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PubMed1994

Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners.

Singular value decomposition (SVD) is deeply rooted in the theory of linear algebra, and because of this is not readily understood by a large group of researchers who could profit from its application. In this paper, we discuss the subject on a level that should be understandable to scientists who are not well versed in linear algebra. However, because it is necessary that certain key concepts in linear algebra be appreciated in order to comprehend what is accomplished by SVD, we present the section, 'Bare basics of linear algebra'. This is followed by a discussion of the theory of SVD. Next we present step-by-step examples to illustrate how SVD is applied to deconvolute a titration involving a mixture of three pH indicators. One noiseless case is presented as well as two cases where either a fixed or varying noise level is present. Finally, we discuss additional deconvolutions of mixed spectra based on the use of the pseudoinverse.

Mathematical Computing↗

PubMed1992

Quantal analysis using maximum entropy noise deconvolution.

When applying quantal analysis to synaptic transmission it is often unclear how much of the measured postsynaptic signal fluctuation arises from random sampling and noise rather than from the probabilistic transmitter release process. Unconstrained noise deconvolution methods do not overcome this because they tend to overfit the data, often giving a misleading picture of the underlying process. Instead, maximum entropy deconvolution provides a solution which is the smoothest, or most featureless, distribution that is still compatible with the data, taking noise and sample size into account. A simple way of achieving this is described, together with results of Monte Carlo simulations which show that the features present in the maximum entropy solution usually reflect the process underlying the data and not random sampling or noise.

Algorithms↗

PubMed1987

A FORTRAN program for deconvolution analysis using the matrix algorithm method with special reference to renography.

A FORTRAN IV program is presented for deconvolution analysis using the matrix algorithm method. With the deconvolution technique retention functions are calculated from time-activity curve data representing both kidneys and blood background. The program computes for each kidney the minimum and maximum time of the retention function. It also calculates the initial amplitudes, absolute as well as relative, and the mean transit time of the retention functions. The design of the program allows for optional reviews of intermediate outputs at important stages. It also allows for the plotting of conventional time-activity curves of both kidneys corrected for blood background. Finally, the program plots the retention functions and some of their characteristics.

Algorithms↗

PubMed1986

Simultaneous analysis of multiple fluorescence decay curves by Laplace transforms. Deconvolution with reference or excitation profiles.

The properties and potentials of the noniterative Laplace deconvolution (LAP2) (M. Ameloot and H. Hendrickx, Biophys. J. 44 (1983) 27) are further investigated. It is shown that LAP2 is exact and that no extrapolations have to be calculated or assumed for the data measured in the actual time window if the impulse response function of the investigated system can be described by a sum of exponentials. The formulas for the LAP2 deconvolution against the measured decay of a reference compound instead of the recorded excitation profile are derived. The procedure for the simultaneous analysis of multiple fluorescence decay curves by LAP2 is described in detail. This global analysis allows one to link any decay parameter, is fast and compares favorably with the nonlinear least-squares iterative reconvolution methods. Because of its short computation time the global analysis by LAP2 provides an efficient way to analyze the fluorescence decay surface in terms of decay associated spectra.

Anthracenes↗

PubMed1980

Deconvolution of compound action potentials and nonlinear features of the PST histogram.

Deconvolution of the compound action potential (CAP) with a uniform unit response (UR) results in the compound PST histogram (CPST). After a logarithmic transformation of the CPST, a second deconvolution of the obtained transformed PST histogram (TPST) with an intensity-dependent norm PST histogram (NPST) may be feasible to determine the excitation pattern (E), reflecting the contributions from the individual nerve fibres. The presented model investigations show that, in spite of nonlinearities, a normalized PST histogram can be assumed. Application to recorded CAPs yields excitation patterns almost as predicted by the model.

Action Potentials↗

PubMed2003

Image-adaptive deconvolution for three-dimensional deep biological imaging.

Deconvolution algorithms are widely used in conventional fluorescence microscopy, but they remain difficult to apply to deep imaging systems such as confocal and two-photon microscopy, due to the practical difficulty of measuring the system's point spread function (PSF), especially in biological experiments. Since a separate PSF measurement performed under the design optical conditions of the microscope cannot reproduce the true experimental conditions prevailing in situ, the most natural approach to solve the problem is to extract the PSF from the images themselves. We investigate here the approach of cropping an approximate PSF directly from the images, by exploiting the presence of small structures within the samples under study. This approach turns out to be practical in many cases, allowing significantly better restorations than with a design PSF obtained by imaging fluorescent beads in gel. We demonstrate the advantages of this approach with a number of deconvolution experiments performed both on artificially blurred and noisy test images, and on real confocal images taken within an in vitro preparation of the mouse hearing organ.

