Abstract: Image deblurring is an important topic in imaging science. In this review, we consider together fluorescence microscopy and optical/infrared astronomy because of two common features: in both cases the imaging system can be described, with a sufficiently good approximation, by a convolution operator, whose kernel is the so-called point-spread function (PSF); moreover, the data are affected by photon noise, described by a Poisson process. This statistical property of the noise, that is common also to emission tomography, is the basis of maximum likelihood and Bayesian approaches introduced in the mid eighties. From then on, a huge amount of literature has been produced on these topics. This review is a tutorial and a review of a relevant part of this literature, including some of our previous contributions. We discuss the mathematical modeling of the process of image formation and detection, and we introduce the so-called Bayesian paradigm that provides the basis of the statistical treatment of the problem. Next, we describe and discuss the most frequently used algorithms as well as other approaches based on a different description of the Poisson noise. We conclude with a review of other topics related to image deblurring such as boundary effect correction, space-variant PSFs, super-resolution, blind deconvolution and multiple-image deconvolution.

Abstract: Density Deconvolution.- Nonparametric Regression with Errors-in-Variables.- Image and Signal Reconstruction.

Abstract: In this paper, we present novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Using a hierarchical Bayesian model, the unknown image, blur, and hyperparameters for the image, blur, and noise priors are estimated simultaneously. A variational inference approach is utilized so that approximations of the posterior distributions of the unknowns are obtained, thus providing a measure of the uncertainty of the estimates. Experimental results demonstrate that the proposed approaches provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.

Abstract: In this paper, we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelty of this model is the use of a sparse kernel-based model for the point spread function (PSF) that allows estimation of both PSF shape and support. In the herein proposed approach, a robust model of the BID errors and an image prior that preserves edges of the reconstructed image are also used. Sparseness, robustness, and preservation of edges are achieved by using priors that are based on the Student's-t probability density function (PDF). This pdf, in addition to having heavy tails, is closely related to the Gaussian and, thus, yields tractable inference algorithms. The approximate variational inference methodology is used to solve the corresponding Bayesian model. Numerical experiments are presented that compare this BID methodology to previous ones using both simulated and real data.

Abstract: We report a multiframe blind deconvolution algorithm that we have developed for imaging through the atmosphere. The algorithm has been parallelized to a significant degree for execution on high-performance computers, with an emphasis on distributed-memory systems so that it can be hosted on commodity clusters. As a result, image restorations can be obtained in seconds to minutes. We have compared and quantified the quality of its image restorations relative to the associated Cramer-Rao lower bounds (when they can be calculated). We describe the algorithm and its parallelization in detail, demonstrate the scalability of its parallelization across distributed-memory computer nodes, discuss the results of comparing sample variances of its output to the associated Cramer-Rao lower bounds, and present image restorations obtained by using data collected with ground-based telescopes.

Abstract: We present CSDeconv, a computational method that determines locations of transcription factor binding from ChIP-seq data. CSDeconv differs from prior methods in that it uses a blind deconvolution approach that allows closely-spaced binding sites to be called accurately. We apply CSDeconv to novel ChIP-seq data for DosR binding in Mycobacterium tuberculosis and to existing data for GABP in humans and show that it can discriminate binding sites separated by as few as 40 bp.

Abstract: The estimation of the time-of-arrival (TOA) and/or time-of-flight (TOF) of the ultrasonic echoes is essential in ultrasonic non-destructive evaluation. In this paper, a sparse deconvolution method is proposed for deconvolving ultrasonic signals. To obtain the transducer pulse-echo wavelet, matching pursuit (MP) method has been used to analyze noisy ultrasonic pulse-echo wavelet and decompose the noisy pulse-echo wavelet into unit-norm vectors, then, the approximation pulse-echo wavelet obtained by the reconstruction result with several large coefficient decomposed unit-norm vectors. A weighting matrix is the central to the efficiency of the sparse deconvolution method. It increases the sparsity of the deconvolution result and decreases the influence of the added noise. The deconvolution gives high-resolution ultrasonic reflectivity function. We can obtain the accurate TOA or TOF from the ultrasonic reflectivity function. Results using real ultrasonic data show the sparse deconvolution method yields good estimates of the spikes associated with the reverberation echoes and the thickness of a steel sample can be calculated by the ultrasonic reflectivity function with a reasonable accuracy.

