Blind Deconvolution Algorithm Research Articles

Geometrical Structures of FIR Manifold and Multichannel Blind Deconvolution

In this paper we study geometrical structures of the manifold of Finite Impulse Response (FIR) filters, and develop a natural gradient learning algorithm for blind deconvolution. First, A Lie group structure is introduced to the FIR manifold and the Riemannian metric is then derived by using the isometric property of the Lie group. The natural gradient on the FIR manifold is obtained by introducing a nonholonomic transformation. The Kullback-Leibler divergence is introduced as the measure of mutual independence of the output signals of the demixing model and a feasible cost function is derived for blind deconvolution. An efficient learning algorithm is presented based on the natural gradient approach and its stability analysis is also provided. Finally, we give computer simulations to demonstrate the performance and effectiveness of the proposed natural gradient algorithm.

Semiparametric model and superefficiency in blind deconvolution

In this paper, we study convergence and efficiency of the batch estimator and natural gradient algorithm for blind deconvolution. First, the blind deconvolution problem is formulated in the framework of a semiparametric model, and a family of estimating functions is derived for blind deconvolution. To improve the learning efficiency of the online algorithm, explicit standardized estimating functions are given and within this framework the superefficiency of batch learning and online natural gradient learning is proven.

A contribution to (neuromorphic) blind deconvolution by flexible approximated Bayesian estimation

‘Bussgang’ deconvolution techniques for blind digital channels equalization rely on a Bayesian estimator of the source sequence defined on the basis of channel/equalizer cascade model which involves the definition of deconvolution noise. In this paper we consider four ‘Bussgang’ blind deconvolution algorithms for uniformly distributed source signals and investigate their numerical performances as well as some of their analytical features. Particularly, we show that the algorithm, introduced by the present author, provided by a flexible (neuromorphic) estimator is effective as it does not require to make any hypothesis about convolutional noise level and exhibits satisfactory numerical performances.

Blind Deconvolution Algorithms for MIMO-FIR Systems Driven by Fourth-order Colored Signals

This paper deals with the blind deconvolution problem of MIMO-FIR channels driven by source signals which are temporally second-order uncorrelated but fourth-order correlated and spatially second- and fourth-order uncorrelated. Recently, we proposed a criterion for solving the blind deconvolution problem [8], [9]. However, we have not yet shown an algorithm to implement our proposed criterion. One of our objectives in the present paper is to propose an iterative algorithm for achieving the blind deconvolution by using this criterion. To achieve this objective, we consider an approach called the non-deflation method. We propose an iterative algorithm based on the method. Moreover, we present a deflation algorithm using this criterion for the blind separation of MIMO constant channels.

Wavelet analysis of acoustic Green’s functions in a shallow ocean environment

Knowledge of the properties of acoustic Green’s functions can assist in the development of effective blind deconvolution algorithms for enhancing the classification performance of active and passive sonar systems. Green’s functions have been produced representing the acoustic propagation of signals in a given shallow ocean multipath environment. Simulated noise-free received signals are the result of convolving the Green’s functions with representative source signals. Wavelet analysis is performed on the Green’s functions, the source signals, and the received signals. Forty different wavelets are tested. Comparison of the wavelet transform coefficients illustrates similarities and differences in signal properties. Significant differences can be exploited to separate the source from the Green’s functions in the multichannel received signals for blind deconvolution source recovery. [Work supported by ONR.]

Statistical analysis of acoustic Green’s functions in a shallow ocean environment

Knowledge of statistical properties of acoustic Green’s functions can assist in the development of effective blind deconvolution algorithms for enhancing the detection and classification performance of active and passive sonar systems. One hundred synthetically generated Green’s functions have been produced representing the acoustic propagation of signals in a given shallow ocean environment. Fourier analysis is performed on the Green’s functions and various statistical properties are calculated in both the time and frequency domains, including examination of properties such as the mean, variance, and the third- and fourth-order moments in both domains. Statistics are also generated for the entire ensemble of Green’s functions as a function of time and frequency. A similar statistical analysis is conducted on the autocorrelation of each of the Green’s functions in both domains. Synthetic noise-free signals are produced by convolving the Green’s functions with representative source signals. Statistical analysis is performed on the resulting signals in both domains for comparison to the results obtained using the Green’s functions alone. Results include large phone-to-phone variations in kurtosis of the Green’s functions and ensemble average kurtosis increasing sharply with time and decaying to zero. [Research supported by ONR.]

