Abstract: Using microphone arrays for estimating source locations and strengths has become common practice in aeroacoustic applications. The classical delay-and-sum approach suffers from low resolution and high sidelobes and the resulting beamforming maps are difficult to interpret. The deconvolution approach for the mapping of acoustic sources (DAMAS) deconvolution algorithm recovers the actual source levels from the contaminated delay-and-sum results by defining an inverse problem that can be represented as a linear system of equations. In this paper, the deconvolution problem is carried onto the sparse signal representation area and a sparsity constrained deconvolution approach (SC-DAMAS) is presented for solving the DAMAS inverse problem. A sparsity preserving covariance matrix fitting approach (CMF) is also presented to overcome the drawbacks of the DAMAS inverse problem. The proposed algorithms are convex optimization problems. Our simulations show that CMF and SC-DAMAS outperform DAMAS and as the noise in the measurements increases, CMF works better than both DAMAS and SC-DAMAS. It is observed that the proposed algorithms converge faster than DAMAS. A modification to SC-DAMAS is also provided which makes it significantly faster than DAMAS and CMF. For the correlated source case, the CMF-C algorithm is proposed and compared with DAMAS-C. Improvements in performance are obtained similar to the uncorrelated case.

Abstract: We construct a new variational method for blind deconvolution of images and inpainting, motivated by recent PDE-based techniques involving the Ginzburg-Landau functional, but using more localized wavelet-based methods. We present results for both binary and grayscale images. Comparable speeds are achieved with better sharpness of edges in the reconstruction.

Abstract: Deconvolution interferometry successfully recovers the impulse response between two receivers without the need for an independent estimate of the source function. Here we extend the method of interferometry by deconvolution to multicomponent data in elastic media. As in the acoustic case, elastic deconvolution interferometry retrieves only causal scattered waves that propagate between two receivers as if one acts as a pseudosource of the point-force type. Interferometry by deconvolution in elastic media also generates artifacts because of a clamped-point boundary condition imposed by the deconvolution process. In seismic-while-drilling (SWD) practice, the goal is to determine the subsurface impulse response from drill-bit noise records. Most SWD technologies rely on pilot sensors and/or models to predict the drill-bit source function, whose imprint is then removed from the data. Interferometry by deconvolution is of most use to SWD applications in which pilot records are absent or provide unreliable estimates of bit excitation. With a numerical SWD subsalt example, we show that deconvolution interferometry provides an image of the subsurface that cannot be obtained by correlations without an estimate of the source autocorrelation. Finally, we test the use of deconvolution interferometry in processing SWD field data acquired at the San Andreas Fault Observatory at Depth (SAFOD). Because no pilot records were available for these data, deconvolution outperforms correlation in obtaining an interferometric image of the San Andreas fault zone at depth.

Abstract: Sparse-spike deconvolution can be viewed as an inverse problem where the locations and amplitudes of a number of spikes reflectivity are estimated from noisy data seismic traces. The main objective is to find the least number of spikes that, when convolved with the available band-limited seismicwaveletestimate,fitthedatawithinagiventolerance errormisfit.Thedetectionofthespikes’timelagsisahighly nonlinearoptimizationproblemthatcanbesolvedusingvery fastsimulatedannealingSA.Amplitudesareeasilyestimated using linear least squares at each SA iteration. At this stage, quadratic regularization is used to stabilize the solution, to reduce its nonuniqueness, and to provide meaningful reflectivitysequences,thusavoidingtheneedtoconstrainthe spikes’time lags and/or amplitudes to force valid solutions. Impedanceconstraintsalsocanbeincludedatthisstage,providing the low frequencies required to recover the acoustic impedance.Oneadvantageoftheproposedmethodoverother sparse-spike deconvolution techniques is that the uncertaintyoftheobtainedsolutionscanbeestimatedstochastically.Further,errorsinthephaseofthewaveletestimatearetolerated,foranoptimumconstant-phaseshiftisobtainedtocalibratetheeffectivewaveletthatispresentinthedata.Results using synthetic data including simulated data for the Marmousi2 modelandfield 3D data show that physically meaningful high-resolution sparse-spike sections can be derived fromband-limitednoisydata,evenwhentheavailablewaveletestimateisinaccurate.

Abstract: In this paper, we present a powerful technique for the blind extraction of direct-sequence code-division multiple access (DS-CDMA) signals from convolutive mixtures received by an antenna array. The technique is based on a generalization of the canonical or parallel factor decomposition (CANDECOMP/PARAFAC) in multilinear algebra. We present a bound on the number of users under which blind separation and deconvolution is guaranteed. The solution is computed by means of an alternating least squares (ALS) algorithm. The excellent performance is illustrated by means of a number of simulations. We include an explicit expression of the Cramer-Rao bound (CRB) of the transmitted symbols.

