Blur identification by the method of generalized cross-validation

Blind Image Deblurring Using a Non-Linear Channel Prior Based on Dark and Bright Channels

Blind image deblurring aims at recovering a clean image from the given blurry image without knowing the blur kernel. Recently proposed dark and extreme channel priors have shown their effectiveness in deblurring various blurry scenarios. However, these two priors fail to help the blur kernel estimation under the particular circumstance that clean images contain neither enough darkest nor brightest pixels. In this paper, we propose a novel and robust non-linear channel (NLC) prior for the blur kernel estimation to fill this gap. It is motivated by a simple idea that the blurring operation will increase the ratio of dark channel to bright channel. This change has been proved to be true both theoretically and empirically. Nonetheless, the presence of the NLC prior introduces a thorny optimization model. To handle it, an efficient algorithm based on projected alternating minimization (PAM) has been established which innovatively combines an approximate strategy, the half-quadratic splitting method, and fast iterative shrinkage-thresholding algorithm (FISTA). Extensive experimental results show that the proposed method achieves state-of-the-art results no matter when it has been applied in synthetic uniform and non-uniform benchmark datasets or in real blurry images.

Application of Blind Deconvolution Based on the New Weighted L1-norm Regularization with Alternating Direction Method of Multipliers in Light Microscopy Images

This study aimed to develop and evaluate a blind-deconvolution framework using the alternating direction method of multipliers (ADMMs) incorporated with weighted L1-norm regularization for light microscopy (LM) images. A presimulation study was performed using the Siemens star phantom prior to conducting the actual experiments. Subsequently, the proposed algorithm and a total generalized variation-based (TGV-based) method were applied to cross-sectional images of a mouse molar captured at 40× and 400× on-microscope magnifications and the results compared, and the resulting images were compared. Both simulation and experimental results confirmed that the proposed deblurring algorithm effectively restored the LM images, as evidenced by the quantitative evaluation metrics. In conclusion, this study demonstrated that the proposed deblurring algorithm can efficiently improve the quality of LM images.

Line-Detection Based on the Sum of Gradient Angle Differences

This paper presents a method to detect line pixels based on the sum of gradient angle differences (SGAD). The gradient angle differences are calculated by comparing the four pairs of gradients arising from eight neighboring pixels. In addition, a method to classify line pixels into ridges and valleys is proposed. Furthermore, a simple line model is defined for simulation experiments. Experiments are conducted with simulation images generated using the simple line model for three line-detection methods: second-derivatives (SD)-based method, extremity-count (EC)-based method, and proposed method. The results of the simulation experiments show that the proposed method produces more accurate line-detection results than the other methods in terms of the root mean square error when the line width is relatively large. In addition, the experiments conducted with natural images show that the SD- and EC-based methods suffer from bifurcation, fragmentation, and missing pixels. By contrast, for the original and the noise-contaminated versions of the natural images, the proposed SGAD-based line-detection method is affected by such problems to a considerably smaller extent than the other two methods.

A Novel Neural Network-Based Method for Decoding and Detecting of the DS8-PSK Scheme in an OCC System

This paper proposes a novel method of training and applying a neural network to act as an adaptive decoder for a modulation scheme used in optical camera communication (OCC). We present a brief discussion on trending artificial intelligence applications, the contemporary ways of applying them in a wireless communication field, such as visible light communication (VLC), optical wireless communication (OWC) and OCC, and its potential contribution in the development of this research area. Furthermore, we proposed an OCC vehicular system architecture with artificial intelligence (AI) functionalities, where dimmable spatial 8-phase shift keying (DS8-PSK) is employed as one out of two modulation schemes to form a hybrid waveform. Further demonstration of simulating the blurring process on a transmitter image, as well as our proposed method of using a neural network as a decoder for DS8-PSK, is provided in detail. Finally, experimental results are given to prove the effectiveness and efficiency of the proposed method over an investigating channel condition.

