Multichannel Blind Deconvolution Research Articles

Retinal image restoration by means of blind deconvolution

Retinal imaging plays a key role in the diagnosis and management of ophthalmologic disorders, such as diabetic retinopathy, glaucoma, and age-related macular degeneration. Because of the acquisition process, retinal images often suffer from blurring and uneven illumination. This problem may seriously affect disease diagnosis and progression assessment. Here we present a method for color retinal image restoration by means of multichannel blind deconvolution. The method is applied to a pair of retinal images acquired within a lapse of time, ranging from several minutes to months. It consists of a series of preprocessing steps to adjust the images so they comply with the considered degradation model, followed by the estimation of the point-spread function and, ultimately, image deconvolution. The preprocessing is mainly composed of image registration, uneven illumination compensation, and segmentation of areas with structural changes. In addition, we have developed a procedure for the detection and visualization of structural changes. This enables the identification of subtle developments in the retina not caused by variation in illumination or blur. The method was tested on synthetic and real images. Encouraging experimental results show that the method is capable of significant restoration of degraded retinal images.

Methods and Apparatus for Blind Separation of Multichannel Convolutive Mixtures in the Frequency Domain

A method and apparatus performing blind source separation using frequency-domain normalized multichannel blind deconvolution. Multichannel mixed signals are frames of N samples including r consecutive blocks of M samples. The frames are separated using separating filters in frequency domain in an overlap-save manner by discrete Fourier transform (DFT). The separated signals are then converted back into time domain using inverse DFT applied to a nonlinear function. Cross-power spectra between separated signals and nonlinear-transformed signals are computed and normalized by power spectra of both separated signals and nonlinear-transformed signals to have flat spectra. Time domain constraint is then applied to preserve first L cross-correlations. These alias-free normalized cross-power spectra are further constrained by nonholonomic constraints. Then, natural gradient is computed by convolving alias-free normalized cross-power spectra with separating filters. After the separating filters length is constrained to L, the separating filters are updated using the natural gradient and normalized to have unit norm. Terminating conditions are checked to determine if separating filters converged.

Convolutive blind source separation by efficient blind deconvolution and minimal filter distortion

Convolutive blind source separation (BSS) usually encounters two difficulties—the filter indeterminacy in the recovered sources and the relatively high computational load. In this paper we propose an efficient method to convolutive BSS, by dealing with these two issues. It consists of two stages, namely, multichannel blind deconvolution (MBD) and learning the post-filters with the minimum filter distortion (MFD) principle. We present a computationally efficient approach to MBD in the first stage: a vector autoregression (VAR) model is first fitted to the data, admitting a closed-form solution and giving temporally independent errors; traditional independent component analysis (ICA) is then applied to these errors to produce the MBD results. In the second stage, the least linear reconstruction error (LLRE) constraint of the separation system, which was previously used to regularize the solutions to nonlinear ICA, enforces a MFD principle of the estimated mixing system for convolutive BSS. One can then easily learn the post-filters to preserve the temporal structure of the sources. We show that with this principle, each recovered source is approximately the principal component of the contributions of this source to all observations. Experimental results on both synthetic data and real room recordings show the good performance of this method.

Multichannel Deconvolution of Seismic Signals Using Statistical MCMC Methods

In this paper, we propose two multichannel blind deconvolution algorithms for the restoration of two-dimensional (2D) seismic data. Both algorithms are based on a 2D reflectivity prior model, and use iterative multichannel deconvolution procedures which deconvolve the seismic data, while taking into account the spatial dependency between neighboring traces. The first algorithm employs in each step a modified maximum posterior mode (MPM) algorithm which estimates a reflectivity column from the corresponding observed trace using the estimate of the preceding reflectivity column. The second algorithm takes into account estimates of both the preceding and subsequent columns in the estimation process. Both algorithms are applied to synthetic and real data and demonstrate better results compared to those obtained by a single-channel deconvolution method. Expectedly, the second algorithm which utilizes more information in the estimation process of each reflectivity column is shown to produce better results than the first algorithm.

Multichannel Blind Deconvolution Using the Stochastic Calculus for the Estimation of the Central Arterial Pressure

A new tool for estimation of both the central arterial pressure and the unknown channel dynamics has been developed. Given two peripheral waveform measurements, this new signal processing algorithm generates two models that represent the distinct branch dynamic behavior associated with the measured signals. The framework for this methodology is based on a Multichannel Blind Deconvolution (MBD) technique that has been reformulated to use Stochastic Calculus (SC). The technique is based on MBD of dynamic system are mathematically analyzed, in order to reconstruct the common unobserved input within an arbitrary scale factor. The convolution process is modeled as a Finite Impulse Response (FIR) filter with unknown coefficients. The source signal is also unknown. Assuming that one of the FIR filter coefficients are time varying, we have been able to get accurate estimation results for the source signal, even though the filter order is unknown. The time varying filter coefficients have been estimated through the SC algorithm, and we have been able to deconvolve the measurements and obtain both the source signal and the convolution path. The positive results demonstrate that the SC approach is superior to conventional methods.

