Abstract: This work extends the Bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems. We address the restoration of images with poor spatial correlation as well as strongly correlated (natural) images. The spatial nonlinearity employed in the final estimation step of the Bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images. For spatially correlated images, the nonlinearity design is rather conducted using a particular wavelet decomposition that, detecting lines, edges, and higher order structures, carries out a task analogous to those of the (preattentive) stage of the human visual system. Experimental results pertaining to restoration of motion blurred text images, out-of-focus spiky images, and blurred natural images are reported.

Abstract: Blind deconvolution is fundamental in signal processing applications and, in particular, the single channel case remains a challenging and formidable problem. This paper considers single channel blind deconvolution in the case where the degraded observed signal may be modeled as the convolution of a nonstationary source signal with a stationary distortion operator. The important feature that the source is nonstationary while the channel is stationary facilitates the unambiguous identification of either the source or channel, and deconvolution is possible, whereas if the source and channel are both stationary, identification is ambiguous. The parameters for the channel are estimated by modeling the source as a time-varyng AR process and the distortion by an all-pole filter, and using the Bayesian framework for parameter estimation. This estimate can then be used to deconvolve the observed signal. In contrast to the classical histogram approach for estimating the channel poles, where the technique merely relies on the fact that the channel is actually stationary rather than modeling it as so, the proposed Bayesian method does take account for the channel's stationarity in the model and, consequently, is more robust. The properties of this model are investigated, and the advantage of utilizing the nonstationarity of a system rather than considering it as a curse is discussed.

Abstract: In order to improve the resolution of seismic images, a blind deconvolution of seismic traces is necessary, since the source wavelet is not known and cannot be considered as a stationary signal. The reflectivity sequence is modeled as a Gaussian mixture, depending on three parameters (high and low reflector variances and reflector density), on the wavelet impulse response, and on the observation noise variance. These parameters are unknown and must be estimated from the recorded trace, which is the reflectivity convolved with the wavelet, plus noise. Two methods are compared in this paper for the parameter estimation. Since we are considering an incomplete data problem, we first consider maximum likelihood estimation by means of a stochastic expectation maximization (SEM) method. Alternatively, proper prior distributions can be specified for all unknown quantities. Then, a Bayesian strategy is applied, based on a Monte Carlo Markov Chain (MCMC) method. Having estimated the parameters, one can proceed to the deconvolution. A maximum posterior mode (MPM) criterion is optimized by means of an MCMC method. The deconvolution capability of these procedures is checked first on synthetic signals and then on the seismic data of the IFREMER ESSR4 campaign, where the wavelet duration blurs the reflectivity, and on the SMAVH high-resolution marine seismic data.

Abstract: A quasi maximum likelihood framework for blind deconvolution of images is presented. We generalize the relative Newton algorithm, previously proposed for quasi maximum likelihood blind source separation and blind deconvolution of time signals, and provide asymptotic analysis of its performance. Smooth approximation of the absolute value is used to model the log probability density function, which is suitable for sparse sources. In addition, we propose a method of sparsification, which allows to perform blind deconvolution of sources with arbitrary distribution, and show how to find optimal sparsifying transformations by training.

Abstract: This paper is a supplement and update to the reviews by Kundur and Hatzinakos (7,8) on blind image deconvolution. Most of the methods reviewed in (7,8) require that the PSF and the original image must be irreducible. However, this irreducibility assumption is not true in some important types of applications, such as when the PSF is Gaussian, which is a good model for many imaging systems. After a brief summary of existing blind deconvolution methods, we report the recent development in this field with an emphasis on Gaussian blind deconvolution and its clinical applications.

Abstract: Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.

Abstract: This paper describes two efficient realizations of an adaptive multichannel blind deconvolution algorithm based on the natural gradient algorithm originally proposed by Amari, Douglas, Cichocki, and Yang. The proposed algorithms use fast convolution and correlation techniques and operate primarily in the frequency domain. Since the cost function minimized by the algorithms is welldefined in the time domain, the algorithms do not suffer from the so-called frequency-domain permutation problem. The proposed algorithm can be viewed as an multi-channel extension of a singlechannel blind deconvolution algorithm recently proposed by the authors.

Abstract: Methods and systems for three-dimensional imaging through turbulence such as produced by the Earth's atmosphere are described. A first light source may direct an output of pulses to a target through atmospheric turbulence. A first image sensor, for example a time of arrival sensor or focal plane, may receive light from the first light source and may be used to record two-dimensional images or image slices of the target. A second light source may also be used. A second image sensor may receive light reflected from the target. An atmospheric point spread function may be derived or calculated by a means for multiframe blind deconvolution from one or more images of the target received at the second image sensor. The point spread function may be used to deblur or improve the resolution of each of the two-dimensional image slices from the first image sensor. The two-dimensional image slices may be combined to form a three-dimensional image of the target.

