Blind Deconvolution Method Based on Precondition Conjugate Gradients

In seismic data processing, blind deconvolution is a key technology. Introduced in this paper is a flow of one kind of blind deconvolution. The optimal precondition conjugate gradients (PCG) in Kyrlov subspace is also used to improve the stability of the algorithm. The computation amount is greatly decreased.

A New Fast Iterative Blind Deconvolution Algorithm

Successful blind image deconvolution algorithms require the exact estimation of the Point Spread Function size, PSF. In the absence of any priori information about the imagery system and the true image, this estimation is normally done by trial and error experimentation, until an acceptable restored image quality is obtained. This paper, presents an exact estimation of the PSF size, which yields the optimum restored image quality for both noisy and noiseless images. It is based on evaluating the detail energy of the wave packet decomposition of the blurred image. The minimum detail energies occur at the optimum PSF size. Having accurately estimated the PSF, the paper also proposes a fast double updating algorithm for improving the quality of the restored image. This is achieved by the least squares minimization of a system of linear equations that minimizes some error functions derived from the blurred image. Moreover, a technique is also proposed to improve the sharpness of the deconvolved images, by constrained maximization of some of the detail wavelet packet energies. Simulation results of several examples have verified that the proposed technique manages to yield a sharper image with higher PSNR than classical approaches.

A novel blind deconvolution algorithm using single frequency bin

Former frequency-domain blind devolution algorithms need to consider a large number of frequency bins and recover the sources in different orders and with different amplitudes in each frequency bin,so they suffer from permutation and amplitude indeterminacy troubles. Based on sliding discrete Fourier transform,the presented deconvolution algorithm can directly recover time-domain sources from frequency-domain convolutive model using single frequency bin. It only needs to execute blind sepa-ration of instantaneous mixture once there are no permutation and amplitude indeterminacy troubles. Compared with former algorithms,the algorithm greatly reduces the computation cost as only one frequency bin is considered. Its good and robust per-formance is demonstrated by simulations when the signal-to-noise-ratio is high.

Multiframe Blind Super Resolution Imaging Based on Blind Deconvolution

As an ill-posed problem, multiframe blind super resolution imaging recovers a high resolution image from a group of low resolution images with some degradations when the information of blur kernel is limited. Note that the quality of the recovered image is influenced more by the accuracy of blur estimation than an advanced regularization. We study the traditional model of the multiframe super resolution and modify it for blind deblurring. Based on the analysis, we proposed two algorithms. The first one is based on the total variation blind deconvolution algorithm and formulated as a functional for optimization with the regularization of blur. Based on the alternating minimization and the gradient descent algorithm, the high resolution image and the unknown blur kernel are estimated iteratively. By using the median shift and add operator, the second algorithm is more robust to the outlier influence. The MSAA initialization simplifies the interpolation process to reconstruct the blurred high resolution image for blind deblurring and improves the accuracy of blind super resolution imaging. The experimental results demonstrate the superiority and accuracy of our novel algorithms.

Astronomical image restoration using variational Bayesian blind deconvolution

An algorithm is presented for image prior combinations based blind deconvolution and applied to astronomical images.Using a hierarchical Bayesian framework, the unknown original image and all required algorithmic parameters are estimated simultaneously. Through utilization of variational Bayesian analysis,approximations of the posterior distributions on each unknown are obtained by minimizing the Kullback-Leibler(KL) distance, thus providing uncertainties of the estimates during the restoration process. Experimental results on both synthetic images and real astronomical images demonstrate that the proposed approaches compare favorably to other state-of-the-art reconstruction methods.

PERFORMANCE OF BLIND DECONVOLUTION IN OPTOACOUSTIC TOMOGRAPHY

In this paper,we consider the use of blind deconvolution for optoacoustic(photoacoustic)imaging and investigate the performance of the method as means for increasing the resolution of the reconstructed image beyond the physical restrictions of the system.The method is demonstrated with optoacoustic measurement obtained from six-day-old mice,imaged in the near-infrared using a broadband hydrophone in a circular scanning configuration.Wefind that estimates of the unknown point spread function,achieved by blind deconvolution,improve the resolution and contrast in the images and show promise for enhancing optoacoustic images.

Blind Deconvolution of Seismic Data Based on the Spearman’s Rho

In this paper, we propose a novel seismic blind deconvolution approach based on the Spearman’s rho in the case of band-limited seismic data with a low dominant frequency and short data records. The Spearman’s rho is a measure of the dependence between two continuous random variables without the influence of the marginal distributions, by which a new criterion for blind deconvolution is constructed. The optimization program for new criterion of blind deconvolution is performed by applying Neidell’s wavelet model to the inverse filter. The noise-free and noisy synthetic data, onshore seismic trace in the Ordos Basin, and offshore stacked section in the Bohai Bay Basin examples show good results of the method.