A Filtering Method for Grain Flow Signals Using EMD Thresholds Optimized by Artificial Bee Colony Algorithm

For the purpose of reducing noise from grain flow signal, this paper proposes a filtering method that is on the basis of empirical mode decomposition (EMD) and artificial bee colony (ABC) algorithm. At first, decomposing noise signal is performed adaptively into intrinsic mode functions (IMFs). Then, ABC algorithm is utilized to determine a proper threshold shrinking IMF coefficients instead of traditional threshold function. Furthermore, a neighborhood search strategy is introduced into ABC algorithm to balance its exploration and exploitation ability. Simulation experiments are conducted on four benchmark signals, and a comparative study for the proposed method and state-of-the-art methods are carried out. The compared results demonstrate that signal to noise ratio (SNR) and root mean square error (RMSE) are obtained by the proposed method. The conduction of which is finished on actual grain flow signal that is with noise for the demonstration of the effect in actual practice.

Reconstruction of Single Image from Multiple Blurry Measured Images

The problem of blind image recovery using multiple blurry images of the same scene is addressed in this paper. To perform blind deconvolution, which is also called blind image recovery, the blur kernel and image are represented by groups of sparse domains to exploit the local and nonlocal information such that a novel joint deblurring approach is conceived. In the proposed approach, the group sparse regularization on both the blur kernel and image is provided, where the sparse solution is promoted by -norm. In addition, the reweighted data fidelity is developed to further improve the recovery performance, where the weight is determined by the estimation error. Moreover, to reduce the undesirable noise effects in group sparse representation, distance measures are studied in the block matching process to find similar patches. In such a joint deblurring approach, a more sophisticated two-step interactive process is needed in which each step is solved by means of the well-known split Bregman iteration algorithm, which is generally used to efficiently solve the proposed joint deblurring problem. Finally, numerical studies, including synthetic and real images, demonstrate that the performance of this joint estimation algorithm is superior to the previous state-of-the-art algorithms in terms of both objective and subjective evaluation standards. The recovery results of real captured images using unmanned aerial vehicles are also provided to further validate the effectiveness of the proposed method.

Image Fusion for Mars Data Using Mix of Robust PCA

Multi-sensor image fusion is the process of combining relevant information from high spatial resolution image and high spectral resolution image. This paper proposes a pansharpening method for the fusion of Mars images obtained by the Mars Reconnaissance Orbiter satellite (PAN) and Mars Odyssey satellite (THEMIS MS). The method is based on some mix of Intensity, Hue, Saturation (IHS) and robust principal component analysis (RPCA) combined with the discrete wavelet transformation (DWT). Meanwhile, the results obtained with that of the other fusion techniques are compared, and a relatively objective comprehensive evaluation for fused image is used. Experiments show that the proposed algorithm has a significant suppression of artificial textures and less spectral distortion, and its running time is acceptable.

Modeling Non-Stationary Asymmetric Lens Blur by Normal Sinh-Arcsinh Model

Images acquired by a camera show lens blur due to imperfection in the optical system even when images are properly focused. Lens blur is non-stationary in a sense that the amount of blur depends on pixel locations in a sensor. Lens blur is also asymmetric in a sense that the amount of blur is different in the radial and tangential directions, and also in the inward and outward radial directions. This paper presents parametric blur kernel models based on the normal sinh-arcsinh distribution function. The proposed models can provide flexible shapes of blur kernels with a different symmetry and skewness to model complicated lens blur due to optical aberration in a properly focused images accurately. Blur of single focal length lenses is estimated, and the accuracy of the models is compared with the existing parametric blur models. An advantage of the proposed models is demonstrated through deblurring experiments.

A novel SURE-based criterion for parametric PSF estimation

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.

Minimum entropy restoration of star field images

In this correspondence, we present an algorithm for restoration of star field images by incorporating both the minimum mean square error and the maximum varimax criteria. It is assumed that the point spread function of the distortion system can be well approximated by a Gaussian function. Simulated annealing (SA) is used to implement the optimization procedure. Simulation results for both Gaussian and square point spread functions with heavy additive independent white Gaussian noise are provided. Visual evaluation of the results indicate that the proposed algorithm performs better than the noncausal Wiener filtering method.