Abstract: 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.

Abstract: Suggestions from the field of image processing to compensate for turbulence effects and restore degraded images include motion-compensated image integration after which the image can be considered as a non-distorted image that has been blurred with a point spread function (PSF) the same size as the pixel motions due to the turbulence. Since this PSF is unknown, a blind deconvolution is still necessary to restore the image. By utilising different blind deconvolution algorithms along with the motion-compensated image integration, several variants of this turbulence compensation method are created. In this paper we discuss the differences of the various blind deconvolution algorithms employed and give a qualitative analysis of the turbulence compensation variants by comparing their respective restoration results. This is done by visual inspection as well as by means of different image quality metrics that analyse the high frequency components.

Abstract: Imaging plays a key role in many diverse areas of application, such as astronomy, remote sensing, microscopy, and tomography. Owing to imperfections of measuring devices (e.g., optical degradations, limited size of sensors) and instability of the observed scene (e.g., object motion, media turbulence), acquired images can be indistinct, noisy, and may exhibit insufficient spatial and temporal resolution. In particular, several external effects blur images. Techniques for recovering the original image include blind deconvolution (to remove blur) and superresolution (SR). The stability of these methods depends on having more than one image of the same frame. Differences between images are necessary to provide new information, but they can be almost unperceivable. State-of-the-art SR techniques achieve remarkable results in resolution enhancement by estimating the subpixel shifts between images, but they lack any apparatus for calculating the blurs. In this paper, after introducing a review of current SR techniques we describe two recently developed SR methods by the authors. First, we introduce a variational method that minimizes a regularized energy function with respect to the high resolution image and blurs. In this way we establish a unifying way to simultaneously estimate the blurs and the high resolution image. By estimating blurs we automatically estimate shifts with subpixel accuracy, which is inherent for good SR performance. Second, an innovative learning-based algorithm using a neural architecture for SR is described. Comparative experiments on real data illustrate the robustness and utilization of both methods.

Abstract: In recent years broadband signal aquisition by sensor arrays, e.g., for speech and audio signals in a hands-free scenario, has become a popular research field in order to separate certain desired source signals from competing or interfering source signals ((blind) source separation or interference cancellation) and to possibly dereverberate them (blind deconvolution). In various practical scenarios, some or even all interfering source signals may be directly accessible and/or some side information on the propagation path is known. In these cases we can tackle the separation problem by supervised adaptation algorithms, e.g., the popular LMS- or RLS-type algorithms, rather than the more involved blind adaptation algorithms. In contrast, for blind estimation, such as in the blind source separation (BSS) scenario where both the propagation paths and the original source signals are unknown, the method of independent component analysis (ICA) is typically applied. Traditionally, the ICA method and supervised adaptation algorithms have been treated as different research areas. In this paper, we establish a conceptually simple, yet fundamental relation between these two worlds. This is made possible using the previously introduced generic broadband adaptive filtering framework, called TRINICON. As we will demonstrate, not only both the well-known blind and supervised adaptive filtering algorithms turn out as special cases of this generic framework, but we also gain various new insights and synergy effects for the development of new and improved adaptation algorithms.

Abstract: We propose a method for the iterative restoration of fluorescence Confocal Laser Scanning Microscope (CLSM) images with parametric estimation of the acquisition system's Point Spread Function (PSF). The CLSM is an optical fluorescence microscope that scans a specimen in 3D and uses a pinhole to reject most of the out-of-focus light. However, the quality of the image suffers from two primary physical limitations. The first is due to the diffraction-limited nature of the optical system and the second is due to the reduced amount of light detected by the photomultiplier tube (PMT). These limitations cause blur and photon counting noise respectively. The images can hence benefit from post-processing restoration methods based on deconvolution. An efficient method for parametric blind image deconvolution involves the simultaneous estimation of the specimen 3D distribution of fluorescent sources and the microscope PSF. By using a model for the microscope image acquisition physical process, we reduce the number of free parameters describing the PSF and introduce constraints. The parameters of the PSF may vary during the course of experimentation, and so they have to be estimated directly from the observation data. We also introduce a priori knowledge of the specimen that permits stabilization of the estimation process and favorizes the convergence. Experiments on simulated data show that the PSF could be estimatedwith a higher degree of accuracy and those done on real data show very good deconvolution results in comparison to the theoretical microscope PSF model.

Abstract: A maximum likelihood blind deconvolution algorithm is derived for incoherent polarimetric imagery using expectation maximization. In this approach, the unpolarized and fully polarized components of the scene are estimated along with the corresponding angles of polarization and channel point spread functions. The scene state of linear polarization is determined unambiguously using this parameterization. Results are demonstrated using laboratory data.