Algorithms↗

PubMed1974

X-ray small angle scattering. A new deconvolution method for evaluating electron density distributions from small angle scattering diagrams.

The direct determination of the electron density distributions of multilayered specimens with a small number of unit cells from X-ray small angle scattering experiments via the Q-function method of Hosemann and Bagchi includes the deconvolution of the so-called Q(o)-function, the generalized Patterson function of one unit cell. In this paper a new and direct deconvolution method on the basis of Fourier series is presented which is suitable for one-dimensional centrosymmetrical (or antisymmetrical) density distributions. A FORTRAN-program has been written which has an execution time of ca. 20 s on an UNIVAC 1106-computer. The procedure has been successfully tested on some convolution functions generated by membrane-type electron density distributions.

Computers↗

PubMed1983

Extension of the performance of Laplace deconvolution in the analysis of fluorescence decay curves.

The original Laplace deconvolution of luminescence data, obtained with pulsed systems, is reviewed. The system of equations from which the luminescence parameters can be determined is generalized for the case that describes the relaxation by a sum of exponentials. Artifacts such as scatter and time-shift can be taken into account. A modification of the original method that eliminates the iterative procedure in the estimation of the cut-off correction is suggested. This modified Laplace method is no longer restricted to the cases where the cut-off error is rather small and the exciting flash has a low tail. The possibility of the combination of several discrete experiments in a single Laplace deconvolution, without introducing new parameters or normalization factors, is shown. The merits of this combination method are demonstrated on a time-resolved depolarization experiment.

Luminescence↗

PubMed1995

Deconvolution of C-phycocyanin beta-84 and beta-155 chromophore absorption and fluorescence spectra of cyanobacterium Mastigocladus laminosus.

Absorption and fluorescence spectra of the C-phycocyanin beta-subunit were quantitatively deconvoluted into component spectra of the beta-84 and beta-155 chromophores. The deconvolution procedure was based on a theoretical treatment of polarization properties. Four kinds of spectra (absorption, emission, emission polarization, and excitation polarization) measured on C-phycocyanin isolated from the cyanobacterium Mastigocladus laminosus were used as the experimental data set. Without any assumption of spectral shape, the absorption and fluorescence spectra of both chromophores were unambiguously resolved and their fluorescence quantum yields were evaluated. By combining the spectra of the alpha-subunit, independently measured, with the resolved spectra of the beta-subunit, the fluorescence and fluorescence polarization spectra and the fluorescence quantum yield of the monomer were estimated; they agree with experimental values to within an acceptable error. Further, the matrix of energy transfer rates in the monomer was estimated; it gave a significantly different result (by up to 40%) from previously estimated ones.

Biophysical Phenomena↗

PubMed1985

Quantitative deconvolution of heavily fused chromatographic peaks of biological components using a multi-wavelength UV detector.

Quantitative deconvolution of a chromatographic peak with extremely low UV absorption (less than 0.005 A.U.) is demonstrated for the analysis of an anaesthetic (ketamine) in rabbit serum. One ketamine metabolite, nor-ketamine, was deconvoluted from a completely fused peak in the three-dimensional chromatogram by using a highly sensitive multi-wavelength UV detector. After injection of ketamine, the nor-ketamine level in the serum increased to 3 micrograms/ml, calculated as ketamine, in 120 min.

Animals↗

PubMed2000

Improvement of the lateral resolution of finite-size hydrophones by deconvolution

In various fields of ultrasound applications, frequencies well above 10 MHz are used. As a consequence of this, ultrasound sensors, especially the piezoelectric hydrophones presently available which are used for the characterization of the respective fields, can no longer be considered as point receivers. By means of numerical deconvolution, the adverse averaging effect caused by the finite sensor size can be revoked. The efficiency of the deconvolution process is dealt with for both numerical simulations and experimental investigations. Best results were obtained using a reconstruction filter consisting of a combination of a Wiener filter, a pruning filter and an additional low-pass filter.

Journal Article↗

PubMed2001

[Study of renal transplant by deconvoluted renogram with 99m Tc-mercaptoacetyltriglycine (Mag3)].

