degrade them with different intensities of simulated blur (gaussian and linear motion), totalling 6000 simulated blur images. We extensively evaluate the performance of state-of-the-art strategies for no-reference blur quantification in different blurring scenarios, and propose a paradigm for blur evaluation in which an effective method is pursued by combining several metrics and low-level image features. We test this paradigm by designing a no-reference quality assessment algorithm for blurred images which combines different metrics in a classifier based upon a neural network structure. Experimental results show that this leads to an improved performance that better reflects the images' ground truth. Finally, based upon the real image database, we show that the proposed method also outperforms other algorithms and metrics in realistic blur scenarios.

Novel cooperative neural fusion algorithms for image restoration and image fusion

To deal with the problem of restoring degraded images with non-Gaussian noise, this paper proposes a novel cooperative neural fusion regularization (CNFR) algorithm for image restoration. Compared with conventional regularization algorithms for image restoration, the proposed CNFR algorithm can relax need of the optimal regularization parameter to be estimated. Furthermore, to enhance the quality of restored images, this paper presents a cooperative neural fusion (CNF) algorithm for image fusion. Compared with existing signal-level image fusion algorithms, the proposed CNF algorithm can greatly reduce the loss of contrast information under blind Gaussian noise environments. The performance analysis shows that the proposed two neural fusion algorithms can converge globally to the robust and optimal image estimate. Simulation results confirm that in different noise environments, the proposed two neural fusion algorithms can obtain a better image estimate than several well known image restoration and image fusion methods.

A joint estimation approach for two-tone image deblurring by blind deconvolution

A new statistical method is proposed for deblurring two-tone images, i.e., images with two unknown grey levels, that are blurred by an unknown linear filter. The key idea of the proposed method is to adjust a deblurring filter until its output becomes two tone. Two optimization criteria are proposed for the adjustment of the deblurring filter. A three-step iterative algorithm (TSIA) is also proposed to minimize the criteria. It is proven mathematically that by minimizing either of the criteria, the original (nonblurred) image, along with the blur filter, will be recovered uniquely (only with possible scale/shift ambiguities) at high SNR. The recovery is guaranteed not only for i.i.d. images but also for correlated and nonstationary images. It does not require a priori knowledge of the statistical parameters or the tone values of the original image; neither does it require a priori knowledge of the phase or other special information (e.g., FIR, symmetry, nonnegativity, etc.) about the blur filter. Numerical experiments are carried out to test the method on synthetic and real images.

Adaptive regularized constrained least squares image restoration

In noisy environments, a constrained least-squares (CLS) approach is presented to restore images blurred by a Gaussian impulse response, where instead of choosing a global regularization parameter, each point in the signal has its own associated regularization parameter. These parameters are found by constraining the weighted standard deviation of the wavelet transform coefficients on the finest scale of the inverse signal by a function r which is a local measure of the intensity variations around each point of the blurred and noisy observed signal. Border ringing in the inverse solution is proposed decreased by manipulating its wavelet transform coefficients on the finest scales close to the borders. If the noise in the inverse solution is significant, wavelet transform techniques are also applied to denoise the solution. Examples are given for images, and the results are shown to outperform the optimum constrained least-squares solution using a global regularization parameter, both visually and in the mean squared error sense.

Blind image restoration by anisotropic regularization

This paper presents anisotropic regularization techniques to exploit the piecewise smoothness of the image and the point spread function (PSF) in order to mitigate the severe lack of information encountered in blind restoration of shift-invariantly and shift-variantly blurred images. The new techniques, which are derived from anisotropic diffusion, adapt both the degree and direction of regularization to the spatial activities and orientations of the image and the PSF. This matches the piecewise smoothness of the image and the PSF which may be characterized by sharp transitions in magnitude and by the anisotropic nature of these transitions. For shift-variantly blurred images whose underlying PSFs may differ from one pixel to another, we parameterize the PSF and then apply the anisotropic regularization techniques. This is demonstrated for linear motion blur and out-of-focus blur. Alternating minimization is used to reduce the computational load and algorithmic complexity.

Multichannel restoration with limited a priori information

We introduce a method for multichannel restoration of images in which there is severely limited knowledge about the undegraded signal, and possibly the noise. We assume that we know the channel degradations and that there will be a significant noise reduction in a postprocessing stage in which multiple realizations are combined. This post-restoration noise reduction is often performed when working with micrographs of biological macromolecules. The restoration filters are designed to enforce a projection constraint upon the entire system. This projection constraint results in a system that provides an oblique projection of the input signal into the subspace defined by the reconstruction device in a direction orthogonal to a space defined by the channel degradations and the restoration filters. The approach achieves noise reduction without distorting the signal by exploiting the redundancy of the measurements.

A recursive algorithm for maximum likelihood-based identification of blur from multiple observations

A maximum likelihood-based method is proposed for blur identification from multiple observations of a scene. When the relations among the blurring functions are known, the estimate of blur obtained using the proposed method is very good. Since direct computation of the likelihood function becomes difficult as the number of images increases, we propose an algorithm to compute the likelihood function recursively.

