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PubMed1998

CODE: a deconvolution program implementing a regularization method of deconvolution constrained to non-negative values. Description and pilot evaluation.

A regularization method of deconvolution constrained to non-negative values is described. The method gives smooth estimates of the input function whilst providing a feasible fit (in terms of least squares) to measurements. A description of the program CODE (constrained deconvolution) which implements the method is given. A new methodology for a pilot evaluation of deconvolution programs is also proposed. The methodology is based on synthetic data. It employs a variety of shapes of the input function, low (1%) and high (15%) values of the measurement error, and incorporates primary (accuracy) and secondary (bias) performance measures. The performance of CODE is evaluated and it is suggested that CODE provides estimates of the input function with acceptable accuracy.

Data Interpretation, Statistical↗
PubMed2005

Automatic program for peak detection and deconvolution of multi-overlapped chromatographic signals part II: peak model and deconvolution algorithms.

Several interlinked algorithms for peak deconvolution by non-linear regression are presented. These procedures, together with the peak detection methods outlined in Part I, have allowed the implementation of an automatic method able to process multi-overlapped signals, requiring little user interaction. A criterion based on the evaluation of the multivariate selectivity of the chromatographic signal is used to auto-select the most efficient deconvolution procedure for each chromatographic situation. In this way, non-optimal local solutions are avoided in cases of high overlap, and short computation times are obtained in situations of high resolution. A new algorithm, fitting both the original signal and the second derivatives is proved to avoid local optima in intermediate coelution situations. This allows achieving the global optimum without the need of background knowledge by the user. A previously reported peak model, a Gaussian with a polynomial standard deviation whose complexity can be modulated to enhance the fitting quality, was applied. However, the original formulation was modified to account baseline outside the peak region. Also, the optimal model complexity was auto-selected via error propagation theory. The method is able to process simultaneously several related chromatograms. The software was tested with both simulated and experimental chromatograms obtained with monolithic silica columns.

Algorithms↗
PubMed2002

A comparison of deconvolution techniques for stress relaxation.

Stress relaxation (or equivalently creep) allows a large range of the relaxation (retardation) spectrum of materials to be examined, particularly at lower frequencies. However, higher frequency components of the relaxation curves (typically of the order of Hertz) are attenuated due to the finite time taken to strain the specimen. This higher frequency information can be recovered by deconvolution of the stress and strain during the loading period. This paper examines the use of three separate deconvolution techniques: numerical (Fourier) deconvolution, semi-analytical deconvolution using a theoretical form of the strain, and deconvolution by a linear approximation method. Both theoretical data (where the exact form of the relaxation function is known) and experimental data were used to assess the accuracy and applicability of the deconvolution methods. All of the deconvolution techniques produced a consistent improvement in the higher frequency data up to the frequencies of the order of Hertz, with the linear approximation method showing better resolution in high-frequency analysis of the theoretical data. When the different deconvolution techniques were applied to experimental data, similar results were found for all three deconvolution techniques. Deconvolution of the stress and strain during loading is a simple and practical method for the recovery of higher frequency data from stress-relaxation experiments.

Algorithms↗
PubMed2006

Multidimensional multichannel FIR deconvolution using Gröbner bases.

We present a new method for general multidimensional multichannel deconvolution with finite impulse response (FIR) convolution and deconvolution filters using Gröbner bases. Previous work formulates the problem of multichannel FIR deconvolution as the construction of a left inverse of the convolution matrix, which is solved by numerical linear algebra. However, this approach requires the prior information of the support of deconvolution filters. Using algebraic geometry and Gröbner bases, we find necessary and sufficient conditions for the existence of exact deconvolution FIR filters and propose simple algorithms to find these deconvolution filters. The main contribution of our work is to extend the previous Gröbner basis results on multidimensional multichannel deconvolution for polynomial or causal filters to general FIR filters. The proposed algorithms obtain a set of FIR deconvolution filters with a small number of nonzero coefficients (a desirable feature in the impulsive noise environment) and do not require the prior information of the support. Moreover, we provide a complete characterization of all exact deconvolution FIR filters, from which good FIR deconvolution filters under the additive white noise environment are found. Simulation results show that our approaches achieve good results under different noise settings.

Algorithms↗
PubMed2006

Model-free deconvolution of femtosecond kinetic data.