Abstract: Atmospheric turbulences blur astronomical images taken by earth-based telescopes. Taking many short-time exposures in such a situation provides noisy images of the same object, where each noisy image has a different blur. Commonly astronomers apply a technique called “Lucky Imaging” that selects a few of the recorded frames that fulfill certain criteria, such as reaching a certain peak intensity (“Strehl ratio”). The selected frames are then averaged to obtain a better image. In this paper we introduce and analyze a new method that exploits all the frames and generates an improved image in an online fashion. Our initial experiments with controlled artificial data and real-world astronomical datasets yields promising results.

Abstract: We consider optimization of hybrid imaging systems including a phase mask for enhancing the depth of field and a digital deconvolution step. We propose an image quality criterion that takes into account the variability of the system's point-spread function along the expected defocus range and the noise enhancement induced by deconvolution. Considering the classical cubic phase mask as an example, we show that the optimization of this criterion may lead to filter parameters that are significantly different from those usually proposed to ensure the strict invariance of the PSF.

Abstract: Blind deconvolution arises naturally when dealing with finite multipath interference on a signal. In this paper we present a new method to protect the signals from the effects of sparse multipath channels — we modulate/encode the signal using random waveforms before transmission and estimate the channel and signal from the observations, without any prior knowledge of the channel other than that it is sparse. The problem can be articulated as follows. The original message x is encoded with an overdetermined m × n (m > n) matrix A whose entries are randomly chosen; the encoded message is given by Ax. The received signal is the convolution of the encoded message with h, the S-sparse impulse response of the channel. We explore three different schemes to recover the message x and the channel h simultaneously. The first scheme recasts the problem as a block l 1 optimization program. The second scheme imposes a rank-1 structure on the estimated signal. The third scheme uses nuclear norm as a proxy for rank, to recover the x and h. The simulation results are presented to demonstrate the efficiency of the random coding and proposed recovery schemes.

Abstract: In this paper, we present a postprocessing approach to tackle the single image focus editing problem. In detail, the proposed method can accomplish the tasks of focus map estimation, image refocusing and defocusing. Given an image with a mixture of focused and defocused objects, we first detect the edges and then estimate the focus map based on the edge blurriness which is depicted explicitly with a well-parameterized model. The image refocusing problem is addressed in an elaborate blind deconvolution framework, where the image prior is modeled well by using both global and local constraints. Especially, we correct the defocused blurry edges to sharp ones with the aid of the parametric edge model and then render this cue as a novel local prior to ensure the sharpness of the refocused image. Experimental results demonstrate that the proposed approach performs well in producing different styles of realistic images from a single input by focus editing.

Abstract: 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.

Abstract: Theoretical and experimental research on the deconvolution algorithm of dwell time in the technology of computer controlled optical surfacing (CCOS) formation is made to get an ultra-smooth surface of space optical element. Based on the Preston equation, the convolution model of CCOS is deduced. Considering the morbidity problem of deconvolution algorithm and the actual situation of CCOS technology, the weighting spatial deconvolution algorithm is presented based on the non-periodic matrix model, which avoids solving morbidity resulting from the noise induced by measurement error. The discrete convolution equation is solved using conjugate gradient iterative method and the workload of iterative calculation in spatial domain is reduced effectively. Considering the edge effect of convolution algorithm, the method adopts a marginal factor to control the edge precision and attains a good effect. The simulated processing test shows that the convergence ratio of processed surface shape error reaches 80%. This algorithm is further verified through an experiment on a numerical control bonnet polishing machine, and an ultra-smooth glass surface with the root-mean-square (RMS) error of 0.0088 \mum is achieved. The simulation and experimental results indicate that this algorithm is steady, convergent, and precise, and it can satisfy the solving requirement of actual dwell time.