Abstract: Blind deconvolution or deblurring is a challenging problem in many signal processing applications as signals and images often suffer from blurring or point spreading with unknown blurring kernels or point-spread functions as well as noise corruption. Most existing methods require certain knowledge about both the signal and the kernel and their performance depends on the amount of prior information regarding the both. Independent component analysis (ICA) has emerged as a useful method for recovering signals from their mixtures. However, ICA usually requires a number of different input signals to uncover the mixing mechanism. In this paper a blind deconvolution and deblurring method is proposed based on the nongaussianity measure of ICA as well as a genetic algorithm. The method is simple and does not require prior knowledge regarding either the image or the blurring process, but is able to estimate or approximate the blurring kernel from a single blurred image. Various blurring functions are described and discussed. The proposed method has been tested on images degraded by different blurring kernels and the results are compared to those of existing methods such as Wiener filter, regularization filter, and the Richardson-Lucy method. Experimental results show that the proposed method outperform these methods.

Abstract: We consider the image reconstruction problem when the original image is assumed to be sparse and when partial knowledge of the point spread function (PSF) is available. In particular, we are interested in recovering the magnetization density given magnetic resonance force microscopy (MRFM) data, and we present an iterative alternating minimization algorithm (AM) to solve this problem. A smoothing penalty is introduced on allowable PSFs to improve the reconstruction. Simulations demonstrate its performance in reconstructing both the image and unknown point spread function. In addition, we develop an optimization transfer approach to solving a total variation (TV) blind deconvolution algorithm presented in a paper by Chan and Wong. We compare the performance of the AM algorithm to the blind TV algorithm as well as to a TV based majorization-minimization algorithm developed by Figueiredo et al.

Abstract: Critical aircraft assets are required to be available when needed, while exhibiting attributes of reliability, robustness, and high confidence under a variety of flight regimes, and maintained on the basis of their current condition rather than on the basis of scheduled maintenance practices. New and innovative technologies must be developed and implemented to address these concerns. Condition-based maintenance requires that the health of critical components/systems be monitored and diagnostic/prognostic strategies be developed to detect and identify incipient failures and predict the failing component's remaining useful life. Typically, vibration and other key indicators onboard an aircraft are severely corrupted by noise, thus curtailing the ability to accurately diagnose and predict failures. This paper introduces a novel blind deconvolution denoising scheme that employs a vibration model in the frequency domain and attempts to arrive at the true vibration signal through an iterative optimization process. Performance indexes are defined and data from a helicopter are used to demonstrate the effectiveness of the proposed approach.

Abstract: We present a method for deconvolution of images by means of an inversion of fractional powers of the Gaussian. The main feature of our model is the introduction of a regularizing term which is also a fractional power of the Laplacian. This term allows us to recover higher frequencies. The model is particularly useful to devise an algorithm for blind deconvolution. We will show, analyze and illustrate through examples the performance of this algorithm.

Abstract: Using microphone arrays for estimating source locations and strengths has become common practice in aeroacoustic applications. The classical delay-and-sum approach suffers from low resolution and high sidelobes and the resulting beamforming maps are difficult to interpret. The deconvolution approach for the mapping of acoustic sources (DAMAS) deconvolution algorithm recovers the actual source levels from the contaminated delay-and-sum results by defining an inverse problem that can be represented as a linear system of equations. In this paper, the deconvolution problem is carried onto the sparse signal representation area and a sparsity constrained deconvolution approach (SC-DAMAS) is presented for solving the DAMAS inverse problem. A sparsity preserving covariance matrix fitting approach (CMF) is also presented to overcome the drawbacks of the DAMAS inverse problem. The proposed algorithms are convex optimization problems. Our simulations show that CMF and SC-DAMAS outperform DAMAS and as the noise in the measurements increases, CMF works better than both DAMAS and SC-DAMAS. It is observed that the proposed algorithms converge faster than DAMAS. A modification to SC-DAMAS is also provided which makes it significantly faster than DAMAS and CMF. For the correlated source case, the CMF-C algorithm is proposed and compared with DAMAS-C. Improvements in performance are obtained similar to the uncorrelated case.

Abstract: The predictive deconvolution algorithm (PD), which is based on second-order statistics, assumes that the primaries and the multiples are implicitly orthogonal. However, the seismic data usually do not satisfy this assumption in practice. Since the seismic data (primaries and multiples) have a non-Gaussian distribution, in this paper we present an improved predictive deconvolution algorithm (IPD) by maximizing the non-Gaussianity of the recovered primaries. Applications of the IPD method on synthetic and real seismic datasets show that the proposed method obtains promising results.

