Image Restoration Applications Research Articles

Image Restoration: Past, Present and Future

Digital Image Restoration is a technique used to recover original image information from degraded images. Digital images lose information because of factors like noise, blurring and camera misfocus. Image restoration plays a significant role in improving the quality of pictures obtained from unmanned aircrafts, poor quality video tape of a crime scene and blurred satellite images. In this paper we review how the field of image restoration has evolved over the years, and how the techniques of image restoration are making inroads into various applications, thus improving users perception. The article also portrays recent advances and patents in the field of image restoration. Keywords: Image deblurring, image restoration, classical approaches to image restoration, adaptive approaches, median filter, image inpainting, inverse filtering, patents on image restoration applications

New PDE-based methods for image enhancement using SOM and Bayesian inference in various discretization schemes

A novel approach is presented in this paper for improving anisotropic diffusion PDE models, based on the Perona–Malik equation. A solution is proposed from an engineering perspective to adaptively estimate the parameters of the regularizing function in this equation. The goal of such a new adaptive diffusion scheme is to better preserve edges when the anisotropic diffusion PDE models are applied to image enhancement tasks. The proposed adaptive parameter estimation in the anisotropic diffusion PDE model involves self-organizing maps and Bayesian inference to define edge probabilities accurately. The proposed modifications attempt to capture not only simple edges but also difficult textural edges and incorporate their probability in the anisotropic diffusion model. In the context of the application of PDE models to image processing such adaptive schemes are closely related to the discrete image representation problem and the investigation of more suitable discretization algorithms using constraints derived from image processing theory. The proposed adaptive anisotropic diffusion model illustrates these concepts when it is numerically approximated by various discretization schemes in a database of magnetic resonance images (MRI), where it is shown to be efficient in image filtering and restoration applications.

Learning Multiscale Sparse Representations for Image and Video Restoration

This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [M. Aharon, M. Elad, and A. M. Bruckstein, IEEE Trans. Signal Process., 54 (2006), pp. 4311–4322], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via orthogonal matching pursuit (OMP) and singular value decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary and overlapping image patches. The proposed framework provides an alternative to predefined dictionaries such as wavelets and is shown to lead to state-of-the-art results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework and accompanies it by numerous examples demonstrating its strength.

Real-time restoration of white-light confocal microscope optical sections

Confocal microscopes (CM) are routinely used for building 3-D images of microscopic structures. Nonideal imaging conditions in a white-light CM introduce additive noise and blur. The optical section images need to be restored prior to quantitative analysis. We present an adaptive noise filtering technique using Karhunen-Loéve expansion (KLE) by the method of snapshots and a ringing metric to quantify the ringing artifacts introduced in the images restored at various iterations of iterative Lucy-Richardson deconvolution algorithm. The KLE provides a set of basis functions that comprise the optimal linear basis for an ensemble of empirical observations. We show that most of the noise in the scene can be removed by reconstructing the images using the KLE basis vector with the largest eigenvalue. The prefiltering scheme presented is faster and does not require prior knowledge about image noise. Optical sections processed using the KLE prefilter can be restored using a simple inverse restoration algorithm; thus, the methodology is suitable for real-time image restoration applications. The KLE image prefilter outperforms the temporal-average prefilter in restoring CM optical sections. The ringing metric developed uses simple binary morphological operations to quantify the ringing artifacts and confirms with the visual observation of ringing artifacts in the restored images.

Fuzzy vector partition filtering technique for color image restoration

A fuzzy vector partition filter is proposed for real color image restoration applications. The filter utilizes the fuzzy ranking technique in the vector partition filtering framework to address a variety of noise corruptions in natural color images. The information of the local sample spread is tracked by the fuzzy ranking through its adaptive fuzzy sample similarity function. The non-stationary statistics of the color image is overcome by partitioning the image into a finite set of underlying local image structures and by applying an optimized nonlinear filter to restore each of the partitions accordingly. The proposed filter has been evaluated using various simulated and real-life noisy images. The results achieved by the filter are comparable to the prior-art methods specially designed for the underlying noise corruption, in terms of standard objective measurements and the subjective picture quality.