Abstract: We discuss approximate maximum-likelihood methods for blind identification and deconvolution. These algorithms are based on particle approximation versions of the expectation-maximization (EM) algorithm. We consider three different methods which differ in the way the posterior distribution of the symbols is computed. The first algorithm is a particle approximation method of the fixed-interval smoothing. The two-filter smoothing and the novel joined-two-filter smoothing involve an additional backward-information filter. Because the state space is finite, it is furthermore possible at each step to consider all the offsprings of any given particle. It is then required to construct a novel particle swarm by selecting, among all these offsprings, particle positions and computing appropriate weights. We propose here a novel unbiased selection scheme, which minimizes the expected loss with respect to general distance functions. We compare these smoothing algorithms and selection schemes in a Monte Carlo experiment. We show a significant performance increase compared to the expectation maximization Viterbi algorithm (EMVA), a fixed-lag smoothing algorithm and the Block constant modulus algorithm (CMA).

Abstract: A method of filtering seismic signals is described using the steps of obtaining the seismic signals generated by activating a seismic source and recording signals emanating from the source at one or more receivers; defining a source signature deconvolution filter to filter the seismic signal, wherein the filter is scaled by a frequency-dependent term based on an estimate of the signal-to-noise (S/N) based on the spectral power of a signal common to a suite of angle-dependent far-field signatures normalized by the total spectral power of the signatures within the angular suite and performing a source signature deconvolution using the source signature deconvolution filter.

Abstract: Fault diagnosis of rolling mills, especially the main drive gearbox, is of great importance to the high quality products and long-term safe operation. However, the useful fault information is usually submerged in heavy background noise under the severe condition. Thereby, a novel method based on multiwavelet sliding window neighboring coefficient denoising and optimal blind deconvolution is proposed for gearbox fault diagnosis in rolling mills. The emerging multiwavelets can seize the important signal processing properties simultaneously. Owing to the multiple scaling and wavelet basis functions, they have the supreme possibility of matching various features. Due to the periodicity of gearbox signals, sliding window is recommended to conduct local threshold denoising, so as to avoid the “overkill” of conventional universal thresholding techniques. Meanwhile, neighboring coefficient denoising, considering the correlation of the coefficients, is introduced to effectively process the noisy signals in every sliding window. Thus, multiwavelet sliding window neighboring coefficient denoising not only can perform excellent fault extraction, but also accords with the essence of gearbox fault features. On the other hand, optimal blind deconvolution is carried out to highlight the denoised features for operators’ easy identification. The filter length is vital for the effective and meaningful results. Hence, the foremost filter length selection based on the kurtosis is discussed in order to full benefits of this technique. The new method is applied to two gearbox fault diagnostic cases of hot strip finishing mills, compared with multiwavelet and scalar wavelet methods with/without optimal blind deconvolution. The results show that it could enhance the ability of fault detection for the main drive gearboxes.

Abstract: In archaeological magnetic prospecting, most targets can be modeled by a single layer of constant burial depth and thickness. With this assumption, recovery of the magnetization distribution of the buried layer from magnetic surface measurements is a 2D deconvolution problem. Because this problem is ill posed, it requires regularization techniques to be solved. In analogy with image reconstruction, the solution showing the resolved subsoil features can be considered a focused version of the blurred and noisy magnetic image. Exploiting image deconvolution tools, two iterative reconstruction methods are applied to minimize the least-squares functional: the standard projected Landweber method and a proposed modification of the iterative space reconstruction algorithm. Different regularization functionals inject a priori information in the optimization problem, and the split-gradient method modifies the algorithms. Numerical simulations in the case of perfect knowledge of the impulse response functions demonstrate that the edge-preserving, total-variation functionals give the best results. An iterative semiblind deconvolution method to estimate the burial depth of the source layer was used with a real data set to test the effectiveness of the method.