Blind Deconvolution of the Aortic Pressure Waveform Using the Malliavin Calculus

Multichannel Blind Deconvolution (MBD) is a powerful tool particularly for the identification and estimation of dynamical systems in which a sensor, for measuring the input, is difficult to place. This paper presents an MBD method, based on the Malliavin calculus MC (stochastic calculus of variations). The arterial network is modeled as a Finite Impulse Response (FIR) filter with unknown coefficients. The source signal central arterial pressure CAP is also unknown. Assuming that many coefficients of the FIR filter are time-varying, we have been able to get accurate estimation results for the source signal, even though the filter order is unknown. The time-varying filter coefficients have been estimated through the proposed Malliavin calculus-based method. We have been able to deconvolve the measurements and obtain both the source signal and the arterial path or filter. The presented examples prove the superiority of the proposed method, as compared to conventional methods.

Multichannel Seismic Deconvolution Using Markov–Bernoulli Random-Field Modeling

In this paper, we present an algorithm for multichannel blind deconvolution of seismic signals, which exploits lateral continuity of Earth layers based on Markov-Bernoulli random-field modeling. The reflectivity model accounts for layer discontinuities resulting from splitting, merging, starting, or terminating layers within the region of interest. We define a set of reflectivity states and legal transitions between the reflector configurations of adjacent traces and subsequently apply the Viterbi algorithm for finding the most likely sequences of reflectors that are connected across the traces by legal transitions. The improved performance of the proposed algorithm and its robustness to noise, compared with a competitive algorithm, are demonstrated using simulated and real seismic data examples, in blind and nonblind scenarios.

Resolution restoration algorithm based on maximum a posteriori from Poisson-Markov distribution and blind multichannel deconvolution

Single input multichannel output (SIMO) imaging system which enhances the spatial resolution by resampling the same scene increasingly has large applications, and the corresponding image restoration algorithm for uncontrollable SIMO has became the subject of current research. By the assumptions of Poisson, Markov stochastic field and regulation of improved multichannel constraint, the multichannel blind image reconstruction is proposed based on maximum a posteriori rules. The algorithm doesn't need to know the prior knowledge such as character, type and distribution of the degraded point spread function (PSF) in each channel. The pixels and PSF are projected into the amplitude restrained set and energy invariable set, respectively, and their estimates converge to the global optimum solutions by the alterative iteration, and finally, the super-resolution image is restored. Algorithm simulations and the real micro-shift, micro-defocus experiments indicate that it has good restoration effect and stability at different signal noise ratios and for different PSF supports.

Simultaneous super-resolution and blind deconvolution

In many real applications, blur in input low-resolution images is a nuisance, which prevents traditional super-resolution methods from working correctly. This paper presents a unifying approach to the blind deconvolution and superresolution problem of multiple degraded low-resolution frames of the original scene. We introduce a method which assumes no prior information about the shape of degradation blurs and which is properly defined for any rational (fractional) resolution factor. The method minimizes a regularized energy function with respect to the high-resolution image and blurs, where regularization is carried out in both the image and blur domains. The blur regularization is based on a generalized multichannel blind deconvolution constraint. Experiments on real data illustrate robustness and utilization of the method.

A Balanced Approach to Multichannel Blind Deconvolution

In some general state-space approaches to the multichannel blind deconvolution problem, e.g., the information backpropagation approach (Zhang and Cichocki 2000), an implicit assumption is usually involved therein, viz., the dimension of the state vector of the mixer is known a priori. In general, if the number of states in the state space is not known a priori, Zhang and Cichocki (2000) suggested using a maximum possible number of states; this procedure will introduce additional delays in the recovered source signals. In this paper, our aim is to relax this assumption. The objective is achieved by using balanced parameterization of the underlying discrete-time dynamical system. Since there are no known balanced parameterization algorithms for discrete-time systems, we need to go through a circuitous route, by first transforming the discrete-time system into a continuous-time system using a bilinear transformation, perform the balanced parameterization on the resulting continuous-time system, and then transform the resulting system back to discrete-time balanced parameterized system using an inverse bilinear transformation. The number of states can be determined by the number of significant singular values in the ensuing singular value decomposition step in the balanced parameterization.

Super-Resolution and Blind Deconvolution For Rational Factors With an Application to Color Images

In many real applications, traditional super-resolution (SR) methods fail to provide high-resolution images due to objectionable blur and inaccurate registration of input low-resolution images. Only integer resolution enhancement factors, such as 2 or 3, are often considered, but non-integer factors between 1 and 2 are also important in real cases. We introduce a method to SR and deconvolution, which assumes no prior information about the shape of degradation blurs, incorporates registration parameters, and is properly defined for any rational (fractional) resolution factor. The method minimizes a regularized energy function with respect to the high-resolution image and blurs, where regularization is carried out in both the image and blur domains. The blur regularization is based on a generalized multi-channel blind deconvolution constraint derived in the paper. An extension to color images is briefly discussed. Experiments on real data illustrate robustness to noise and other advantages of the method.

