Standard Deconvolution Techniques Research Articles

Improving deconvolution methods in biology through open innovation competitions: an application to the connectivity map.

MotivationDo machine learning methods improve standard deconvolution techniques for gene expression data? This article uses a unique new dataset combined with an open innovation competition to evaluate a wide range of approaches developed by 294 competitors from 20 countries. The competition’s objective was to address a deconvolution problem critical to analyzing genetic perturbations from the Connectivity Map. The issue consists of separating gene expression of individual genes from raw measurements obtained from gene pairs. We evaluated the outcomes using ground-truth data (direct measurements for single genes) obtained from the same samples.ResultsWe find that the top-ranked algorithm, based on random forest regression, beat the other methods in accuracy and reproducibility; more traditional gaussian-mixture methods performed well and tended to be faster, and the best deep learning approach yielded outcomes slightly inferior to the above methods. We anticipate researchers in the field will find the dataset and algorithms developed in this study to be a powerful research tool for benchmarking their deconvolution methods and a resource useful for multiple applications.Availability and implementationThe data is freely available at clue.io/data (section Contests) and the software is on GitHub at https://github.com/cmap/gene_deconvolution_challengeSupplementary informationSupplementary data are available at Bioinformatics online.

Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach.

The deconvolution process is a key step for quantitative evaluation of fluorescence lifetime imaging microscopy (FLIM) samples. By this process, the fluorescence impulse responses (FluoIRs) of the sample are decoupled from the instrument response (InstR). In blind deconvolution estimation (BDE), the FluoIRs and InstR are jointly extracted from a dataset with minimal a priori information. In this work, two BDE algorithms are introduced based on linear combinations of multi-exponential functions to model each FluoIR in the sample. For both schemes, the InstR is assumed with a free-form and a sparse structure. The local perspective of the BDE methodology assumes that the characteristic parameters of the exponential functions (time constants and scaling coefficients) are estimated based on a single spatial point of the dataset. On the other hand, the same exponential functions are used in the whole dataset in the global perspective, and just the scaling coefficients are updated for each spatial point. A least squares formulation is considered for both BDE algorithms. To overcome the nonlinear interaction in the decision variables, an alternating least squares (ALS) methodology iteratively solves both estimation problems based on non-negative and constrained optimizations. The validation stage considered first synthetic datasets at different noise types and levels, and a comparison with the standard deconvolution techniques with a multi-exponential model for FLIM measurements, as well as, with two BDE methodologies in the state of the art: Laguerre basis, and exponentials library. For the experimental evaluation, fluorescent dyes and oral tissue samples were considered. Our results show that local and global perspectives are consistent with the standard deconvolution techniques, and they reached the fastest convergence responses among the BDE algorithms with the best compromise in FluoIRs and InstR estimation errors.

Learning to do multiframe wavefront sensing unsupervised: Applications to blind deconvolution

Context. Observations from ground-based telescopes are severely perturbed by the presence of the Earth’s atmosphere. The use of adaptive optics techniques has allowed us to partly overcome this limitation. However, image-selection or post-facto image-reconstruction methods applied to bursts of short-exposure images are routinely needed to reach the diffraction limit. Deep learning has recently been proposed as an efficient way to accelerate these image reconstructions. Currently, these deep neural networks are trained with supervision, meaning that either standard deconvolution algorithms need to be applied a priori or complex simulations of the solar magneto-convection need to be carried out to generate the training sets. Aims. Our aim here is to propose a general unsupervised training scheme that allows multiframe blind deconvolution deep learning systems to be trained with observations only. The approach can be applied for the correction of point-like as well as extended objects. Methods. Leveraging the linear image formation theory and a probabilistic approach to the blind deconvolution problem produces a physically motivated loss function. Optimization of this loss function allows end-to-end training of a machine learning model composed of three neural networks. Results. As examples, we apply this procedure to the deconvolution of stellar data from the FastCam instrument and to solar extended data from the Swedish Solar Telescope. The analysis demonstrates that the proposed neural model can be successfully trained without supervision using observations only. It provides estimations of the instantaneous wavefronts, from which a corrected image can be found using standard deconvolution techniques. The network model is roughly three orders of magnitude faster than applying standard deconvolution based on optimization and shows potential to be used on real-time at the telescope.

