Total variation blind deconvolution

We present a blind deconvolution algorithm based on the total variational (TV) minimization method proposed by Acar and Vogel (1994). The motivation for regularizing with the TV norm is that it is extremely effective for recovering edges of images as well as some blurring functions, e.g., motion blur and out-of-focus blur. An alternating minimization (AM) implicit iterative scheme is devised to recover the image and simultaneously identify the point spread function (PSF). Numerical results indicate that the iterative scheme is quite robust, converges very fast (especially for discontinuous blur), and both the image and the PSF can be recovered under the presence of high noise level. Finally, we remark that PSFs without sharp edges, e.g., Gaussian blur, can also be identified through the TV approach.     

Relative optimization for blind deconvolution

We propose a relative optimization framework for quasi-maximum likelihood (QML) blind deconvolution and the relative Newton method as its particular instance. Special Hessian structure allows fast Newton system construction and solution, resulting in a fast-convergent algorithm with iteration complexity comparable to that of gradient methods. We also propose the use of rational infinite impulse response (IIR) restoration kernels, which constitute a richer family of filters than the traditionally used finite impulse response (FIR) kernels. We discuss different choices of nonlinear functions that are suitable for deconvolution of super- and sub-Gaussian sources and formulate the conditions under which the QML estimation is stable. Simulation results demonstrate the efficiency of the proposed methods.     

Bayesian techniques for blind deconvolution

This paper introduces extended Bayesian filters (EBFs), a new family of blind deconvolution filters for digital communications. The blind deconvolution problem is formulated as a nonlinear and non-Gaussian fixed-lag minimum mean square error filtering problem, and the EBF is derived as a suboptimal recursive estimator. The model-based setting makes extensive use of the transmitted symbol and noise distributions. A key feature of the EBF is that the filter lag can be chosen to be larger than the channel length, while the complexity is exponential in a parameter which is typically chosen to be smaller than both the channel length and the filter lag. Extensive simulations characterizing the performance of EBFs in severe intersymbol interference channels are presented. The fast convergence and robust equalization of the EBFs are demonstrated for uncoded linearly modulated signals [e.g., differentially encoded quaternary phase shift keying (QPSK)] transmitted over unknown channels. Comparisons are made to other blind symbol-by-symbol demodulation algorithms. The results show that the EBF provides much better performance (at increased complexity) compared to the constant modulus algorithm and the extended Kalman filter, and achieves a better performance-complexity trade-off than other Bayesian demodulation algorithms. The simulations also show that the EBF is applicable with large constellations and shaped modulations     

Super-exponential methods for blind deconvolution

A class of iterative methods for solving the blind deconvolution problem, i.e. for recovering the input of an unknown possibly nonminimum-phase linear system by observation of its output, is presented. These methods are universal do not require prior knowledge of the input distribution, are computationally efficient and statistically stable, and converge to the desired solution regardless of initialization at a very fast rate. The effects of finite length of the data, finite length of the equalizer, and additive noise in the system on the attainable performance (intersymbol interference) are analyzed. It is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems. Recursive and sequential algorithms are also developed, which allow real-time implementation and adaptive equalization of time-varying systems     

基于盲反卷积的盲自适应滤波器设计

通过盲反卷积的算法来实现盲自适应滤波,阐述了盲反卷积滤波器的工作原理及基本结构模型,通过调整滤波器系数来实现滤波,以便更好地跟踪信号的变化,最终实现自适应滤波,并借用Matlab仿真平台设计出自适应滤波器,验证了它的设计性能。     

Bussgang blind deconvolution for impulsive signals

Many blind deconvolution algorithms have been designed to extract digital communications signals corrupted by intersymbol interference (ISI). Such algorithms generally fail when applied to signals with impulsive characteristics, such as acoustic signals. While it is possible to stabilize such procedures in many cases by imposing unit-norm constraints on the adaptive equalizer coefficient vector, these modifications require costly divide and square-root operations. In this paper, we provide a theoretical analysis and explanation as to why unconstrained Bussgang-type algorithms are generally unsuitable for deconvolving impulsive signals. We then propose a novel modification of one such algorithm (the Sato algorithm) to enable it to deconvolve such signals. Our approach maintains the algorithmic simplicity of the Sato algorithm, requiring only additional multiplies and adds to implement. Sufficient conditions on the source signal distribution to guarantee local stability of the modified Sato algorithm about a deconvolving solution are derived. Computer simulations show the efficiency of the proposed approach as compared with various constrained and unconstrained blind deconvolution algorithms when deconvolving impulsive signals.     