Modeling the performance of image restoration from motion blur

When dealing with motion blur there is an inevitable trade-off between the amount of blur and the amount of noise in the acquired images. The effectiveness of any restoration algorithm typically depends on these amounts, and it is difficult to find their best balance in order to ease the restoration task. To face this problem, we provide a methodology for deriving a statistical model of the restoration performance of a given deblurring algorithm in case of arbitrary motion. Each restoration-error model allows us to investigate how the restoration performance of the corresponding algorithm varies as the blur due to motion develops. Our modeling treats the point-spread-function trajectories as random processes and, following a Monte-Carlo approach, expresses the restoration performance as the expectation of the restoration error conditioned on some motion-randomness descriptors and on the exposure time. This allows to coherently encompass various imaging scenarios, including camera shake and uniform (rectilinear) motion, and, for each of these, identify the specific exposure time that maximizes the image quality after deblurring.

Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

A Kullback-Leibler divergence approach to blind image restoration

A new algorithm for maximum-likelihood blind image restoration is presented in this paper. It is obtained by modeling the original image and the additive noise as multivariate Gaussian processes with unknown covariance matrices. The blurring process is specified by its point spread function, which is also unknown. Estimations of the original image and the blur are derived by alternating minimization of the Kullback-Leibler divergence between a model family of probability distributions defined using the linear image degradation model and a desired family of probability distributions constrained to be concentrated on the observed data. The algorithm presents the advantage to provide closed form expressions for the parameters to be updated and to converge only after few iterations. A simulation example that illustrates the effectiveness of the proposed algorithm is presented.

Blind deconvolution using generalized cross-validation approach to regularization parameter estimation

In this paper, we propose and present an algorithm for total variation (TV)-based blind deconvolution. Both the unknown image and blur can be estimated within an alternating minimization framework. With the generalized cross-validation (GCV) method, the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps. Experimental results confirm that the performance of the proposed algorithm is better than variational Bayesian blind deconvolution algorithms with Student's-t priors or a total variation prior.

Blind image deconvolution using machine learning for three-dimensional microscopy

In this work, we propose a novel method for the regularization of blind deconvolution algorithms. The proposed method employs example-based machine learning techniques for modeling the space of point spread functions. During an iterative blind deconvolution process, a prior term attracts the point spread function estimates to the learned point spread function space. We demonstrate the usage of this regularizer within a Bayesian blind deconvolution framework and also integrate into the latter a method for noise reduction, thus creating a complete blind deconvolution method. The application of the proposed algorithm is demonstrated on synthetic and real-world three-dimensional images acquired by a wide-field fluorescence microscope, where the need for blind deconvolution algorithms is indispensable, yielding excellent results.

Two-dimensional blind Bayesian deconvolution of medical ultrasound images

A new approach to 2-D blind deconvolution of ultrasonic images in a Bayesian framework is presented. The radio-frequency image data are modeled as a convolution of the point-spread function and the tissue function, with additive white noise. The deconvolution algorithm is derived from statistical assumptions about the tissue function, the point-spread function, and the noise. It is solved as an iterative optimization problem. In each iteration, additional constraints are applied as a projection operator to further stabilize the process. The proposed method is an extension of the homomorphic deconvolution, which is used here only to compute the initial estimate of the point-spread function. Homomorphic deconvolution is based on the assumption that the point-spread function and the tissue function lie in different bands of the cepstrum domain, which is not completely true. This limiting constraint is relaxed in the subsequent iterative deconvolution. The deconvolution is applied globally to the complete radiofrequency image data. Thus, only the global part of the point-spread function is considered. This approach, together with the need for only a few iterations, makes the deconvolution potentially useful for real-time applications. Tests on phantom and clinical images have shown that the deconvolution gives stable results of clearly higher spatial resolution and better defined tissue structures than in the input images and than the results of the homomorphic deconvolution alone.