Enhancing the recovery of a temporal sequence of images using joint deconvolution

In this work, we address the reconstruction of spatial patterns that are encoded in light fields associated with a series of light pulses emitted by a laser source and imaged using photon-counting cameras, with an intrinsic response significantly longer than the pulse delay. Adopting a Bayesian approach, we propose and demonstrate experimentally a novel joint temporal deconvolution algorithm taking advantage of the fact that single pulses are observed simultaneously by different pixels. Using an intensified CCD camera with a 1000-ps gate, stepped with 10-ps increments, we show the ability to resolve images that are separated by a 10-ps delay, four time better compared to standard deconvolution techniques.

A Framework for Fast Image Deconvolution With Incomplete Observations.

In image deconvolution problems, the diagonalization of the underlying operators by means of the fast Fourier transform (FFT) usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather slow methods or, otherwise, use inexact convolution models, resulting in the occurrence of artifacts in the enhanced images. In this paper, we propose a new deconvolution framework for images with incomplete observations that allows us to work with diagonalized convolution operators, and therefore is very fast. We iteratively alternate the estimation of the unknown pixels and of the deconvolved image, using, e.g., an FFT-based deconvolution method. This framework is an efficient, high-quality alternative to existing methods of dealing with the image boundaries, such as edge tapering. It can be used with any fast deconvolution method. We give an example in which a state-of-the-art method that assumes periodic boundary conditions is extended, using this framework, to unknown boundary conditions. Furthermore, we propose a specific implementation of this framework, based on the alternating direction method of multipliers (ADMM). We provide a proof of convergence for the resulting algorithm, which can be seen as a "partial" ADMM, in which not all variables are dualized. We report experimental comparisons with other primal-dual methods, where the proposed one performed at the level of the state of the art. Four different kinds of applications were tested in the experiments: deconvolution, deconvolution with inpainting, superresolution, and demosaicing, all with unknown boundaries.

Orthogonal matching pursuit applied to the deconvolution approach for the mapping of acoustic sources inverse problem.

Microphone arrays and beamforming have become a standard method to localize aeroacoustic sources. Deconvolution techniques have been developed to improve spatial resolution of beamforming maps. The deconvolution approach for the mapping of acoustic sources (DAMAS) is a standard deconvolution technique, which has been enhanced via a sparsity approach called sparsity constrained deconvolution approach for the mapping of acoustic sources (SC-DAMAS). In this paper, the DAMAS inverse problem is solved using the orthogonal matching pursuit (OMP) and compared with beamforming and SC-DAMAS. The resulting noise source maps show that OMP-DAMAS is an efficient source localization technique in the case of uncorrelated or correlated acoustic sources. Moreover, the computation time is clearly reduced as compared to SC-DAMAS.

Ultrasonic Inspection of Composite Materials Using Minimum Entropy Deconvolution

In this work, the Minimum Entropy Deconvolution (MED) method, developed for ultrasonic signals, is used to address the problem of delamination defect detection in Composite Materials. Standard deconvolution techniques suppose that the wavelet is minimum phase but generally make no assumptions about the amplitude distribution of the primary reflection coefficient sequence. For a white reflection sequence the assumption of a Gaussian distribution means that recovery of the true phase of the wavelet is impossible; however, a non-Gaussian distribution in theory allows recovery of the phase. It is generally recognized that primary reflection coefficients typically have a non-Gaussian amplitude distribution. The minimum entropy deconvolution (MED) method supposes whiteness but seek to exploit the non-Gaussianity. This method do not assume minimum phase. The deconvolution filter is defined by the maximization of a function called the objective. The algorithm is tested on simulated data and also tested on real ultrasonic data from multilayered composite materials.

Image Deconvolution Using a General Ridgelet and Curvelet Domain

We carry out deconvolution by transforming the data into a new general discrete Radon domain that can handle any assumed boundary conditions for the associated matrix inversion problem. For each associated component (projection), one can then apply deconvolution routines to smaller (and possibly better) conditioned matrix inversion problems than the matrix inversion problem for the entire image. We demonstrate this new scheme by adaptively deconvolving these components using a combination of regularized inversion and wavelet filtering techniques. This procedure allows us to provide image estimates based on a generalized ridgelet frame. We then devise methods for carrying out this scheme locally to provide estimates based on generalized multiscaled ridgelets which are then filtered and combined to form an estimate from a curvelet-like domain. The techniques presented here suggest a whole new paradigm for developing deconvolution algorithms that incorporate leading deconvolution schemes. Various experimental results show that our methods can perform significantly better than standard deconvolution techniques.