Multiple frame projection based blind deconvolution

Important a priori information available for blind deconvolution in problems such as astronomical imaging and remote sensing is the information in the multiple frame images in which the object is common for each frame but the point spread function varies. A projection based blind deconvolution algorithm for solving the multiple frame case is proposed     

Three-dimensional blind deconvolution of SPECT images

Thanks to its ability to yield functionally rather than anatomically-based information, the three-dimensional (3-D) SPECT imagery technique has become a great help in the diagnostic of cerebrovascular diseases. Nevertheless, due to the imaging process, the 3-D single photon emission computed tomography (SPECT) images are very blurred and, consequently, their interpretation by the clinician is often difficult and subjective. In order to improve the resolution of these 3-D images and then to facilitate their interpretation, we propose herein to extend a recent image blind deconvolution technique (called the nonnegativity support constraint-recursive inverse filtering deconvolution method) in order to improve both the spatial and the interslice resolution of SPECT volumes. This technique requires a preliminary step in order to find the support of the object to be restored. In this paper, we propose to solve this problem with an unsupervised 3-D Markovian segmentation technique. This method has been successfully tested on numerous real and simulated brain SPECT volumes, yielding very promising restoration results.     

Regularization of RIF blind image deconvolution

Blind image restoration is the process of estimating both the true image and the blur from the degraded image, using only partial information about degradation sources and the imaging system. Our main interest concerns optical image enhancement, where the degradation often involves a convolution process. We provide a method to incorporate truncated eigenvalue and total variation regularization into a nonlinear recursive inverse filter (RIF) blind deconvolution scheme first proposed by Kundar, and by Kundur and Hatzinakos (1996, 1998). Tests are reported on simulated and optical imaging problems.     

Multidimensional system identification through blind deconvolution

By invoking characteristics of the recently introduced zero-sheet of the spectrum of a signal having finite (or compact) support, it is noted that the multidimensional system identification problem should be solvable through blind deconvolution, that is, the system response function should be inferrable in the absence of prior knowledge of the signal which excites the system. It is pointed out that practical blind deconvolution can only be effected iteratively at present. An iterative blind identification algorithm is described and is illustrated by recovery of images from blurred versions contaminated with noise of varying levels. Successful blind deconvolution is achieved without invoking prior knowledge of either the forms or the supports of either the original images or the point spread functions, which respectively correspond to exciting signals and response functions.     

Weighted least-squares blind deconvolution of non-minimum phasesystems

A new algorithm based on a weighted least-squares technique is proposed that allows online deconvolution of non-minimum phase systems with neither knowledge of the system's impulse response nor source statistics except for source signal moments up to the fourth order. Using computer simulations and computational complexity evaluation, the authors illustrate and compare the performances and the features of the proposed method with those of other techniques found in the literature     

Improved convergence of projection based blind deconvolution

Since the projection based blind deconvolution algorithm has a slow convergence rate, two methods to speed up the algorithm are proposed. The first method is based on the addition of a momentum term to the update rule. The second method is based on the adaptation of the step size. From the simulation results, we can see that the convergence rate is significantly improved by using either of these two methods     

Cascade neural networks for multichannel blind deconvolution

The authors present a new simple but efficient and powerful extension of Bussgang-type blind equalisation algorithms which can extract multiple source signals from their unknown convolutive mixtures. A cascade neural network is proposed, where each module consists of an equalisation subnetwork and a deflation subnetwork. This approach can adopt any blind equalisation algorithm (which has been developed for the equalisation of a single channel). It can also be applied when the number of source signals is not known in advance. Extensive computer simulation results confirm the validity and high efficiency of the proposed method     

A cartoon-plus-texture image decomposition model for blind deconvolution

In this paper, we study a blind deconvolution problem by using an image decomposition technique. Our idea is to make use of a cartoon-plus-texture image decomposition procedure into the deconvolution problem. Because cartoon and texture components can be represented differently in images, we can adapt suitable regularization methods to restore their components. In particular, the total variational regularization is used to describe the cartoon component, and Meyer’s G-norm is employed to model the texture component. In order to obtain the restored image automatically, we also use the generalized cross validation method efficiently and effectively to estimate their corresponding regularization parameters. Experimental results are reported to demonstrate that the visual quality of restored images by using the proposed method is very good, and is competitive with the other testing methods.     