Though shorter laser pulses can also be produced, pulses of the 100 fs range are typically used in femtosecond kinetic measurements, which are comparable to characteristic times of the studied processes, making detection of the kinetic response functions inevitably distorted by convolution with the pulses applied. A description of this convolution in terms of experiments and measurable signals is given, followed by a detailed discussion of a large number of available methods to solve the convolution equation to get the undistorted kinetic signal, without any presupposed kinetic or photophysical model of the underlying processes. A thorough numerical test of several deconvolution methods is described, and two iterative time-domain methods (Bayesian and Jansson deconvolution) along with two inverse filtering frequency-domain methods (adaptive Wiener filtering and regularization) are suggested to use for the deconvolution of experimental femtosecond kinetic data sets. Adaptation of these methods to typical kinetic curve shapes is described in detail. We find that the model-free deconvolution gives satisfactory results compared to the classical "reconvolution" method where the knowledge of the kinetic and photophysical mechanism is necessary to perform the deconvolution. In addition, a model-free deconvolution followed by a statistical inference of the parameters of a model function gives less biased results for the relevant parameters of the model than simple reconvolution. We have also analyzed real-life experimental data and found that the model-free deconvolution methods can be successfully used to get undistorted kinetic curves in that case as well. A graphical computer program to perform deconvolution via inverse filtering and additional noise filters is also provided as Supporting Information. Though deconvolution methods described here were optimized for femtosecond kinetic measurements, they can be used for any kind of convolved data where measured experimental shapes are similar.

Journal Article↗
PubMed1997

Non-parametric deconvolution provides an objective assessment of GH responsiveness to GH-releasing stimuli in normal subjects.

OBJECTIVE: Deconvolution analysis has been proposed as an effective method for analysing the physiology of GH secretion. In the literature, it has been applied to spontaneous secretion data characterized by long and uniform sampling paradigms. In the present study we investigated the applicability of non-parametric deconvolution to the analysis of response-to-stimuli (RTS) data characterized by infrequent and non-uniform sampling. PATIENTS: Thirty-six healthy adult male volunteers (age range 24-37 years) were randomly subdivided into two groups (group I, n = 30; group II, n = 6). DESIGN: Subjects of group I were tested with a single 1 microgram/kg body weight GH-releasing hormone (GHRH) bolus, administered at 0 minutes. Subjects of group II were tested, in random order, with a 4- or 5-day interval, with (1) two consecutive 1 microgram/kg body weight GHRH boluses at 0 and 120 minutes and (2) two consecutive 1 microgram/kg body weight hexarelin boluses, administered at 0 and 120 minutes. MEASUREMENTS: GH levels were determined at 0, 15, 30, 45, 60, 90 and 120 minutes (group I) and -30, 0, 15, 30, 45, 60, 120, 135, 150, 165, 180 and 240 minutes (group II). A numerically efficient regularization-based non-parametric deconvolution algorithm incorporating non-negativity constraints was used to estimate the time profile of the instantaneous secretion rate (ISR). Confidence limits allowing for both measurement error and kinetic model uncertainty were computed using a Monte-Carlo procedure. In order to validate the deconvolution method, a simulated benchmark problem was set up. RESULTS: The analysis of the benchmark problem showed that the proposed method is capable of providing an accurate reconstruction of the ISR (as measured by the root mean square (RMS) error). Moreover, it appeared that reliable confidence limits cannot be obtained unless the kinetic model uncertainty is taken into account. The analysis of the data showed a clear rise in the ISR subsequent to the first bolus (either GHRH or hexarelin), with most of the response occurring within 60 minutes of the stimulus. In group I, it was also seen that discarding the samples collected at times 90 and 120 minutes only marginally affected the estimate of the cumulated ISR over 0-60 minutes (the variation was always less than 3%). The analysis of GH responsiveness to repeated stimuli (group II) showed that the amount of hormone secreted after the second bolus was clearly reduced in comparison with the elicited by the first stimulus, most of the response occurring within 60 minutes of the injection. The amount of GH secreted after the second stimulus ranged from 13 to 36% (GHRH 17-36%; hexarelin 13-36%) of the overall amount of hormone secreted after time 0 minutes. CONCLUSIONS: Even with relatively few samples, non-parametric deconvolution of response-to-stimulus data is capable of providing a reliable, smooth and non-negative estimate of the GH instantaneous secretion rate that offers a realistic representation of the GH secretory dynamics. The non-parametric approach compares favourably with respect to discrete deconvolution methods, that yield discontinuous instantaneous secretion rates profiles, and parametric methods that would require more stringent assumptions on the shape of the instantaneous secretion rate. When assessing confidence limits it is essential to take into account both measurement error and kinetic model uncertainty. Using deconvolution in normal subjects, the estimated instantaneous secretion rate between 0 and 60 minutes is scarcely affected by samples taken after time 60 minutes. Since most of the secretory response takes place during this time interval, there is motivation for investigating the use of shorter sampling protocols in conjunction with deconvolution analysis. Although pulse detection and the assessment of the shape of spontaneous pulses have not been investigated, it could be interesting to apply non-parametric deconvolution to spontaneous sec