AIM: To evaluate the usefulness of the 99mTc-MAG3 renogram deconvolution and its derived parameters in kidney graft function monitoring. MATERIAL AND METHOD: 221 renograms were studied: 64 were diagnosed as functioning graft (FG), 37 as functioning graft with elevated serum creatinine (FG2), 59 as acute tubular necrosis (ATN), 30 as acute rejection (AR), 20 as urinary tract obstruction (OBS) and 11 as cyclosporine nephrotoxicity (TNX). The parameters evaluated were: maximal activity of conventional renogram and mean transit time (MTT), time to reach 20% (T20) and 80% (T80) of the height of the RRF and initial uptake (IU) from the deconvoluted renal retention function (RRF). RESULTS: MTT and T20 were significantly longer and IU significantly lower in non-functioning grafts. However, MTT and T20 became shorter than in FG when graft function is severely impaired. CONCLUSION: IU, MTT and T20 are more useful than maxim activity of renogram in monitoring kidney graft function and in evaluating renal dysfunction severity. IU is a very sensitive and early parameter.

Adult↗

PubMed2001

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.

Journal Article↗

PubMed2003

Deconvolution of electron diffraction patterns of amorphous materials formed with convergent beam.

To perform reduced density function (G(r)) analysis on electron diffraction patterns of amorphous materials formed with convergent beams, the effects of convergence must be removed from the diffraction data. Assuming electrons incident upon the sample in different directions are incoherent, this can be done using deconvolution (Ultramicroscopy 76 (1999) 115). In this letter we show that the combination of an energy filtering transmission electron microscope with an image plate, increases the accuracy with which diffraction data can be measured and, subsequently, the accuracy of the deconvolution.

Algorithms↗

PubMed2003

Rapid MR imaging by sensitivity profile indexing and deconvolution reconstruction (SPID).

A new parallel MR imaging technique, which uses localized information from the elements of a multi-coil array to accelerate imaging, is described. The technique offers an alternative reconstruction approach to currently available techniques (e.g., SMASH and SENSE). Following a partial k-space data acquisition, image reconstruction in this approach proceeds in two steps: first, fitting the measured coil sensitivities to a set of partially localized target functions, a blurred intermediate image of the studied object is produced. Blurring is obtained in a systematic manner, forming images of the studied object convolved with a known convolution kernel. Full spatial resolution is then recovered by deconvolution of the blurred images with the known kernel function. The technique offers flexibility in the arrangement of the acquired signal data k-lines, and a mechanism for controlling reconstruction quality through the convolution the deconvolution procedure. The technique was validated in phantom and in vivo imaging experiments demonstrating high time reduction factors.

Brain↗

PubMed1997

Rapid deconvolution of NMR powder spectra by weighted fast Fourier transformation.

The resolution enhancement conferred by numerical deconvolution of powder pattern spectra to spectra characteristic of a single alignment greatly simplifies solid state NMR spectral analysis. This is especially beneficial when the spectrum is a superposition of signals from multiple environments or sites of labelling. We have developed an innovative method to deconvolute (depake) spectra governed by axially symmetric second rank tensor interactions which possess a P2(cos theta) dependence upon orientation, where theta is the angle between the symmetry axis and the external magnetic field. Our approach differs substantially from previously published procedures which are iterative or require matrix inversion and, hence, are slow. The new method, instead, utilizes weighting functions in time and frequency domains to facilitate a rapidly executed solution based upon fast Fourier transformation (FFT). Its efficacy is demonstrated with 2H and 31P NMR data for model membranes.

Fourier Analysis↗

PubMed2003

Handling of computational in vitro/in vivo correlation problems by Microsoft Excel: III. Convolution and deconvolution.

Convolution and deconvolution are the classical in-vitro-in-vivo correlation tools to describe the relationship between input and weighting/response in a linear system, where input represents the drug release in vitro, weighting/response any body response in vivo. While functional treatment, e.g. in terms of polyexponential or Weibull distribution, is more appropriate for general survey or prediction, numerical algorithms are useful for treating actual experimental data. Deconvolution is not considered an algorithm by its own, but the inversion of a corresponding convolution. MS Excel is shown to be a useful tool for all these applications.

Algorithms↗

PubMedDate not supplied

Band deconvolution analysis of the absorption and magnetic circular dichroism spectral data of a planar phthalocyanine dimer.

The electronic absorption and magnetic circular dichroism spectral data of a phthalocyanine dicopper complex that is deduced to be very planar and to share a common benzene ring have been studied by band deconvolution analysis. The results were compared with those of the molecular orbital (MO) calculations within the framework of the Pariser-Parr-Pople (PPP) approximation. The results of the band deconvolution analysis are in good agreement with those of the PPP calculations, allowing many bands to be reasonably assigned on the basis of the MO calculations. The validity of the PPP method for the MO calculation of large molecules is also emphasized.

Circular Dichroism↗