A generalized least absolute deviation method for parameter estimation of autoregressive signals

This paper proposes a generalized least absolute deviation (GLAD) method for parameter estimation of autoregressive (AR) signals under non-Gaussian noise environments. The proposed GLAD method can improve the accuracy of the estimation of the conventional least absolute deviation (LAD) method by minimizing a new cost function with parameter variables and noise error variables. Compared with second- and high-order statistical methods, the proposed GLAD method can obtain robustly an optimal AR parameter estimation without requiring the measurement noise to be Gaussian. Moreover, the proposed GLAD method can be implemented by a cooperative neural network (NN) which is shown to converge globally to the optimal AR parameter estimation within a finite time. Simulation results show that the proposed GLAD method can obtain more accurate estimates than several well-known estimation methods in the presence of different noise distributions.

A unified approach to superresolution and multichannel blind deconvolution

This paper presents a new approach to the blind deconvolution and superresolution problem of multiple degraded low-resolution frames of the original scene. We do not assume any prior information about the shape of degradation blurs. The proposed approach consists of building a regularized energy function and minimizing it with respect to the original image and blurs, where regularization is carried out in both the image and blur domains. The image regularization based on variational principles maintains stable performance under severe noise corruption. The blur regularization guarantees consistency of the solution by exploiting differences among the acquired low-resolution images. Several experiments on synthetic and real data illustrate the robustness and utilization of the proposed technique in real applications.

Multiresolution imaging of MEG cortical sources using an explicit piecewise model

Imaging neural generators from MEG magnetic fields is often considered as a compromise between computationally-reasonable methodology that usually yields poor spatial resolution on the one hand, and more sophisticated approaches on the other hand, potentially leading to intractable computational costs. We approach the problem of obtaining well-resolved source images with unexcessive computation load with a multiresolution image model selection (MiMS) technique. The building blocks of the MiMS source model are parcels of the cortical surface which can be designed at multiple spatial resolutions with the combination of anatomical and functional priors. Computation charge is reduced owing to 1) compact parametric models of the activation of extended brain parcels using current multipole expansions and 2) the optimization of the generalized cross-validation error on image models, which is closed-form for the broad class of linear estimators of neural currents. Model selection can be complemented by any conventional imaging approach of neural currents restricted to the optimal image support obtained from MiMS. The estimation of the location and spatial extent of brain activations is discussed and evaluated using extensive Monte-Carlo simulations. An experimental evaluation was conducted with MEG data from a somatotopic paradigm. Results show that MiMS is an efficient image model selection technique with robust performances at realistic noise levels.

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.

Blind image restoration with eigen-face subspace

Performance of conventional image restoration methods is sensitive to signal-to-noise ratios. For heavily blurred and noisy human facial images, information contained in the eigen-face subspace can be used to compensate for the lost details. The blurred image is decomposed into the eigen-face subspace and then restored with a regularized total constrained least square method. With Generalized cross-validation, a cost function is deduced to include two unknown parameters: the regularization factor and one parameter relevant to point spread function. It is shown that, in minimizing the cost function, the cost function dependence of any one unknown parameter can be separated from the other one, which means the cost function can be considered roughly, depending on single variable in an iterative algorithm. With realistic constraints on the regularized factor, a global minimum for the cost function is achieved to determine the unknown parameters. Experiments are presented to demonstrate the effectiveness and robustness of the new method.

Fast image restoration without boundary artifacts

Fast Fourier transform (FFT)-based restorations are fast, but at the expense of assuming that the blurring and deblurring are based on circular convolution. Unfortunately, when the opposite sides of the image do not match up well in intensity, this assumption can create significant artifacts across the image. If the pixels outside the measured image window are modeled as unknown values in the restored image, boundary artifacts are avoided. However, this approach destroys the structure that makes the use of the FFT directly applicable, since the unknown image is no longer the same size as the measured image. Thus, the restoration methods available for this problem no longer have the computational efficiency of the FFT. We propose a new restoration method for the unknown boundary approach that can be implemented in a fast and flexible manner. We decompose the restoration into a sum of two independent restorations. One restoration yields an image that comes directly from a modified FFT-based approach. The other restoration involves a set of unknowns whose number equals that of the unknown boundary values. By summing the two, the artifacts are canceled. Because the second restoration has a significantly reduced set of unknowns, it can be calculated very efficiently even though no circular convolution structure exists.