Adult↗
PubMed2004

Deconvolution of confocal images of dihydropyridine and ryanodine receptors in developing cardiomyocytes.

Colocalization of dihydropyridine (DHPR) and ryanodine (RyR) receptors, a key determinant of Ca(2+)-induced Ca2+ release, was previously estimated in 3-, 6-, 10-, and 20-day-old rabbit ventricular myocytes by immunocytochemistry and confocal microscopy. We now report on the effects of deconvolution (using a maximum-likelihood estimation algorithm) on the calculation of colocalization indexes. Clusters of DHPR and RyR can be accurately represented as point sources of fluorescence, which enables a model of their relative distributions to be constructed using images of point spread functions to simulate their fluorescence inside a cell. This model was used to investigate the effects of deconvolution on colocalization as a function of separation distance. Deconvolution resulted in significant improvements in both axial and transverse resolutions, producing significant increases in clarity. Comparisons of intensity profiles (full-width half-maximum) pre- and postdeconvolution showed decreased dispersion of the fluorescent signal and a corresponding decrease in false colocalization as determined by fluorescence modeling. This hypothesis was extended to physiological data previously collected. The number of colocalized voxels was quantified after deconvolution, and the degree of colocalization of DHPR with RyR decreased significantly after deconvolution in all age groups: 3 days (62 +/- 2% before deconvolution, 43 +/- 3 after deconvolution) to 20 days old (79 +/- 1% before deconvolution, 63 +/- 2% after deconvolution). The data demonstrate that confocal images should be deconvolved before any quantitative analysis, such as colocalization index determination, to minimize the detrimental effects of out-of-focus light in coincident voxels.

Algorithms↗
PubMed2003

Heuristic charge assignment for deconvolution of electrospray ionization mass spectra.

We propose a new algorithm for deconvolution of electrospray ionization mass spectra based on direct assignment of charge to the measured signal at each mass-to-charge ratio (m/z). We investigate two heuristics for charge assignment: the entropy-based heuristic is adapted from a deconvolution algorithm by Reinhold and Reinhold;10 the multiplicative-correlation heuristic is adapted from the multiplicative-correlation deconvolution algorithm of Hagen and Monnig.6 The entropy-based heuristic is insensitive to overestimates of z(max), the maximum ion charge. We test the deconvolution algorithm on two single-component samples: the measured spectrum of human beta-endorphin has two prominent and one very weak line whereas myoglobin has a well-developed quasi-gaussian envelope of 17 peaks. In both cases, the deconvolution algorithm gives a clean deconvoluted spectrum with one dominant peak and very few artefacts. The relative heights of the peaks due to the parent molecules in the deconvoluted spectrum of a mixture of two peptides, which are expected to ionize with equal efficiency, give an accurate measure of their relative concentration in the sample.

Algorithms↗
PubMed2005

Deconvolution microscopy.

Since its introduction in 1983, deconvolution microscopy has become a key image-processing tool for visualizing the cellular structures of fixed and living specimens in three dimensions and at subresolution scale. The last 20 years have seen the development of many different applications based on deconvolution microscopy, including a wide variety of optical setup and deconvolution algorithms. This chapter aims to summarize and to describe in detail the major features of this technology, from theoretical aspects to practical solutions. It will begin by explaining the principle of image formation in three-dimensional optical sectioning microscopy. As deconvolution microscopy provides, in essence, a means of overcoming the limits of optical microscopy, the second part of this chapter is dedicated to the theoretical and experimental description of image generation through a microscope. Methods will be detailed for the determination of point spread function, as a crucial step for the characterization of any optical system and a key preliminary step for image deconvolution. The challenges faced and the various possibilities for determining this function precisely will be discussed. All possible sources of aberrations and image degradation processes will be discussed. In the third part of this chapter, we will introduce the acquisition setup and requirements for compliance between acquisition and deconvolution processes. Typical setups for fixed and living cell observation will be detailed, with key features for optimizing speed and reducing artifacts. In the fourth and last part of this chapter, we will describe, in theoretical terms, the various restoration algorithms commonly used in the field of optical microscopy and will provide results obtained with some of the commercially available packages. We shall conclude by considering the prospects for future solutions (currently under development) aiming to handle more easily the huge amounts of data generated by rapid multi-dimensional living cell microscopy. Designed for use by standard cell biologists and hardware and software engineers and developers, this chapter has been written to provide a clear explanation of the wide-reaching and powerful domain of deconvolution microscopy.