AN IMPROVED FAST BLIND DECONVOLUTION ALGORITHM BASED ON DECORRELATION AND BLOCK MATRIX

In order to alleviate the shortcomings of most blind deconvolution algorithms,this paper proposes an improved fast algorithm for blind deconvolution based on decorrelation technique and broadband block matrix.Althougth the original algorithm can overcome the shortcomings of current blind deconvolution algorithms,it has a constraint that the number of the source signals must be less than that of the channels.The improved algorithm deletes this constraint by using decorrelation technique.Besides,the improved algorithm raises the separation speed in terms of improving the computing methods of the output signal matrix.Simulation results demonstrate the validation and fast separation of the improved algorithm.

ITERATIVE MULTICHANNEL BLIND DECONVOLUTION METHOD FOR TEMPORALLY COLORED SOURCES

An iterative separation approach, i.e. source signals are extracted and removed one by one, is proposed for multichannel blind deconvolution of colored signals. Each source signal is extracted in two stages: a filtered version of the source signal is first obtained by solving the generalized eigenvalue problem, which is then followed by a single channel blind deconvolution based on ensemble learning. Simulation demonstrates the capability of the approach to perform efficient mutichannel blind deconvolution.

A Modified Eigenvector Method for Blind Deconvolution of MIMO Systems Using the Matrix Pseudo-Inversion Lemma

Recently we have developed an eigenvector method (EVM) which can achieve the blind deconvolution (BD) for MIMO systems. One of attractive features of the proposed algorithm is that the BD can be achieved by calculating the eigenvectors of a matrix relevant to it. However, the performance accuracy of the EVM depends highly on computational results of the eigenvectors. In this paper, by modifying the EVM, we propose an algorithm which can achieve the BD without calculating the eigenvectors. Then the pseudo-inverse which is needed to carry out the BD is calculated by our proposed matrix pseudo-inversion lemma. Moreover, using a combination of the conventional EVM and the modified EVM, we will show its performances comparing with each EVM. Simulation results will be presented for showing the effectiveness of the proposed methods.

Blind Deconvolution Processing of Loop Inductance Signals for Vehicle Reidentification

Vehicle reidentification is an elegant solution for gathering several pieces of valuable traffic information, e.g., space mean speed, travel time, vehicle tracking, and origin/destination data. Recently, a number of vehiclereidentification algorithms utilizing inductive loop signals have been proposed to take advantage of the widespread availability of loop detectors. These algorithms, however, all directly utilize the raw inductance signals for pattern matching and feature extraction without deconvolution. The raw loop signals are essentially a convolved output between the true vehicle inductance signature and the loop system function, and thus a deconvolution is needed in order to expose the detailed features of individual vehicles. The purpose of this paper is to present a recent investigation on restoration of true inductance signatures by applying a blind deconvolution process. The main advantage of blind deconvolution over the conventional deconvolution is that the computation does not require modeling of a precise loop-detector system function. Experimental results show that the proposed blind deconvolution reveals much more detailed features of inductance signals and, as a result, increases the vehicle reidentification accuracy.

Wavelet-based deconvolution of ultrasonic signals in nondestructive evaluation

In this paper, the inverse problem of reconstructing reflectivity function of a medium is examined within a blind deconvolution framework. The ultrasound pulse is estimated using higher-order statistics, and Wiener filter is used to obtain the ultrasonic reflectivity function through wavelet-based models. A new approach to the parameter estimation of the inverse filtering step is proposed in the nondestructive evaluation field, which is based on the theory of Fourier-Wavelet regularized deconvolution (ForWaRD). This new approach can be viewed as a solution to the open problem of adaptation of the ForWaRD framework to perform the convolution kernel estimation and deconvolution interdependently. The results indicate stable solutions of the esti- mated pulse and an improvement in the radio-frequency (RF) signal taking into account its signal-to-noise ratio (SNR) and axial resolution. Simulations and experiments showed that the proposed approach can provide robust and optimal estimates of the reflectivity function.

Inspection of the Output of a Convolution and Deconvolution Process from the Leading Digit Point of View—Benford’s Law

In the communication field, during transmission, a source signal undergoes a convolutive distortion between its symbols and the channel impulse response. This distortion is referred to as Intersymbol Interference (ISI) and can be reduced significantly by applying a blind adaptive deconvolution process (blind adaptive equalizer) on the distorted received symbols. But, since the entire blind deconvolution process is carried out with no training symbols and the channel’s coefficients are obviously unknown to the receiver, no actual indication can be given (via the mean square error (MSE) or ISI expression) during the deconvolution process whether the blind adaptive equalizer succeeded to remove the heavy ISI from the transmitted symbols or not. Up to now, the output of a convolution and deconvolution process was mainly investigated from the ISI point of view. In this paper, the output of a convolution and deconvolution process is inspected from the leading digit point of view. Simulation results indicate that for the 4PAM (Pulse Amplitude Modulation) and 16QAM (Quadrature Amplitude Modulation) input case, the number “1” is the leading digit at the output of a convolution and deconvolution process respectively as long as heavy ISI exists. However, this leading digit does not follow exactly Benford’s Law but follows approximately the leading digit (digit 1) of a Gaussian process for independent identically distributed input symbols and a channel with many coefficients.