Blind deconvolution of 3D transmitted light brightfield micrographs.

The blind deconvolution algorithm for 3D transmitted light brightfield (TLB) microscopy, published previously [Holmes et al. Handbook of Biological Confocal Microscopy (1995)], is summarized with example images. The main emphasis of this paper is to discuss more thoroughly the importance and usefulness of this method and to provide more detailed evidence, some being quantitative, of its necessity. Samples of horseradish peroxidase (HRP)-stained pyramidal neurones were prepared and evaluated for the ability to see fine structures clearly, including the dendrites and spines. It is demonstrated that the appearance of fine spine structure, and means of identifying spine categories, is made possible by using blind deconvolution. A comparison of images of the same sample from reflected light confocal microscopy, which is the conventional light microscopic way of viewing the 3D structure of these HRP-stained samples, shows that the blind deconvolution method is far superior for clearly showing the structure with less distortion and better resolution of the spines. The main significance of this research is that it is now possible to obtain clear images of 3D structure by light microscopy of absorbing stains. This is important because the TLB microscope is probably the most widely used modality in the life-science laboratory, yet, until now, there has been no reliable means for it to provide visualization of 3D structure clearly. The main importance of the blind deconvolution approach is that it obviates the need to measure the point spread function of the optical system, so that it now becomes realistic to provide a 3D light microscopic deconvolution method that can be pervasively used by microscopists.

Convergence of the alternating minimization algorithm for blind deconvolution

Blind deconvolution refers to the image processing task of restoring the original image from a blurred version without the knowledge of the blurring function. One approach that has been proposed recently [T. Chan, C. Wong, IEEE Trans. Image Process. 7 (1998) 370–375; Y. You, M. Kaveh, IEEE Trans. Image Process. 5 (1996) 416–428] is a joint minimization model in which an objective function is set up consisting of three terms: the data fitting term, and the regularization terms for the image and the blur. This model implicitly defines a one-parameter family of blurred images and point spread functions (PSFs), from which the user can decide, usually using additional information, which is the “best” restored image. To find a local minimum of the objective function, we use an alternating minimization (AM) procedure [Y. You, M. Kaveh, IEEE Trans. Image Process. 5 (1996) 416–428] in which we fix either the blur or the image and minimize respect to the other variable, each step of which is a standard non-blind deconvolution problem. While the model is not convex and thus allows multiple solutions, we have found that the AM procedure always converges globally, but with the converged solution depending on the initial guess. In this paper, we give an analysis of the AM procedure which explains the convergence behavior and the observed robustness of the method.

Transpose properties in the stability and performance of the classic adaptive algorithms for blind source separation and deconvolution

This paper presents a tutorial review of the problem of Blind Source Separation (BSS) and the properties of the classic adaptive algorithms when either the score-function or a general (nonscore) nonlinearity is employed in the algorithm. In new findings it is shown that the separating solution for both sub- and super-Gaussian signals can be stabilized by an algorithm employing any given nonlinearity. For these separating solutions the steady-state error levels are also given in terms of the nonlinearity and the pdfs of the source signals. These results show that a transpose symmetry exists between the nonlinear algorithms for sub- and super-Gaussian signals. The behavior of the algorithm is then detailed when the ideal score-function nonlinearity is replaced by a general (hard saturation or u 3) nonlinearity. The phases of convergence to decorrelated output signals and then to recovery of the source signals are explained. The results are then extended to single- and multi-channel deconvolution and shown by analysis and extensive simulation to hold for mixed and convolved source signals. The results allow the design of stable algorithms for multichannel blind deconvolution with a general nonlinearity when sub- and super-Gaussian source signals are present.

A two-stage algorithm for MIMO blind deconvolution of nonstationary colored signals

A new two-stage algorithm is proposed for the deconvolution of multi-input multi-output (MIMO) systems with colored input signals. While many blind deconvolution algorithms in the literature utilize high order statistics of the output signal for white input signals, the additional information contained in colored input signals allows the design of second-order statistical algorithms. In fact, practical signal sources such as speech signals do have distinct, nonstationary, colored power spectral densities. We present a two-stage signal separation approach in which the first step utilizes a matrix pencil between output auto-correlation matrices at different delays, whereas the second stage adopts a subspace method to identify and deconvolve MIMO systems.