Determination of point spread function for a flat-panel X-ray imager and its application in image restoration

We investigate the image blur estimation methods, namely modified the Richardson–Lucy (R–L) estimator and the Wiener estimator. Based on the empirical model of the PSF, an image restoration is applied to radiological images. The accuracy of the PSF estimation under the Poisson noise and readout electronic noise is significantly better for the R–L estimator than the Wiener estimator. In the image restoration using the 2-D PSF from the R–L estimator, the result shows a good improvement in the low and middle range of spatial frequency.

Centroidal Voronoi Tessellation Algorithms for Image Compression, Segmentation, and Multichannel Restoration

Centroidal Voronoi tessellations (CVT's) are special Voronoi tessellations for which the generators of the tessellation are also the centers of mass (or means) of the Voronoi cells or clusters. CVT's have been found to be useful in many disparate and diverse settings. In this paper, CVT-based algorithms are developed for image compression, image segmenation, and multichannel image restoration applications. In the image processing context and in its simplest form, the CVT-based methodology reduces to the well-known k-means clustering technique. However, by viewing the latter within the CVT context, very useful generalizations and improvements can be easily made. Several such generalizations are exploited in this paper including the incorporation of cluster dependent weights, the incorporation of averaging techniques to treat noisy images, extensions to treat multichannel data, and combinations of the aforementioned. In each case, examples are provided to illustrate the efficiency, flexibility, and effectiveness of CVT-based image processing methodologies.

FLANN Detector Based Filtering of Images Corrupted by Impulse Noise

We present a novel non-linear scheme for image restoration based on neuro-detector using Functional Link Artificial Neural Network (FLANN) followed by an improved spatial filter. The method is applied to images corrupted by impulse noise with varying strengths and different noise probability. The neural detector is based on the concept of training or learning by examples. When trained properly, the detector used to detect impulse noise in any image degraded by impulse noise. Hence, the method is suitable for real time image restoration applications. The simulated results obtained from the proposed scheme outperforms existing approaches are highly satisfactory and it outperforms the earlier suggested methods in terms of residual NSR in restored images.

Factorized Banded Inverse Preconditioners for Matrices with Toeplitz Structure

In this paper, we study factorized banded inverse preconditioners for matrices with Toeplitz structure. We show that if a Toeplitz matrix T has certain off-diagonal decay property, then the factorized banded inverse preconditioner approximates T-1 accurately, and the spectra of these preconditioned matrices are clustered around 1. In nonlinear image restoration applications, Toeplitz-related systems of the form I + T*DT are required to solve, where D is a positive nonconstant diagonal matrix. We construct inverse preconditionersfor such matrices. Numerical results show that the performance of our proposed preconditioners are superior to that of circulant preconditioners. A two-dimensional nonlinear image restoration example is also presented to demonstrate the effectiveness of the proposed preconditioner.

Observing Shape from Defocused Images

Accommodation cues are measurable properties of an image that are associated with a change in the geometry of the imaging device. To what extent can three-dimensional shape be reconstructed using accommodation cues alone? This question is fundamental to the problem of reconstructing shape from focus (SFF) and shape from defocus (SFD) for applications in inspection, microscopy, image restoration and visualization. We address it by studying the “observability” of accommodation cues in an analytical framework that reveals under what conditions shape can be reconstructed from defocused images. We do so in three steps: (1) we characterize the observability of any surface in the presence of a controlled radiance (“weak observability”), (2) we conjecture the existence of a radiance that allows distinguishing any two surfaces (“sufficient excitation”) and (3) we show that in the absence of any prior knowledge on the radiance, two surfaces can be distinguished up to the degree of resolution determined by the complexity of the radiance (“strong observability”). We formulate the problem of reconstructing the shape and radiance of a scene as the minimization of the information divergence between blurred images, and propose an algorithm that is provably convergent and guarantees that the solution is admissible, in the sense of corresponding to a positive radiance and imaging kernel.