A variational approach for Bayesian blind image deconvolution

In this paper, the blind image deconvolution (BID) problem is addressed using the Bayesian framework. In order to solve for the proposed Bayesian model, we present a new methodology based on a variational approximation, which has been recently introduced for several machine learning problems, and can be viewed as a generalization of the expectation maximization (EM) algorithm. This methodology reaps all the benefits of a "full Bayesian model" while bypassing some of its difficulties. We present three algorithms that solve the proposed Bayesian problem in closed form and can be implemented in the discrete Fourier domain. This makes them very cost effective even for very large images. We demonstrate with numerical experiments that these algorithms yield promising improvements as compared to previous BID algorithms. Furthermore, the proposed methodology is quite general with potential application to other Bayesian models for this and other imaging problems.     

Frequency-domain blind deconvolution based on mutual information rate

In this paper, a new blind single-input single-output (SISO) deconvolution method based on the minimization of the mutual information rate of the deconvolved output is proposed. The method works in the frequency domain and requires estimation of the signal probability density function. Thus, the algorithm uses higher order statistics (except for Gaussian source) and allows non-minimum-phase filter estimation. In practice, the criterion contains a regularization term for limiting noise amplification as in Wiener filtering. The score function estimation, which represents a key point of the algorithm, is detailed, and the most robust estimate is selected. Finally, experiments point to the relevance of the proposed algorithm: 1) any filter, minimum phase or not, can be estimated and 2) on actual data (underwater explosions, seismovolcanic phenomena), this deconvolution algorithm provides good results with a better tradeoff between deconvolution quality and noise amplification than existing methods.     

Boosting normalized sparsity regularization for blind image deconvolution

We focus on blind image deconvolution, which has attracted intensive attentions since Fergus et al.’s influential work in 2006. Among the current literature, the daring idea of imposing the normalized sparsity measure on blind image deblurring is a recent spotlight, which is, nevertheless, far from practical use in terms of estimating accuracy, efficiency, as well as robustness. To boost its performance, we propose a novel method via coupling the normalized sparsity measure with the total generalized variation, which, however, does not fit the blind deblurring problem. By use of operator splitting and alternating direction method of multipliers, a numerical scheme is derived, leading to a more accurate, efficient, and robust blind deblurring algorithm. Numerous blind deblurring results on both benchmark data and real-world blurred images demonstrate the competitive or even better performance compared against the state of the art.     

A recursive soft-decision approach to blind image deconvolution

This paper presents a new approach to blind image deconvolution based on soft-decision blur identification and hierarchical neural networks. Traditional blind algorithms require a hard-decision on whether the blur satisfies a parametric form before their formulations. As the blurring function is usually unknown a priori, this precondition inhibits the incorporation of parametric blur knowledge domain into the restoration schemes. The new technique addresses this difficulty by providing a continual soft-decision blur adaptation with respect to the best-fit parametric structure throughout deconvolution. The approach integrates the knowledge of well-known blur models without compromising its flexibility in restoring images degraded by nonstandard blurs. An optimization scheme is developed where a new cost function is projected and minimized with respect to the image and blur domains. A nested neural network, called the hierarchical cluster model is employed to provide an adaptive, perception-based restoration. Its sparse synaptic connections are instrumental in reducing the computational cost of restoration. Conjugate gradient optimization is adopted to identify the blur due to its computational efficiency. The approach is shown experimentally to be effective in restoring images degraded by different blurs.     

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 unified balanced approach to multichannel blind deconvolution

In this paper, we explore the application of a common operator used in systems theory, viz., the delta operator, to formulate a unified theory of multichannel blind deconvolution (MBD) which is valid in both discrete and continuous time domains. Apart from providing a unified treatment of MBD problems, this formulation permits a smooth transition of the demixer from a discrete time domain to a continuous time domain when the sampling rate is high. Furthermore we give a unified treatment of a balanced parameterized state space formulation to solving the MBD problem in both discrete and continuous time domains when the number of states is unknown.