Super-exponential algorithms for multichannel blind deconvolution

Multichannel blind deconvolution has been receiving increasing attention. Shalvi and Weinstein proposed an attractive approach to single-channel blind deconvolution called the super-exponential methods. The objective of this correspondence is to extend the Shalvi and Weinstein (1993, 1994) approach to the multichannel case and present super-exponential algorithms for multichannel blind deconvolution. We propose three approaches to multichannel blind deconvolution. In the first one, we present a multichannel super-exponential algorithm. In the second one, we present a super-exponential deflation algorithm. In the third one, we present a two-stage super-exponential algorithm.

An enhanced NAS-RIF algorithm for blind image deconvolution

We enhance the performance of the nonnegativity and support constraints recursive inverse filtering (NAS-RIF) algorithm for blind image deconvolution. The original cost function is modified to overcome the problem of operation on images with different scales for the representation of pixel intensity levels. Algorithm resetting is used to enhance the convergence of the conjugate gradient algorithm. A simple pixel classification approach is used to automate the selection of the support constraint. The performance of the resulting enhanced NAS-RIF algorithm is demonstrated on various images.

Noise robust one-dimensional blind deconvolution of medical ultrasound images

Recently, several blind cepstral deconvolution methods for medical ultrasound images were compared experimentally. The results indicated that the generalized cepstrum or the complex cepstrum with phase unwrapping give the blind homomorphic deconvolution algorithms with the best performance. However, the frequency domain phase unwrapping for pulse estimation, which is an essential part of both methods, is sensitive to the sensor noise when the values of the spectrum are small due to the randomness of the tissue response. The noise introduces abrupt changes in the phase. The phase degradation due to the noise causes variable spatial and gray scale resolution in image sequences following deconvolution. This paper introduces a noise robust Bayesian phase unwrapping method using a noncausal Markov random chain model. The prior regularizing term accounts for the noise and smoothes the phase. The phase unwrapping is formulated as a least mean square optimization problem. The optimization is done noniteratively by solving a difference equation using the cosine transform. The resulting improvement in radial and lateral blind deconvolution is demonstrated on six short ultrasound image sequences recorded in vitro or in vivo.

A novel geometry for SPECT imaging associated with the EM-type blind deconvolution method

Image quality of single-photon emission computerized tomography (SPECT) is essentially determined by the count sensitivity of the detector and the geometry of the collimator. The authors introduce a novel geometry for a dual-head SPECT imaging system (Park Medical Systems Inc., Lachine, Quebec) to improve the count sensitivity. The imaging system is equipped with a coded aperture and a parallel hole collimators. The camera head equipped with the coded aperture collimator is used to acquire count-rich projection images, and the other head with the parallel hole collimator is used to acquire high resolution projection images. To further improve the image resolution of the projections, two expectation-maximization-type blind deconvolution (EMBD) algorithms were derived. The algorithms were evaluated using elliptical cylindrical rod phantom and human hand data. The coded aperture and parallel hole projections were acquired simultaneously using the dual-head SPECT imaging system. The acquired coded aperture projections were decoded using the standard uniformly redundant array (URA) decoding technique to yield decoded projections. The projections acquired from the parallel hole collimator head were incorporated into the decoded images in the EMBD restoration process. Using the coded aperture collimator, the count sensitivity was markedly increased, 8-fold for the phantom data and approximately 20-fold for the hand data, as compared to the parallel hole collimator. Also, image quality of the SPECT projections was significantly improved when the EMBD algorithms were implemented on the projections. Thus, the dual-head SPECT imaging system associated with the EM-type blind deconvolution algorithms may be a preferred system for low-count SPECT imaging.

Wavelet transform domain blind deconvolution

This paper presents a utility of orthogonal wavelet transform in kurtosis-based blind deconvolution algorithm termed as EVA. In general, eigenvalues of the matrix at EVA issue are unchanged by an orthogonal transform alone. However, we note that wavelet transformation creates nearly lower triangle matrix. This utility promotes the faster convergence of well known power method in eigenvector calculation. We also present the potential applicability of this type of EVA in speech signal processing.