A fast BNM (Best Neighborhood Matching): Algorithm and parallel processing for image restoration

AbstractBest Neighborhood Matching (BNM) algorithm is a good approach of error concealment in terms of restored image quality. However, this kind of error concealment algorithm is commonly computation‐intensive, which restricts their real applications on large‐scale image or video sequence restoration. In this article, we propose a fast method, named Jump and look around Best Neighborhood Matching (JBNM), which reduces computing time to one sixth of that by BNM, while the quality of the restored images remains almost the same. To further reduce processing time and meet large‐scale image restorations, a parallel JBNM working on a cluster of workstations is proposed. Several critical techniques, including reading policy, overlap stripe data distribution, and communication strategies, have been developed to obtain high performance. Both theoretical analysis and experiment results indicate that our parallel JBNM provides an efficient technique for image restoration applications. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 13, 189–200, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10057

A note on the fast algorithm for block Toeplitz systems with tensor structure

We study the solutions of block Toeplitz systems T mn x= b by using the preconditioned conjugate gradient (PCG) method. Here T mn = T m ⊗ T n and T i, i=m,n are Toeplitz matrices. In [X. Jin, Appl. Math. Comput. 73 (1995) 115–124], Jin introduced a fast algorithm for these systems by applying the PCG method. This fast algorithm allows a tensor problem to be reduced to a one-dimensional problem. It was proved that if the mn-by- mn system is well conditioned, then the PCG method converges superlinearly and only O( mnlog mn) operations are required in solving the preconditioned system. However, only well-conditioned systems were considered in Jin, 1995. In this paper, we apply this fast algorithm with the { ω}-circulant preconditioners proposed in [D. Potts, G. Steidl, Preconditioners for Ill-Conditioned toeplitz matrices, BIT, to be appeared] to solve the ill-conditioned systems. Numerical results are included to illustrate the effectiveness of the algorithm for solving the preconditioned systems by using the PCG method. An application in image restoration is also given.

Quality measures in applications of image restoration.

We describe a new method for the estimation of image quality in image restoration applications. We demonstrate this technique on a simulated data set of fluorescent beads, in comparison with restoration by three different deconvolution methods. Both the number of iterations and a regularisation factor are varied to enforce changes in the resulting image quality. First, the data sets are directly compared by an accuracy measure. These values serve to validate the image quality descriptor, which is developed on the basis of optical information theory. This most general measure takes into account the spectral energies and the noise, weighted in a logarithmic fashion. It is demonstrated that this method is particularly helpful as a user-oriented method to control the output of iterative image restorations and to eliminate the guesswork in choosing a suitable number of iterations.

Genetic-based fuzzy hybrid multichannel filters for color image restoration

On the design of multichannel filters, especially in color image restoration, it is not easy to simultaneously achieve three objectives: noise attenuation, chromaticity retention, and edges or details preservation. In this paper we propose a new class of multichannel filters, called genetic-based fuzzy hybrid multichannel (GFHM) filters, to reach these three objectives simultaneously. The design of GFHM filters is mainly based on human concept (heuristic rules) and genetic algorithms. Because the human concept can be readily and efficiently expressed by fuzzy implicative rules, GFHM filters can take the useful characteristics of filtering behavior of three filters: a vector median, a vector directional, and an identity filter. Since genetic algorithms possess the global-searching capability for an optimal solution, they are able to effectively optimize GFHM filters to improve the filtering performance. In color image restoration applications, extensive simulation results illustrate that GFHM filters not only achieve these three objectives but also possess the robust and the adaptive capability; moreover, these simulation results also demonstrate that the performance of GFHM filters outperforms that of other proposed filtering techniques.