Explicit Deconvolution of Wellbore-Storage-Distorted Well-Test Data

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 103216, "Explicit Deconvolution of Wellbore-Storage- Distorted Well-Test Data," by O. Bahabanian, SPE, D. Ilk, SPE, N. Hosseinpour-Zonoozi, SPE, and T.A. Blasingame, SPE, Texas A&M U., prepared for the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September. The analysis and interpretation of wellbore-storage-distorted pressure-transient-test data remain significant challenges. Deconvolution (i.e., conversion of a variable-rate-distorted pressure profile into the pressure profile for an equivalent constant-rate-production sequence) has been in limited use as a conversion mechanism for the last 25 years. Unfortunately, standard deconvolution techniques require accurate measurements of flow rate and pressure at downhole (or sandface) conditions. While accurate pressure measurements are commonplace, the measurement of sandface flow rates is rare, essentially nonexistent in practice. An explicit (direct) deconvolution of wellbore-storage-distorted pressure-test data that uses only those pressure data was developed. Introduction To eliminate wellbore-storage effects in pressure-transient-test data, several methods have been proposed. An approximate direct method corrects the pressure-transient data distorted by wellbore storage into the equivalent-pressure function for the constant-rate case. Despite its simplicity, it has several shortcomings such as limited accuracy and erroneous skin-factor estimation. Rate-normalization techniques have been used to correct for wellbore-storage effects, and these methods were successful in some cases. The most appropriate application of rate normalization is its use for pressure-transient data influenced by continuously varying flow rates. Application of rate normalization requires sandface-flow-rate measurements and generally yields a shifted result trend that has the correct slope but incorrect intercept on a semilog graph (i.e., incorrect skin factor). Material-balance deconvolution has been shown to be a practical approach for the analysis of pressure-transient data distorted by wellbore-storage effects. In particular, this approach remedies the issue of a poor skin-factor estimate that typically is obtained with rate normalization. Material-balance deconvolution also is thought to require continuously varying sandface-flow-rate measurements. It is shown that sandface flow rates can be approximated from the observed pressure data. Methodology This work was put forth as an attempt to provide a set of simple, explicit deconvolution formulas that could be used on wellbore-storage-distorted pressure-transient-test data. The material-balance deconvolution was successful and should be considered sufficiently accurate for use as a practical tool for field applications. The other major method considered was the direct β-deconvolution algorithm modified to estimate the β-parameter from pressure rather than flow-rate data as originally proposed. The modification of the β-deconvolution algorithm, given only in terms of pressure variables, also was successful.

Signal analysis of impulse response functions in MR and CT measurements of cerebral blood flow

The impulse response function (IRF) of a localized bolus in cerebral blood flow codes important information on the tissue type. It is indirectly accessible both from MR and CT imaging methods, at least in principle. In practice, however, noise and limited signal resolution render standard deconvolution techniques almost useless. Parametric signal descriptions look more promising, and it is the aim of this contribution to develop some improvements along this line.

Image-spectroscopy – II. The removal of plural scattering from extended energy-filtered series by Fourier deconvolution

The increased spectral information obtained by acquiring an EFTEM image-series over several hundred eV allows plural scattering to be removed from loss images using standard deconvolution techniques developed for the quantification of EEL spectra. In this work, both Fourier-log and Fourier-ratio deconvolution techniques have been applied successfully to such image-series. Application of the Fourier-log technique over an energy-loss range of several hundred eV has been achieved by implementation of a novel method that extends the effective dynamic range of EFTEM image-series acquisition by over four orders of magnitude. Experimental results show that the removal of plural scattering from EFTEM image-series gives a significant improvement in quantification for thicker specimen regions. Further, the recovery of the single-scattering distribution using the Fourier-log technique over an extended energy-loss range is shown to result in an increase in both the ionisation-edge jump-ratio and the signal-to-noise ratio.