Algorithms↗
PubMed2006

A pooling-deconvolution strategy for biological network elucidation.

The generation of large-scale data sets is a fundamental requirement of systems biology. But despite recent advances, generation of such high-coverage data remains a major challenge. We developed a pooling-deconvolution strategy that can dramatically decrease the effort required. This strategy, pooling with imaginary tags followed by deconvolution (PI-deconvolution), allows the screening of 2(n) probe proteins (baits) in 2 x n pools, with n replicates for each bait. Deconvolution of baits with their binding partners (preys) can be achieved by reading the prey's profile from the 2 x n experiments. We validated this strategy for protein-protein interaction mapping using both proteome microarrays and a yeast two-hybrid array, demonstrating that PI-deconvolution can be used to identify interactions accurately with fewer experiments and better coverage. We also show that PI-deconvolution can be used to identify protein-small molecule interactions inferred from profiling the yeast deletion collection. PI-deconvolution should be applicable to a wide range of library-against-library approaches and can also be used to optimize array designs.

Computational Biology↗
PubMed2003

Blind deconvolution applied to acoustical systems identification with supporting experimental results.

Many acoustical applications require the analysis of a signal that is corrupted by an unknown filtering function. Examples arise in the areas of noise or vibration control, room acoustics, structural vibration analysis, and speech processing. Here, the observed signal can be modeled as the convolution of the desired signal with an unknown system impulse response. Blind deconvolution refers to the process of learning the inverse of this unknown impulse response and applying it to the observed signal to remove the filtering effects. Unlike classical deconvolution, which requires prior knowledge of the impulse response, blind deconvolution requires only reasonable prior estimates of the input signal's statistics. The significant contribution of this work lies in experimental verification of a blind deconvolution algorithm in the context of acoustical system identification. Previous experimental work concerning blind deconvolution in acoustics has been minimal, as previous literature concerning blind deconvolution uses computer simulated data. This paper examines experiments involving three classical acoustic systems: driven pipe, driven pipe with open side branch, and driven pipe with Helmholtz resonator side branch. Experimental results confirm that the deconvolution algorithm learns these systems' inverse impulse responses, and that application of these learned inverses removes the effects of the filters.

Journal Article↗
PubMed1983

Radionuclide angiocardiography: an improved deconvolution technique for improvement after suboptimal bolus injection.

Deconvolution is a mathematical technique used to improve radionuclide angiocardiography after suboptimal injection of radiopharmaceutical. A new deconvolution algorithm designed to be relatively insensitive to the random errors that occur in experimental data was tested. First-pass radionuclide angiocardiography using iridium-191m was performed to quantitate left-to-right shunting in normal dogs and dogs with atrial septal defects. Deconvolution was used to correct for injection shape. Four quantitation techniques were studied (good injection/no deconvolution, good injection/deconvolution, fragmented injection/no deconvolution, fragmented injection/deconvolution). The mean (p less than .001) and standard deviation (p less than .0001) of the fragmented injection/no deconvolution technique were significantly different from the other three techniques, which were not significantly different from each other (mean or standard deviation) at the p = 0.05 level. This deconvolution method made it possible to accurately quantitate left-to-right shunts even with fragmented injections.

Animals↗
PubMed1996

Deconvolution: a novel signal processing approach for determining activation time from fractionated electrograms and detecting infarcted tissue.