Adaptive fuzzy hybrid multichannel filters for removal of impulsive noise from color images

On the design of multichannel filters, especially in color image restoration, it is not easy to simultaneously achieve three objectives: noise attenuation, chromaticity retention, and edges or details preservation. In this paper, we propose a new class of multichannel filters called adaptive fuzzy hybrid multichannel (AFHM) filters to achieve these three objectives simultaneously. Our novel approach is mainly based on human concept (heuristic rules) and provides a significant framework to take the merits of filtering behavior of three filters: a vector median (VM) filter, a vector directional (VD) filter, and an identity filter. On the design of an AFHM filter, our approach is a powerful and flexible scheme to achieve these three objectives because human concept can be efficiently expressed by fuzzy implicative rules for improving the filtering performance. The AFHM filters are able to effectively inherit the merits of filtering behaviors of these three filters in color image restoration applications. This is the first paper to include human concept to design multichannel filters. Moreover, a faster convergence property of the learning algorithm is investigated to reduce the time complexity of the AFHM filters. Extensive simulation results illustrate that AFHM filters not only achieve these three objectives but also possess the robust and adaptive capabilities, and demonstrate that the performance of AFHM filters outperforms that of other proposed filtering techniques.

ℒ-M-S filters for image restoration applications

A new filtering architecture is proposed, generalizing some previously introduced multilevel median filters. An efficient design procedure for the new filtering architecture is demonstrated for image restoration application. Simulation results show a good noise rejection performance, combined with a fine detail preservation capability.

Inverse Toeplitz preconditioners for ill-posed problems

It has been shown recently that iterative regularization using conjugate gradient type methods for image restoration problems can be effectively preconditioned with circulant approximations. Here it is shown that the theoretical properties of this approach are not restricted to circulant matrices. Specifically, a Toeplitz approximate inverse preconditioning scheme for discrete ill-posed problems is considered. It is proved that the preconditioned system approximates the prolate matrix, and that this property implies that fast convergence of conjugate gradient type methods can be expected. In addition, it is shown that these results can be generalized to two-dimensional problems. An image restoration application is used to demonstrate the properties of the preconditioner.

Kronecker product and SVD approximations in image restoration

Image restoration applications often result in ill-posed least squares problems involving large, structured matrices. One approach used extensively is to restore the image in the frequency domain, thus providing fast algorithms using fast Fourier transforms (FFTs). This is equivalent to using a circulant approximation to a given matrix. Iterative methods may also be used effectively by exploiting the structure of the matrix. While iterative schemes are more expensive than FFT-based methods, it has been demonstrated that they are capable of providing better restorations. As an alternative, we propose an approximate singular value decomposition (SVD), which can be used in a variety of applications. Used as a direct method, the computed restorations are comparable to iterative methods but are computationally less expensive. In addition, the approximate SVD may be used with the generalized cross validation method to choose regularization parameters. It is also demonstrated that the approximate SVD can be an effective preconditioner for iterative methods.

MRL-filters: a general class of nonlinear systems and their optimal design for image processing

A class of morphological/rank/linear (MRL)-filters is presented as a general nonlinear tool for image processing. They consist of a linear combination between a morphological/rank filter and a linear filter. A gradient steepest descent method is proposed to optimally design these filters, using the averaged least mean squares (LMS) algorithm. The filter design is viewed as a learning process, and convergence issues are theoretically and experimentally investigated. A systematic approach is proposed to overcome the problem of nondifferentiability of the nonlinear filter component and to improve the numerical robustness of the training algorithm, which results in simple training equations. Image processing applications in system identification and image restoration are also presented, illustrating the simplicity of training MRL-filters and their effectiveness for image/signal processing.

Image restoration using a conjugate gradient-based adaptive filtering algorithm

A new two-dimensional (2-D) recursive conjugate gradient (RCG) algorithm is developed for adaptive filtering. This algorithm is based on the conjugate gradient method of optimization and therefore has a fast convergence characteristic. The RCG is computationally simpler than the recursive least square (RLS) algorithm. The RCG algorithm with the equation-error and output-error methods is investigated for application in image restoration. Simulation results show that the new algorithm significantly outperforms existing algorithms in the restoration of noisy images.