Multichannel blind seismic deconvolution using dynamic programming

In this paper, we present an algorithm for multichannel blind deconvolution of seismic signals, which exploits lateral continuity of earth layers by dynamic programming approach. We assume that reflectors in consecutive channels, related to distinct layers, form continuous paths across channels. We introduce a quality measure for evaluating the quality of a continuous path, and iteratively apply dynamic programming to find the best continuous paths. The improved performance of the proposed algorithm and its robustness to noise, compared to a competitive algorithm, are demonstrated through simulations and real seismic data examples.

Estimation of the Number of Partial Discharge Sources Using Multichannel Blind Deconvolution of Electromagnetic Waves

We propose a method to estimate the number of partial discharge sources in multipath environment using the multichannel blind deconvolution method called the super-exponential deflation method. Blind deconvolution is a method of recovering transmitted signals from only observed signals without any a priori knowledge of the source signals. The deflation approach can extract a source signal which is non-Gaussian from the observed signals one by one. The deflation approach is repeated until all non-Gaussian signals are extracted, in which case the input signals become close to Gaussian noise. The eigenvalues of the spatial correlation matrix of the input signals indicate whether the input signals are Gaussian noise or not. Thus, the proposed method estimates the number of PD sources by repeating the deflation approach and analyzing the eigenvalues.

A variational Bayesian approach to number of sources estimation for multichannel blind deconvolution

Most traditional multichannel blind deconvolution algorithms rely on some assumptions on the mixing model, e.g. the number of sources is known a priori; and the mixing environment is noise-free. Unfortunately, these assumptions are not necessarily true in practice. In this paper, we will relax the assumption placed on the number of sources by studying a state space mixing model where the number of sources is assumed to be unknown but not greater than the number of sensors. Based on this mixing model, we will formulate the estimation of the number of sources problem as a model order selection problem. Model comparison, as a common method of model order selection, usually involves the evaluation of multi-variable integrals which is computationally intractable. A variational Bayesian method is therefore used to overcome this multi-variable integral issue. The problem is solved by approximating the true, complicated posteriors with a set of independent, simple, tractable posteriors. To realize the objective of optimal approximation, we maximize an objective function called negative free energy. We will derive a variational Bayesian algorithm, in which the number of sources will be estimated through two approaches: automatic relevance determination and comparison of the optimized negative free energy. The proposed variational Bayesian algorithm will be evaluated on both artificially generated examples, and practical signals.

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.

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 ab...

Multi-channel blind deconvolution algorithm for multiple-input multiple-output DS/CDMA system

Direct sequence spread spectrum transmission can be realized at low SNR, and has low probability of detection. It is aly problem how to obtain the original users' signal in a non-cooperative context. In practicality, the DS/CDMA sources received are linear convolute mixing. A more complex multichannel blind deconvolution MBD algorithm is required to achieve better source separation. An improved MBD algorithm for separating linear convolved mixtures of signals in CDMA system is proposed. This algorithm is based on minimizing the average squared cross-output-channel-correlation. The mixture coefficients are totally unknown, while some knowledge about temporal model exists. Results show that the proposed algorithm can bring about the exactness and low computational complexity.

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.

Multichannel Blind Deconvolution Using a Generalized Gaussian Source Model

In this paper, we present an algorithm for the problem of multi-channel blind deconvolution which can adapt to un-known sources with both sub-Gaussian and super-Gaussian probability density distributions using a generalized gaussian source model. We use a state space representation to model the mixer and demixer respectively, and show how the parameters of the demixer can be adapted using a gradient descent algorithm incorporating the natural gradient extension. We also present a learning method for the unknown parameters of the generalized Gaussian source model. The performance of the proposed generalized Gaussian source model on a typical example is compared with those of other algorithm, viz the switching nonlinearity algorithmproposed by Lee et al. [8].

Approach to blind image deconvolution by multiscale subband decomposition and independent component analysis

A single-frame multichannel blind image deconvolution technique has been formulated recently as a blind source separation problem solved by independent component analysis (ICA). The attractive feature of this approach is that neither origin nor size of the spatially invariant blurring kernel has to be known. To enhance the statistical independence among the hidden variables, we employ multiscale analysis implemented by wavelet packets and use mutual information to locate a subband with the least dependent components, where the basis matrix is learned by means of standard ICA. We show that the proposed algorithm is capable of performing blind deconvolution of nonstationary signals that are not independent and identically distributed processes. The image poses these properties. The algorithm is tested on experimental data and compared with state-of-the-art single-frame blind image deconvolution algorithms. Our good experimental results demonstrate the viability of the proposed concept.