Recognition of blurred images by the method of moments

The article is devoted to the feature-based recognition of blurred images acquired by a linear shift-invariant imaging system against an image database. The proposed approach consists of describing images by features that are invariant with respect to blur and recognizing images in the feature space. The PSF identification and image restoration are not required. A set of symmetric blur invariants based on image moments is introduced. A numerical experiment is presented to illustrate the utilization of the invariants for blurred image recognition. Robustness of the features is also briefly discussed.

A regularization approach to joint blur identification and image restoration

The primary difficulty with blind image restoration, or joint blur identification and image restoration, is insufficient information. This calls for proper incorporation of a priori knowledge about the image and the point-spread function (PSF). A well-known space-adaptive regularization method for image restoration is extended to address this problem. This new method effectively utilizes, among others, the piecewise smoothness of both the image and the PSF. It attempts to minimize a cost function consisting of a restoration error measure and two regularization terms (one for the image and the other for the blur) subject to other hard constraints. A scale problem inherent to the cost function is identified, which, if not properly treated, may hinder the minimization/blind restoration process. Alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased. Two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented. Good performance is observed with numerically and photographically blurred images, even though no stringent assumptions about the structure of the underlying blur operator is made.

Identification of image and blur parameters in frequency domain using the EM algorithm

We extend a method presented previously, which considers the problem of the semicausal autoregressive (AR) parameter identification for images degraded by observation noise only. We propose a new approach to identify both the causal and semicausal AR parameters and blur parameters without a priori knowledge of the observation noise power and the PSF of the degradation. We decompose the image into 1-D independent complex scalar subsystems resulting from the vector state-space model by using the unitary discrete Fourier transform (DFT). Then, by applying the expectation-maximization (EM) algorithm to each subsystem, we identify the AR model and blur parameters of the transformed image. The AR parameters of the original image are then identified by using the least squares (LS) method. The restored image is obtained as a byproduct of the EM algorithm.

Solution of inverse problems in image processing by wavelet expansion

We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results.

The mean field theory in EM procedures for blind Markov random field image restoration

A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.

Blur identification by residual spectral matching

The estimation of the point spread function (PSF) for blur identification, often a necessary first step in the restoration of real images, method is presented. The PSF estimate is chosen from a collection of candidate PSFs, which may be constructed using a parametric model or from experimental measurements. The PSF estimate is selected to provide the best match between the restoration residual power spectrum and its expected value, derived under the assumption that the candidate PSF is equal to the true PSF. Several distance measures were studied to determine which one provides the best match. The a priori knowledge required is the noise variance and the original image spectrum. The estimation of these statistics is discussed, and the sensitivity of the method to the estimates is examined analytically and by simulations. The method successfully identified blurs in both synthetically and optically blurred images.

Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation

The application of regularization to ill-conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution. The value of the regularization parameter depends on the variance of the noise in the data. The problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined. An error analysis based on an objective mean-square-error (MSE) criterion is used to motivate regularization. Two approaches for choosing the regularization parameter and estimating the noise variance are proposed. The proposed and existing methods are compared and their relationship to linear minimum-mean-square-error filtering is examined. Experiments are presented that verify the theoretical results.

Blur identification by the method of generalized cross-validation

The point spread function (PSF) of a blurred image is often unknown a priori; the blur must first be identified from the degraded image data before restoring the image. Generalized cross-validation (GCV) is introduced to address the blur identification problem. The GCV criterion identifies model parameters for the blur, the image, and the regularization parameter, providing all the information necessary to restore the image. Experiments are presented which show that GVC is capable of yielding good identification results. A comparison of the GCV criterion with maximum-likelihood (ML) estimation shows the GCV often outperforms ML in identifying the blur and image model parameters.

A full-plane block Kalman filter for image restoration

A two-dimensional method which uses a full-plane image model to generate a more accurate filtered estimate of an image that has been corrupted by additive noise and full-plane blur is presented. Causality is maintained within the filtering process by using multiple concurrent block estimators. In addition, true state dynamics are preserved, resulting in an accurate Kalman gain matrix. Simulation results on a test image corrupted by additive white Gaussian noise are presented for various image models and compared to those of the previous block Kalman filtering methods.

Maximum likelihood parametric blur identification based on a continuous spatial domain model

A formulation for maximum-likelihood (ML) blur identification based on parametric modeling of the blur in the continuous spatial coordinates is proposed. Unlike previous ML blur identification methods based on discrete spatial domain blur models, this formulation makes it possible to find the ML estimate of the extent, as well as other parameters, of arbitrary point spread functions that admit a closed-form parametric description in the continuous coordinates. Experimental results are presented for the cases of 1-D uniform motion blur, 2-D out-of-focus blur, and 2-D truncated Gaussian blur at different signal-to-noise ratios.