Deconvolution can be used in electrooptic studies to correct for non-ideal electric excitation pulses only when the electric dipole moment of the studied molecules is predominantly induced

The electric field pulses used for most measurements of transient electrooptic properties such as birefringence and dichroism, are rectangular and assumed to be ideal, but in practice do all such pulses have non-zero rise and fall times. Claims have been made that this non-ideality may be taken into account by employing standard deconvolution techniques. We find that this approach yields exact results in the zero electric field limit when the electric dipole moment of the studied macromolecules is predominantly induced. However, for finite electric field strengths and/or macromolecules with partly or fully permanent electric dipole moments, we find that the deconvolution method yields erroneous estimates of the electrooptic relaxation times. When the decay time of the electric pulse and the electrooptic decay time are equal, and the system is operated in the Kerr domain, this systematic error for macromolecules with purely permanent electric dipole moment equals 37%. In a research field where the uncertainty of the reported relaxation times normally is assumed to be only a few percent this is an error that may seriously mislead unsuspecting users. We find that this systematic error can readily be avoided by employing standard numerical integration of a set of coupled first-order differential equations instead of the standard deconvolution techniques.

Analytic minimum information deconvolution and its application to ocean bottom seismometer data

Seismic refraction/wide angle reflection data for the study of the earth's crust generally lack resolution due to the low frequency wavelets from seismic sources. Standard deconvolution techniques to improve resolution of the data are limited by phase‐shifted waveforms such as supercritical reflections from the Moho as well as various refraction phases from the crust. We extended the minimum information deconvolution technique to the analytic formulation to deconvolve seismic data that contain phase‐shifted wavelets. When applied to a seismogram, analytic deconvolution yields the amplitude of the earth's impulse response function in the form of the signal envelope. An application example with ocean bottom seismometer data acquired along the Canadian continental margin of the Atlantic shows a remarkable improvement in resolution by compressing the wavelets effectively.

Snapshot Imaging with the Australia Telescope Compact Array

AbstractRadio snapshot imaging is an efficient observing method which allows several sources to be observed in the one session. Snapshot observing with the Australia Telescope Compact Array (ATCA) involves special difficulties, as the small number of antennas combined with the short total integration time leads to high sidelobe levels in the raw images. The images can be improved markedly by standard deconvolution techniques, but more care is required in their use because of the difficulty in distinguishing real emission from artefacts. This study, based on a set of snapshot observations of strong sources at 5 GHz, gives guidance on both the planning of observations and the data reduction. We show that snapshot imaging with the 6 km ATCA can achieve a dynamic range of 100–200:1 provided certain conditions are met, namely a peak flux density > 100 mJy, an angular size ≤ 30″ and an hour-angle coverage spanning at least six well-separated 5-minute cuts. When observing weak sources it is essential for calibration sources to be selected carefully and observed frequently.

Improving the resolution of ultrasonic echoes from thin bondlines using cepstral processing

The measurement of the transit time of an ultrasonic pulse through the adhesive layer of a bonded joint can be an important indicator of the cohesive strength of the bond. However, when the pulse length is long in comparison with its transit time through the adhesive, it becomes impossible to resolve the echoes from the front and back faces of the bondline, and hence to deduce the transit time. In such cases, it is possible to improve the resolution by deconvolving the pulse shape from the impulse response of the adhesive layer. Standard deconvolution techniques are dependent on an accurate knowledge of the pulse shape in order to facilitate this deconvolution, whereas cepstral processing is a deconvolution technique for which no a priori pulse shape information is required. Using this technique it is found that it is possible to resolve the echoes of typical broadband ultrasonic pulses from layers of half the thickness that it is possible to resolve without signal processing. The line spacing of the cepstrum determines the digital accuracy of the transit time measurement. This line spacing is inversely proportional to the time domain sampling frequency. Hence, in order to obtain good time domain resolution, a high sampling frequency is required. However, it is found that it is essential that the signal contains significant energy up to the Nyquist frequency (half the sampling frequency) to minimize cepstral noise. This limits the improvement in resolution which can be obtained with a given transducer.