Abstract: Super-resolution reconstruction (SRR) produces a high-resolution image from multiple low-resolution images. Many image SRR algorithms assume that the blurring process, i.e., point spread function (PSF) of the imaging system is known in advance. However, the blurring process is not known or is known only to within a set of parameters in many practical applications. In this letter, we propose an approach for solving the joint blur identification and image SRR based on the principle similar to the variable projection method. The approach can avoid some shortcomings of cyclic coordinate descent optimization procedure. We also propose an efficient implementation based on Lanczos algorithm and Gauss quadrature theory. Experimental results are presented to demonstrate the effectiveness of our method.

Abstract: A new algorithm has been developed for performing blind deconvolution on degraded images. The algorithm naturally preserves the nonnegative constraint on the iterative solutions of blind deconvolution and can produce a restored image of high resolution. Furthermore, benefiting from the multiplicative form, the algorithm is free from the instability of numerical computation. Results of applying the algorithm to simulated and real degraded images are reported.

Abstract: This paper proposes an integrated method for the blind separation and dereverberation of convolutive audio mixtures. The proposed method is based on multichannel blind deconvolution in the frequency domain. Significant points to be emphasized are as follows: (1) The objective function for optimizing the deconvolution system is derived based on a time-varying all-pole model of source signals, which was proven to be effective for single source dereverberation. This provides the proposed method with the capacity for both separation and dereverberation. (2) An efficient optimization algorithm is developed. This algorithm is realized by decomposing the deconvolution system into an instantaneous separation part and a multichannel auto-regressive part. Illustrative experimental results with an RT 60 of 0.6 seconds are reported, where the proposed method showed superiority over a conventional frequency-domain blind separation method.

Abstract: This paper addresses the problem of classifying signals that have been corrupted by noise and unknown linear time-invariant (LTI) filtering such as multipath, given labeled uncorrupted training signals. A maximum a posteriori approach to the deconvolution and classification is considered, which produces estimates of the desired signal, the unknown channel, and the class label. For cases in which only a class label is needed, the classification accuracy can be improved by not committing to an estimate of the channel or signal. A variant of the quadratic discriminant analysis (QDA) classifier is proposed that probabilistically accounts for the unknown LTI filtering, and which avoids deconvolution. The proposed QDA classifier can work either directly on the signal or on features whose transformation by LTI filtering can be analyzed; as an example a classifier for subband-power features is derived. Results on simulated data and real Bowhead whale vocalizations show that jointly considering deconvolution with classification can dramatically improve classification performance over traditional methods over a range of signal-to-noise ratios.

Abstract: In the simplest case, the matrix inversion Lemma gives an explicit formula of the inverse of a positive-definite matrix A added to a rank-one matrix bbH as follows:(A + bbH )-1 = A-1-A-1 b(1 + bH A-1b)-1bHA-1. It is well known in the literature that this formula is very useful to develop a recursive least-squares algorithm for the recursive identification of linear systems or the design of adaptive filters. We extend this result to the case when the matrix A is singular and present a matrix pseudo-inversion lemma along with some illustrative examples. Such a singular case may occur in a situation where a given problem is overdeter-mined in the sense that it has more equations than unknowns. This lemma is important in its own right, but in order to show the usefulness of the lemma, we apply it to develop an adaptive super-exponential algorithm for the blind deconvolution of multi-input multi-output systems.

Abstract: In this paper we present a new algorithm for restoring an object from multiple undersampled low-resolution (LR) images that are degraded by optical blur and additive white Gaussian noise. We formulate the multiframe superresolution problem as maximum a posteriori estimation. The prior knowledge that the object is sparse in some domain is incorporated in two ways: first we use the popular l(1) norm as the regularization operator. Second, we model wavelet coefficients of natural objects using generalized Gaussian densities. The model parameters are learned from a set of training objects, and the regularization operator is derived from these parameters. We compare the results from our algorithms with an expectation-maximization (EM) algorithm for l(1) norm minimization and also with the linear minimum-mean-squared error (LMMSE) estimator. Using only eight 4 x 4 pixel downsampled LR images the reconstruction errors of object estimates obtained from our algorithm are 5.5% smaller than by the EM method and 14.3% smaller than by the LMMSE method.

Abstract: Sparse deconvolution is a classical subject in digital signal processing, having many practical applications. Support vector machine (SVM) algorithms show a series of characteristics, such as sparse solutions and implicit regularization, which make them attractive for solving sparse deconvolution problems. Here, a sparse deconvolution algorithm based on the SVM framework for signal processing is presented and analyzed, including comparative evaluations of its performance from the points of view of estimation and detection capabilities, and of robustness with respect to non-Gaussian additive noise.