Multichannel blind deconvolution of spatially misaligned images

Existing multichannel blind restoration techniques assume perfect spatial alignment of channels, correct estimation of blur size, and are prone to noise. We developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral. This stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise. We observe that the exact knowledge of the blur size is not necessary, and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process.

A soft double regularization approach to parametric blind image deconvolution

This paper proposes a blind image deconvolution scheme based on soft integration of parametric blur structures. Conventional blind image deconvolution methods encounter a difficult dilemma of either imposing stringent and inflexible preconditions on the problem formulation or experiencing poor restoration results due to lack of information. This paper attempts to address this issue by assessing the relevance of parametric blur information, and incorporating the knowledge into the parametric double regularization (PDR) scheme. The PDR method assumes that the actual blur satisfies up to a certain degree of parametric structure, as there are many well-known parametric blurs in practical applications. Further, it can be tailored flexibly to include other blur types if some prior parametric knowledge of the blur is available. A manifold soft parametric modeling technique is proposed to generate the blur manifolds, and estimate the fuzzy blur structure. The PDR scheme involves the development of the meaningful cost function, the estimation of blur support and structure, and the optimization of the cost function. Experimental results show that it is effective in restoring degraded images under different environments.

Efficient blind image restoration using discrete periodic radon transform

Restoring an image from its convolution with an unknown blur function is a well-known ill-posed problem in image processing. Many approaches have been proposed to solve the problem and they have shown to have good performance in identifying the blur function and restoring the original image. However, in actual implementation, various problems incurred due to the large data size and long computational time of these approaches are undesirable even with the current computing machines. In this paper, an efficient algorithm is proposed for blind image restoration based on the discrete periodic Radon transform (DPRT). With DPRT, the original two-dimensional blind image restoration problem is converted into one-dimensional ones, which greatly reduces the memory size and computational time required. Experimental results show that the resulting approach is faster in almost an order of magnitude as compared with the traditional approach, while the quality of the restored image is similar.

Multichannel blind iterative image restoration

Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately in a single-channel framework, serious conceptual and numerical problems are often encountered. Very recently, an eigenvector-based method (EVAM) was proposed for a multichannel framework which determines perfectly convolution masks in a noise-free environment if channel disparity, called co-primeness, is satisfied. We propose a novel iterative algorithm based on recent anisotropic denoising techniques of total variation and a Mumford-Shah functional with the EVAM restoration condition included. A linearization scheme of half-quadratic regularization together with a cell-centered finite difference discretization scheme is used in the algorithm and provides a unified approach to the solution of total variation or Mumford-Shah. The algorithm performs well even on very noisy images and does not require an exact estimation of mask orders. We demonstrate capabilities of the algorithm on synthetic data. Finally, the algorithm is applied to defocused images taken with a digital camera and to data from astronomical ground-based observations of the Sun.

Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement

In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cross-validation method (GCV). We propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory, reducing the computational complexity of the GCV. Data-driven PSF and regularization parameter estimation experiments with synthetic and real image sequences are presented to demonstrate the effectiveness and robustness of our method.

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.

Perfect blind restoration of images blurred by multiple filters: theory and efficient algorithms

We address the problem of restoring an image from its noisy convolutions with two or more unknown finite impulse response (FIR) filters. We develop theoretical results about the existence and uniqueness of solutions, and show that under some generically true assumptions, both the filters and the image can be determined exactly in the absence of noise, and stably estimated in its presence. We present efficient algorithms to estimate the blur functions and their sizes. These algorithms are of two types, subspace-based and likelihood-based, and are extensions of techniques proposed for the solution of the multichannel blind deconvolution problem in one dimension. We present memory and computation-efficient techniques to handle the very large matrices arising in the two-dimensional (2-D) case. Once the blur functions are determined, they are used in a multichannel deconvolution step to reconstruct the unknown image. The theoretical and practical implications of edge effects, and "weakly exciting" images are examined. Finally, the algorithms are demonstrated on synthetic and real data.