BACKGROUND: Two important signal processing applications in electrophysiology are activation mapping and characterization of the tissue substrate from which electrograms are recorded. We hypothesize that a novel signal-processing method that uses deconvolution is more accurate than amplitude, derivative, and manual activation time estimates. We further hypothesize that deconvolution quantifies changes in morphology that detect electrograms recorded from regions of myocardial infarction. METHODS AND RESULTS: To determine the accuracy of activation time estimation, 600 unipolar electrograms were calculated with a detailed computer model using various degrees of coupling heterogeneity to model infarction. Local activation time was defined as the time of peak inward sodium current in the modeled myocyte closest to the electrode. Deconvolution, minimum derivative, and maximum amplitude were calculated. Two experienced electrophysiologists blinded to the computer-determined activation times marked their estimates of activation time. F tests compared the variance of activation time estimation for each method. To evaluate the performance of deconvolution to detect infarction, 380 unipolar electrograms were recorded from 10 dogs with infarcts resulting from ligation of the left anterior descending coronary artery. The amplitude, duration, number of inflections, peak frequency, bandwidth, minimum derivative, and deconvolution were calculated. Metrics were compared by Mann-Whitney rank-sum tests, and receiver operating curves were plotted. CONCLUSIONS: Deconvolution estimated local activation time more accurately than the other metrics (P < .0001). Furthermore, the algorithm quantified changes in morphology (P < .0001) with superior performance, detecting electrograms recorded from regions of myocardial infarction. Thus, deconvolution, which incorporates a priori knowledge of electrogram morphology, shows promise to improve present clinical metrics.

Algorithms↗
PubMed2003

Deconvolution algorithm based on automatic cutoff frequency selection for EPR imaging.

The large line-width associated with electron paramagnetic resonance imaging (EPRI) requires effective algorithms to deconvolve the true spatial profiles of spins from the measured projection data. The commonly used Fourier transform (FT) deconvolution algorithm is easy to implement but suffers from the division-by-zero problem. As a result, a couple of parameters are used to control the deconvolution performance. However, this is inconvenient and the deconvolution results are subject to the experience of the operators. In the present work we examined FT deconvolution for EPRI, and proposed an automatic algorithm to determine the cutoff frequency by calculating the piecewise variance of the division result of the Fourier amplitude spectra. The deconvolution algorithm and the filtered back-projection image reconstruction algorithm were implemented and validated using 3D phantom and in vivo imaging data. It was clearly observed that the image resolution improved after deconvolution with the proposed algorithm.

Algorithms↗
PubMed1983

Deconvolution analysis of radionuclide angiocardiography curves: problems arising from fragmented bolus injections.

Deconvolution analysis of radionuclide angiocardiography time-activity curves (TAC) in the cases of fragmented bolus injections was studied by using a new deconvolution technique based on the maximum a posteriori estimator. This method was first tested by simulation studies which showed its capability for accurate handling of deconvolution both for single and double peak input functions. These simulations have proved this technique to have advantages over a Fourier transform division method used with a low-pass filter. In patient studies, deconvolution of pulmonary TAC by superior vena caval TAC produced poor results in double peak (fragmented) bolus injections, compared with single peak bolus injections (SPBI). This discrepancy seems to be due to the fact that the postulates of linearity and invariance, on which deconvolution analysis is based, do not hold for the 'cardiopulmonary system' which extends from the superior vena cava to the lung. The differences between the model and the real system appear unimportant for SPBI. However, differences become apparent for fragmented bolus injections. Deconvolution analysis should be avoided with this type of input function in this cardiopulmonary system.

Aged↗
PubMed1995

A nonparametric subject-specific population method for deconvolution: I. Description, internal validation, and real data examples.

In a pharmacokinetics context deconvolution facilitates the following: (i) Given data obtained after intravascular (generally intravenous) input one may estimate the disposition function; (ii) given the disposition function and data obtained after extravascular administration one may estimate the extravascular to vascular input rate function. In general if the data can be represented by the convolution of two functions, of which one is unknown, deconvolution allows the estimation of the unknown one. Attention has been given in the past to deconvolution and in particular to its nonparametric variants. However, in a population context (multiple observations collected in each of a group of subjects) the use of nonparametric deconvolution is limited to either analyzing each subject separately or to analyzing the aggregate response from the population without specifying subject-specific characteristics. To our knowledge a fully nonparametric deconvolution method in which subject specificity is explicitly taken into account has not been reported. To do so we use so-called "longitudinal splines." A longitudinal spline is a nonparametric function composed of a template spline, in common to all subjects, and of a distortion spline representing the difference of the subject's function from the template. Using longitudinal splines for input rate or disposition function one obtains a solution to the problem of taking subject specificity into account in a nonparametric deconvolution context. To obtain estimates of longitudinal splines we consider three different methods: (1) parametric nonlinear mixed effect, (2) least squares, and (3) two-stage. Results obtained in one simulated and two real data analyses are shown.

Least-Squares Analysis↗