Analysis and deconvolution of some J′≠0 rovibronic transitions in the high resolution S1←S fluorescence excitation spectrum of pyrazine

Fluorescence excitation spectra are reported for several J′≠0 rotational members of the 000 band of the S1(1B3u)←S0(1A1g) electronic transition of pyrazine at a resolution of about 10 MHz. The transitions studied, namely R(0)–R(2) and P(2)–P(4), are each split into a large number of sharp lines ascribed, as in the case of the previously studied P(1) (J′=0) transition, to coupling with the lowest triplet state T1(3B3u). Despite this complexity, we show in this paper that it is possible to separate the lines into clusters of transitions that terminate in the same K′ component of the electronically excited, mixed S1–T1 state. This demonstrates that K′ is a good quantum number, at least at low J′ in the zero-order S1 state. From this analysis, we determine the rotational constants of the S0 and S1 states. We also determine: (i) the relative cluster intensities; (ii) the coupled T1 level densities; and (iii) by using standard deconvolution techniques, the S1–T1 coupling matrix elements, each as a function of J′,K′. Cluster intensities decrease with increasing J′, but K′=0 clusters are significantly less intense than K′≠0 clusters in the fluorescence excitation spectra. Observed triplet level densities in each cluster exceed by an order of magnitude the calculated density of rovibronic states if selection rules appropriate to the D2h point group are taken into account. Neither the observed level densities nor the coupling matrix elements (which vary from less than 5 MHz to more than 500 MHz) show a clear-cut systematic dependence on J′ or K′, although K′=0 levels appear to be more strongly coupled than K′≠0 levels. Possible explanations for these results and their implications for intersystem crossing dynamics in the isolated molecule are discussed.

Non‐Gaussian reflectivity, entropy, and deconvolution

Standard deconvolution techniques assume that the wavelet is minimum phase but generally make no assumptions about the amplitude distribution of the primary reflection coefficient sequence. For a white reflection sequence the assumption of a Gaussian distribution means that recovery of the true phase of the wavelet is impossible; however, a non‐Gaussian distribution in theory allows recovery of the phase. It is generally recognized that primary reflection coefficients typically have a non‐Gaussian amplitude distribution. Deconvolution techniques that assume whiteness but seek to exploit the non‐Gaussianity include Wiggins’ minimum entropy deconvolution (MED), Claerbout’s parsimonious deconvolution, and Gray’s variable norm deconvolution. These methods do not assume minimum phase. The deconvolution filter is defined by the maximization of a function called the objective. I examine these and other MED‐type deconvolution techniques. Maximizing the objective by setting derivatives to zero results in most cases in a deconvolution filter which is the solution of a highly nonlinear Toeplitz matrix equation. Wiggins’ original iterative approach to the solution is suitable for some methods, while for other methods straightforward iterative perturbation approaches may be used instead. The likely effects on noise of the nonlinearities involved are demonstrated as extremely varied. When the form of an objective remains constant with iteration, the most general description of the method is likelihood ratio maximization; when the form changes, a method seeks to maximize relative entropy at each iteration. I emphasize simple and useful link between three methods and the use of M-estimators in robust statistics. In attempting to assess the accuracy of the techniques, the choice between different families of distributions for modeling the distribution of reflection coefficients is important. The results provide important insights into methods of constructing and understanding the statistical implications and behavior of a chosen nonlinearity. A new objective is introduced to illustrate this, and a few particular preferences expressed. The methods are compared with the zero‐memory nonlinear deconvolution approach of Godfrey and Rocca (1981); for their approach, two distinctly different yet statistically comparable models for reflection coefficients are seen to give surprisingly similarly shaped nonlinearities. Finally, it is shown that each MED‐type method can be viewed as the minimization of a particular configurational entropy expression, where some suitable ratio plays the role of a probability.

Advanced deconvolution techniques for coded aperture imaging

The standard deconvolution technique for coded aperture imaging is cross correlation with the relevant mask pattern. In practice such an imaging system is imperfect, giving incomplete coding, and direct cross correlation with the mask introduces “ghosting” and enhanced noise fluctuations. This paper describes the application of image processing techniques such as the Wiener Filter and the Maximum Entropy Method to deconvolving the recorded shadow pattern and illustrates the advantage of such methods using a computer simulation of a wide field camera for X-ray astronomy.