Blind image deconvolution using a robust GCD approach

In this correspondence, a new viewpoint is proposed for estimating an image from its distorted versions in presence of noise without the a priori knowledge of the distortion functions. In z-domain, the desired image can be regarded as the greatest common polynomial divisor among the distorted versions. With the assumption that the distortion filters are finite impulse response (FIR) and relatively coprime, in the absence of noise, this becomes a problem of taking the greatest common divisor (GCD) of two or more two-dimensional (2-D) polynomials. Exact GCD is not desirable because even extremely small variations due to quantization error or additive noise can destroy the integrity of the polynomial system and lead to a trivial solution. Our approach to this blind deconvolution approximation problem introduces a new robust interpolative 2-D GCD method based on a one-dimensional (1-D) Sylvester-type GCD algorithm. Experimental results with both synthetically blurred images and real motion-blurred pictures show that it is computationally efficient and moderately noise robust.

Exact image deconvolution from multiple FIR blurs

We address the problem of restoring an image from its noisy convolutions with two or more blur functions (channels). Deconvolution from multiple blurs is, in general, better conditioned than from a single blur, and can be performed without regularization for moderate noise levels. We characterize the problem of missing data at the image boundaries, and show that perfect reconstruction is impossible (even in the no-noise case) almost surely unless there are at least three channels. Conversely, when there are at least three channels, we show that perfect reconstruction is not only possible almost surely in the absence of noise, but also that it can be accomplished by finite impulse response (FIR) filtering. Such FIR reconstruction is vastly more efficient computationally than the least-squares solution, and is suitable for low noise levels. Even in the high-noise case, the estimates obtained by FIR filtering provide useful starting points for iterative least-squares algorithms. We present results on the minimum possible sizes of such deconvolver filters. We derive expressions for the mean-square errors in the FIR reconstructions, and show that performance comparable to that of the least-squares reconstruction may be obtained with relatively small deconvolver filters. Finally, we demonstrate the FIR reconstruction on synthetic and real data.

Image restoration and reconstruction with a Bayesian approach

We have extended Johnson's Bayesian method for image restoration and reconstruction by introducing diagonal line sites, using symmetric neighborhood configurations, and employing an additional hyperparameter for estimation of line sites. A general formulation for arbitrary neighborhood configurations was derived. The major part of this paper deals with the conduct of computer simulations intended to examine the effect of the hyperparameters, the diagonal line sites, and the size of the neighborhood configuration on the performance of the proposed Bayesian method. We show that, for optimal performance, distinct hyperparameters should be used for the intensity sites and line sites. The results also suggest that a large neighborhood configuration should be used. By comparing the near-optimal restored images, we demonstrated that the use of diagonal line sites, along with the symmetric configurations thus made possible, can effectively remove the blocky edge artifacts and produce images of better quality. When the method was applied to positron emission tomography (PET) image reconstruction, our results showed that the quality of the reconstructed images was improved for both computer-simulated and real patient PET data.

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.

Regularized constrained total least squares image restoration

In this paper, the problem of restoring an image distorted by a linear space-invariant (LSI) point-spread function (PSF) that is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible even for large images. An error analysis of the RCTLS estimate, based on the mean-squared-error (MSE) criterion, is performed to verify its superiority over the constrained total least-squares (CTLS) estimate. Numerical experiments for different errors in the PSF are performed to test the RCTLS estimator. Objective and visual comparisons are presented with the linear minimum mean-squared-error (LMMSE) and the regularized least-squares (RLS) estimator. Our experiments show that the RCTLS estimator reduces significantly ringing artifacts around edges as compared to the two other approaches.

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.