Abstract: The problem of blind source separation (BSS) and system identification for multiple-input multiple-output (MIMO) auto-regressive (AR) mixtures is addressed in this paper. Two new time-domain algorithms for system identification and BSS are proposed based on the Gaussian mixture model (GMM) for sources distribution. Both algorithms are based on the generalized expectation-maximization (GEM) method for joint estimation of the MIMO-AR model parameters and the GMM parameters of the sources. The first algorithm is derived under the assumption of unstructured input signal statistics, while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption. These methods are tested via simulations using synthetic and audio signals. The system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well-known multidimensional Yule-Walker solution followed by an instantaneous BSS method. The results show that the proposed algorithms outperform the Yule-Walker based approach. The BSS performances were compared to other convolutive BSS methods. The results show that the proposed algorithms achieve higher signal-to-interference ratio (SIR) compared to the other tested methods.

Abstract: Abstract A new robust algorithm for the pressure/rate deconvolution problem, described by Duhamel's convolution integral, which is a first-kind linear Volterra integral equation, has been developed. A transformation of the convolution integral to a nonlinear one is used to impose explicitly the positivity constraint on the solution. The weighted least-squares method with regularization on the solution by a curvature constraint has been used for computation of the convolution kernel (impulse function or deconvolved pressure) of the system. The algorithm takes into account the errors (or noise) in both the left-hand-side (measured pressures) and flow rate measurements (normally, the time dependent inner boundary condition) of the convolution integral. The solution algorithm also allows one to adjust flow rates and/or the initial reservoir pressure (an initial condition for the solution) during calculations, where both flow rate and the initial pressure may contain some level of uncertainty. For validation of the results of the algorithm, three synthetic examples are presented.

Abstract: There has recently been considerable interest in applying Total Variation regularization with an l1 data fidelity term to the denoising of images subject to salt and pepper noise, but the extension of this formulation to more general problems, such as deconvolution, has received little attention. We consider this problem, comparing the performance of l1-TV deconvolution, computed via our Iteratively Reweighted Norm algorithm, with an alternative variational approach based on Mumford-Shah regularization. The l1-TV deconvolution method is found to have a significant advantage in reconstruction quality, with comparable computational cost.

Abstract: Linear space-invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions. A ringing metric to evaluate the quality of images restored using iterative deconvolution algorithms is presented. According to the types of ringing artifacts, two ringing metrics are used to assess the restored images based on the analysis of ringing artifacts. An overall ringing metric is presented based on the two ringing metrics. The experimental results validate that the proposed method performs well over a wide range of restoration image ringing level assessments. Consequently, the proposed model has a good agreement with the ratings from an observer in subjective experiments.

Abstract: Using the modern time series analysis method and white noise estimation theory, under the linear minimal variance optimal information fusion criterion, a multisensor information fusion white noise deconvolution filter is presented for systems with correlated noises. The formula of computing covariances among filtering errors of sensors is presented, which can be applied to compute the optimal fused weighting matrices. Compared with the single sensor case, the accuracy of the fused filter is improved. It can be applied to signal processing in oil seismic exploration. A simulation example for information fusion Bernoulli-Gaussian white noise deconvolution filter shows its effectiveness.

Abstract: We consider the parametric analysis of frequency-domain optical coherence tomography (OCT) signals. A Monte Carlo (Gibbs sampler) detection-estimation method for determining the depths and reflection coefficients of tissue interfaces (reflective sites in the tissue) is proposed. Our method is blind since it estimates the instrumentation-dependent “fringe” function along with the tissue parameters. Sparsity of the detected interfaces is enforced by an impulse detector and a modified Bernoulli-Gaussian prior with a minimum distance constraint. Numerical results using synthetic and real signals demonstrate the excellent performance and fast convergence of our method.

Abstract: In this paper, we consider continuous solution methods for migration deconvolution imaging in seismic inverse problems. Direct migration methods, using the adjoint operator L*, usually yield a lower resolution or blurred image. Linearized migration deconvolution requires solving a least-squares migration (LSM) problem. However, we notice that the direct LSM method is unstable in computation which is a severe obstacle for visual explanation. We study regularized mathematical model. We fist formulate the problem by incorporating regularizing constraints, and then employ iterative gradient methods for migration deconvolution and inversion. A hybrid gradient technique for ill-posed migration inverse problem is proposed. To show the potential for application of the proposed method, we perform synthetic one-, two- and three-dimensional seismogram for seismic migration inversion. Numerical performance indicates that the proposed method is very promising for practical seismic migration imaging.