Abstract: Many acoustical applications require the analysis of a signal that is corrupted by an unknown filtering function. Examples arise in the areas of noise or vibration control, room acoustics, structural vibration analysis, and speech processing. Here, the observed signal can be modeled as the convolution of the desired signal with an unknown system impulse response. Blind deconvolution refers to the process of learning the inverse of this unknown impulse response and applying it to the observed signal to remove the filtering effects. Unlike classical deconvolution, which requires prior knowledge of the impulse response, blind deconvolution requires only reasonable prior estimates of the input signal’s statistics. The significant contribution of this work lies in experimental verification of a blind deconvolution algorithm in the context of acoustical system identification. Previous experimental work concerning blind deconvolution in acoustics has been minimal, as previous literature concerning blind deconvolution uses computer simulated data. This paper examines experiments involving three classical acoustic systems: driven pipe, driven pipe with open side branch, and driven pipe with Helmholtz resonator side branch. Experimental results confirm that the deconvolution algorithm learns these systems’ inverse impulse responses, and that application of these learned inverses removes the effects of the filters.

Abstract: 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.

Abstract: A new method for deconvolution of one-dimensional and multidimensional data is suggested. The proposed algorithm is local in the sense that the deconvolved data at a given point depend only on the value of the experimental data and their derivatives at the same point. In a regularized version of the algorithm the deconvolution is constructed iteratively with the help of an approximate deconvolution operator that requires only the low-order derivatives of the data and low-order integral moments of the point-spread function. This algorithm is expected to be particularly useful in applications in which only partial knowledge of the point-spread function is available. We tested and compared the proposed method with some of the popular deconvolution algorithms using simulated data with various levels of noise.

Abstract: Convolution is a linear operation, and, consequently, can be formulated as a linear system of equations. If only the output of the system (the convolved signal) is known, then the problem is blind so that given one equation, two unknowns are sought. Here, the blind deconvolution problem is solved using independent component analysis (ICA). To facilitate this, several time lagged versions of the convolved signal are extracted and used to construct realizations of a random vector. For ICA, this random vector is the, so called, mixture vector, created by the matrix-vector multiplication of the two unknowns, the mixing matrix and the source vector. Due to the properties of convolution, the mixing matrix is banded with its nonzero elements containing the convolution’s filter. This banded property is incorporated into the ICA algorithm as prior information, giving rise to a banded ICA algorithm (B-ICA) which is, in turn, used in a new blind deconvolution method. B-ICA produces as many independent components as the dimension of the filter; whereas for blind deconvolution, only one signal is sought (the deconvolved signal). Fortunately, the convolutional model provides additional information which enables one best independent component to be extracted from the pool of candidate solutions. This, in turn, yields estimates of both the filter and the deconvolved signal.

Abstract: The paper proposes a new wavelet-based Bayesian approach to image deconvolution, under the space-invariant blur and additive white Gaussian noise assumptions. Image deconvolution exploits the well known sparsity of the wavelet coefficients, described by heavy-tailed priors. The present approach admits any prior given by a linear (finite of infinite) combination of Gaussian densities. To compute the maximum a posteriori (MAP) estimate, we propose a generalized expectation maximization (GEM) algorithm where the missing variables are the Gaussian modes. The maximization step of the EM algorithm is approximated by a stationary second order iterative method. The result is a GEM algorithm of O(N log N) computational complexity. In comparison with state-of-the-art methods, the proposed algorithm either outperforms or equals them, with low computational complexity.

Abstract: Deconvolution is a necessary tool for the exploitation of adaptive optics corrected images, because the correction is partial. The Maximum A Posteriori (MAP) framework is used to derive a deconvolution method (MISTRAL) that combines the data with our knowledge of the noise statistics as well as our prior information about the object and the variability of the Point Spread Function. The deconvolution of experimental and scientific data illustrates the capabilities of this method.

Abstract: The all-pole model is often used to approximate rational transfer functions parsimoniously. In many applications, such as single channel blind deconvolution, an estimate of the channel is required. However, in general, attempting to model the entire channel spectrum by a single all-pole model leads to a large computational load. Hence, it is better to model a particular frequency band of the spectrum by an all-pole model, reducing a single high-dimensional optimisation to a number of low-dimensional ones. If each subband is completely decoupled from the others, and does not enforce any continuity, there are discontinuities in the spectrum at the subband boundaries. Continuity is ensured by constraining the subband parameters such that the end points at one subband boundary are matched to the spectrum in the adjacent subbands. This is formulated in the Bayesian probabilistic framework.

Abstract: This work deals with the processing of GPR (ground penetrating radar) signals for AP (anti-personnel) mine detection. It focuses on two steps in this processing, namely the deconvolution of the system impulse response, and the extraction of target features for classification. The objective of the work is to find discriminant and robust target features by means of time-frequency analysis. Deconvolution is an ill-posed inverse problem, which can be solved with regularization methods. In this paper a deconvolution algorithm, based on the iterative v-method, is proposed. For discriminant feature selection the Wigner distribution (WD) is considered. Singular value decomposition (SVD) along with the concept of the center of mass as the most robust feature are used for feature extraction from the WD. The proposed normalized time-frequency-energetic features have a good discriminant power, which doesn't degrade with increasing object depth.