A cumulant-based super-exponential algorithm for blind deconvolution of multi-input multi-output systems

In this paper, a cumulant-based method for blind deconvolution of a multi-input multi-output system is proposed. The core of the method is an algorithm which extracts one of the input signals using the output signals as data only. This algorithm is a non-trivial generalization of the Shalvi–Weinstein algorithm for single-input single-output blind deconvolution and converges in super-exponential rate after a finite number of iterations. By using this algorithm recursively, all the input signals can be extracted. In its basic form, the algorithm applies when the input signals are non-Gaussian independent identical distributed. The algorithm is also extended to the case where the input signals are general regular processes. Computer simulation results are presented to demonstrate the convergence behavior of the proposed method as well as its efficacy for blind deconvolution.

Iterative multiframe superresolution algorithms for atmospheric-turbulence-degraded imagery

The subject of interest is the superresolution of atmospheric-turbulence-degraded, short-exposure imagery, where superresolution refers to the removal of blur caused by a diffraction-limited optical system along with recovery of some object spatial-frequency components outside the optical passband. Photon-limited space object images are of particular interest. Two strategies based on multiple exposures are explored. The first is known as deconvolution from wave-front sensing, where estimates of the optical transfer function (OTF) associated with each exposure are derived from wave-front-sensor data. New multiframe superresolution algorithms are presented that are based on Bayesian maximum a posteriori and maximum-likelihood formulations. The second strategy is known as blind deconvolution, in which the OTF associated with each frame is unknown and must be estimated. A new multiframe blind deconvolution algorithm is presented that is based on a Bayesian maximum-likelihood formulation with strict constraints incorporated by using nonlinear reparameterizations. Quantitative simulation of imaging through atmospheric turbulence and wave-front sensing are used to demonstrate the superresolution performance of the algorithms.

Total variation blind deconvolution

In this paper, we present a blind deconvolution algorithm based on the total variational (TV) minimization method proposed. 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 psf's without sharp edges, e.g., Gaussian blur, can also be identified through the TV approach.

Standard PDA for measuring the size of inhomogeneous droplets

A method to obtain the diameter of inhomogeneous droplets by using phase-Doppler anemometry (PDA) is described. Inhomogeneities included in a fluid droplet disturb light scattered by the droplet. Consequently the phase difference measured between two Doppler bursts deviates from the value calculated by geometrical optics theory for a droplet of diameter d. Because evaluation of the measured phase differences is based on a linear relationship between phase difference and particle diameter the accuracy of PDA is deteriorated. The difference between the real and the measured diameters of such droplets can be characterized by convolution with a Gaussian probability function. For monodisperse droplets and for a given type of inhomogeneity the standard deviation of the Gaussian function increases linearly with increasing mass concentration of these inhomogeneity. Applying infrared laser-PDA (IR-PDA) with a wavelength of 1312 nm, the measuring range to investigate droplets of, for instance, water-latex suspensions containing 450 nm polystyrene spheres can be extended to suspensions with six times the measurable concentration standard PDA using a He-Ne laser at nm. The relative improvement obtained by applying IR-PDA (in comparison with a standard PDA system equipped with a 632.8 nm laser) can be estimated by the decrease of the extinction efficiency of the inclusions with laser wavelength. The linear relation between extinction E and standard deviation can be used by a blind deconvolution algorithm. Starting from the measured diameter distribution of the inhomogeneous droplets the real diameter distribution and the standard deviation of each size class of the particles can be calculated by the algorithm. From this standard deviation it is possible to determine the extinction E and the mass concentration of the inhomogeneities.

On the use of Lyapunov criteria to analyze the convergence of blind deconvolution algorithms

We present an approach to determine sufficient conditions for the global convergence of iterative blind deconvolution algorithms using finite impulse response (FIR) deconvolution filters. The novel technique, which incorporates Lyapunov's direct method, is general, flexible, and can be easily adapted to analyze the behavior of many types of nonlinear iterative signal processing algorithms. Specifically, we find sufficient conditions to guarantee a unique solution for the NAS-RIF algorithm used for blind image restoration. We determine that in many cases, there exists a tradeoff between the quality of the deconvolution result and the uniqueness of the solution. A procedure to determine the length of the deconvolution filter to guarantee a unique solution is established.