Blind-restoration-based blind separation method for permuted motion blurred images

A novel single-channel blind separation algorithm for permuted motion blurred images is proposed by using blind restoration in this paper. Both the motion direction and the length of the point spread function （PSF） are estimated by Radon transformation and extrema a detection. Using the estimated blur parameters, the permuted image is restored by performing the L-R blind restoration method. The permutation mixing matrices can be accurately estimated by classifying the ringing effect in the restored image, thereby the source images can be separated. Simulation results show a better separation efficiency for the permuted motion blurred image with various permutation operations. The proposed algorithm indicates a better performance on the robustness against Gaussian noise and lossy JPEG compression.

An Approximated Expression for the Residual ISI Obtained by Blind Adaptive Equalizer and Biased Input Signals

Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.

BLIND ADAPTIVE XPIC BASED ON HOS

This paper presents a new blind XPIC and a new adaptive blind deconvolutional algorithm based on HOS processing, which separates and equalizes the signals in real time. The simulation results demonstrate that the performance of the proposed adaptive blind algorithm,compared with the conventional algorithms, is outstanding with the feature of feasibility, stability and fast convergence rate.

BLIND SPEECH SEPARATION FOR ROBOTS WITH INTELLIGENT HUMAN-MACHINE INTERACTION

Speech recognition rate will deteriorate greatly in human-machine interaction when the speaker's speech mixes with a bystander's voice. This paper proposes a time-frequency approach for Blind Source Seperation (BSS) for intelligent Human-Machine Interaction(HMI). Main idea of the algorithm is to simultaneously diagonalize the correlation matrix of the pre-whitened signals at different time delays for every frequency bins in time-frequency domain. The prososed method has two merits: (1) fast convergence speed; (2) high signal to interference ratio of the separated signals. Numerical evaluations are used to compare the performance of the proposed algorithm with two other deconvolution algorithms. An efficient algorithm to resolve permutation ambiguity is also proposed in this paper. The algorithm proposed saves more than 10% of computational time with properly selected parameters and achieves good performances for both simulated convolutive mixtures and real room recorded speeches.

Two Blind Adaptive Equalizers Connected in Series for Equalization Performance Improvement

A variable step-size parameter is usually used to accelerate the convergence speed of a blind adaptive equalizer with N1 + N2 -1 coefficients where N1 and N2 are odd values. In this paper we show that improved equalization performance is achieved when using two blind adaptive equalizers connected in series where the first and second blind adaptive equalizer have N1 and N2 coefficients respectively compared with the case where a single blind adaptive equalizer is applied with N1 + N2 -1 coefficients. It should be pointed out that the same algorithm (cost function) is used for updating the filter taps for the different equalizers and that a fixed step-size parameter is used. Simulation results show that for the low signal to noise ratio (SNR) environment and for the case where the convergence speed is slow due to the channel characteristics, the new method has a faster convergence speed with a factor of approximately two while leaving the system with approximately the same or lower residual intersymbol interference (ISI).

Blind Deblurring Based on L_0 Norm from Salient Edges

Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvolution. Experiments show that the details of the image destroy the structure of the kernel, especially when the blur kernel is large. So we extract the image structure with salient edges by the method based on RTV. In addition, the traditional method for motion blur kernel estimation based on sparse priors is conducive to gain a sparse blur kernel. But these priors do not ensure the continuity of blur kernel and sometimes induce noisy estimated results. Therefore we propose the kernel refinement method based on L0 to overcome the above shortcomings. In terms of non-blind deconvolution we adopt the L1/L2 regularization term. Compared with the traditional method, the method based on L1/L2 norm has better adaptability to image structure, and the constructed energy functional can better describe the sharp image. For this model, an effective algorithm is presented based on alternating minimization algorithm.

Convergence Curve for Non-Blind Adaptive Equalizers

In this paper a closed-form approximated expression is proposed for the Intersymbol Interference (ISI) as a function of time valid during the entire stages of the non-blind adaptive deconvolution process and is suitable for the noisy, real and two independent quadrature carrier input case. The obtained expression is applicable for type of channels where the resulting ISI as a function of time can be described with an exponential model having a single time constant. Based on this new expression for the ISI as a function of time, the convergence time (or number of iteration number required for convergence) of the non-blind adaptive equalizer can be calculated. Up to now, the equalizer’s performance (convergence time and ISI as a function of time) could be obtained only via simulation when the channel coefficients were known. The new proposed expression for the ISI as a function of time is based on the knowledge of the initial ISI and channel power (which is measurable) and eliminates the need to carry out any more the above mentioned simulation. Simulation results indicate a high correlation between the simulated and calculated ISI (based on our proposed expression for the ISI as a function of time) during the whole deconvolution process for the high as well as for the low signal to noise ratio (SNR) condition.