Abstract: This paper proposes an adaptive blind image deconvolution scheme based on fuzzy K-nearest-neighbor (FKNN) algorithm. It is well known that most point-spread functions (PSFs) satisfy up to a certain degree of parametric structure. The method incorporates such knowledge about the PSF structure by estimating the PSF according to its K nearest neighbors. Through a process of neighbor generation, model matching, and fuzzy weighted mean filtering, FKNN provides a robust estimate for the blur. This further improves the convergence performance in blind deconvolution process. Experimental results show that it is effective in restoring degraded images where there is little prior knowledge about the blur.

Abstract: A new method for the recovery of noisy and blurred color images is presented. The image is reconstructed and the blurring kernel is approximated, under the assumption of linearity and spatial invariance of the blurring kernel. It is done by combining the Beltrami operator, which was introduced as a general framework for low-level vision, with the scheme of the blind deconvolution, which was introduced for the recovery of blurred and noisy gray value images. Consequently, image and kernel edges are preserved due to the adaptive smoothing feature of this operator. The color channels are coupled by a Riemannian structure, which is defined on the color image. The functional minimization scheme is presented and results of applying it in the recovery of blurred and noisy color images are illustrated.

Abstract: This paper presents a novel deconvolution algorithm designed to estimate the impulse response of buried objects based on ground penetrating radar (GPR) signals. The impulse response is a rich source of information about the buried object and therefore very useful for intelligent signal processing of GPR data. For example, it can be used in a target classification scheme to reduce the false alarm rate in demining operations. Estimating the target impulse response from the incident and scattered radar signals is a basic deconvolution problem. However, noise sensitivity and ground dispersion prevent the use of simple deconvolution methods like linear least squares deconvolution. Instead, a new deconvolution algorithm has been developed that computes estimates adhering to a physical impulse response model and that can be characterized by a limited number of parameters. It is shown that the new algorithm is robust with respect to noise and that it can deal with ground dispersion. The general performance of the algorithm has been tested on data generated by finite-difference time-domain (FDTD) simulations. The results demonstrate that the algorithm can distinguish between different dielectric and metal targets, making it very suitable for use in a classification scheme. Moreover, since the estimated impulse responses have physical meaning they can be related to target characteristics such as size and material properties. A direct application of this is the estimation of the permittivity of a dielectric target from its impulse response and that of a calibration target.

Abstract: Superresolution is the problem of reconstructing a single high-resolution image from several blurred and down-sampled low-resolution versions of it. We solve this problem for the case of unknown blurring functions. The image and functions must have finite support, and the number of low-resolution images must equal or exceed the number of pixels in each blurring function. Using a 2-D polyphase decomposition of the image, we show that the obvious reformulation as an MIMO blind deconvolution problem fails unless the grid of downsampling is chosen carefully, in which case 2X2 downsampling can be achieved. We also show that irregular sampling allows reconstruction of an MXM high-resolution image from L 2 low-resolution images blurred with an LXL blurring function can be achieved with as few as L 2 + (M/L) 2 pixels in each low-resolution image. Illustrative examples illustrate the points with explicit numbers.

Abstract: A blind deconvolution problem is newly stated with the following conditions: the point-spread function is band limited, both the object and the point-spread function are nonnegative, and the solution is to be a diffraction-limited object. A blind deconvolution method was developed that can easily be applied to problems in optics because of the conditions used. The performance of the method is investigated with computer simulations.

Abstract: In this paper, some basic concepts and techniques on seismic blind deconvolution are given in the view of dynamic system in detail Linear and non-linear seismic blind deconvolution can be discussed in the same frame of Blind System Identification The authors claimed that, as the method for solving instant mixing blind deconvolution(Blind Separation), Independent Component Analysis(ICA) may be a promising solution for generalized seismic blind deconvolution by introducing two possible programs based on ICAWT5"HZ

Abstract: We propose a new novel two-stage blind separation and deconvolution (BSD) algorithm for a real convolutive mixture of temporally correlated signals, in which a new Single-Input Multiple-Output (SIMO)-model-based ICA (SIMO-ICA) and blind multichannel inverse filtering are combined. SIMO-ICA consists of multiple ICAs and a fidelity controller, and each ICA runs in parallel under fidelity control of the entire separation system. SIMO-ICA can separate the mixed signals, not into monaural source signals but into SIMO-model-based signals from independent sources as they are at the microphones. Thus, the separated signals of SIMOICA can maintain the spatial qualities of each sound source. After the separation by SIMO-ICA, a simple blind deconvolution technique based on multichannel inverse filtering for the SIMO model can be applied even when the mixing system is the nonminimum phase system and each source signal is temporally correlated. The experimental results obtained under the reverberant condition reveal that the sound quality of the separated signals in the proposed method is superior to that in the conventional ICA-based BSD.