On deconvolution methods

Several methods for solving efficiently the one-dimensional deconvolution problem are proposed. The problem is to solve the

     

High-order cumulant-based blind deconvolution of Raman spectra

The spectra recorded by a dispersion spectrophotometer are usually distorted by the response function of the instrument. To improve the resolving power, double or triple cascade spectrophotometers with narrow slits have been employed, but the total flux of the radiation available decreases accordingly, resulting in a low signal-to-noise ratio and a longer measuring time. The actual spectra can be restored approximately by mathematically removing the effects of the measuring instruments. Based on the Shalvi-Weinstein criterion, a (6, 2)-order normalized cumulant-based blind deconvolution algorithm for Raman spectral data is proposed. The actual spectral data and the unit-impulse response of the measuring instruments can be estimated simultaneously. By conducting experiments on real Raman spectra of some organic compounds, it is shown that this algorithm has a robust performance and fast convergence behavior and can improve the resolving power and correct the relative intensity distortion considerably.     

Higher order spectra based deconvolution of ultrasound images

We address the problem of improving the spatial resolution of ulrasound images through blind deconvolution. The ultrasound image formation process in the RF domain can be expressed as a spatio-temporal convolution between the tissue response and the ultrasonic system response, plus additive noise. Convolutional components of the dispersive attenuation and aberrations introduced by propagating through the object being imaged are also incorporated in the ultrasonic system response. Our goal is to identify and remove the convolutional distortion in order to reconstruct the tissue response, thus enhancing the diagnostic quality of the ultrasonic image. Under the assumption of an independent, identically distributed, zero-mean, non-Gaussian tissue response, we were able to estimate distortion kernels using bicepstrum operations on RF data. Separate 1D distortion kernels were estimated corresponding to axial and lateral image lines and used in the deconvolution process. The estimated axial kernels showed similarities to the experimentally measured pulse-echo wavelet of the imaging system. Deconvolution results from B-scan images obtained with clinical imaging equipment showed a 2.5-5.2 times gain in lateral resolution, where the definition of the resolution has been based on the width of the autocovariance function of the image. The gain in axial resolution was found to be between 1.5 and 1.9     

Deconvolution of Lorentzian broadened spectra part I: Direct deconvolution

A method is discussed of deconvolution of Lorentzian broadened experimental spectra directly in the “time” domain, that is, in the domain of the independent spectroscopic variable. The method consist in a numerical convolution of the spectrum with a deconvoluting function which is calculated in conformity with an theoretical analysis of the sampled form of the input and output spectra and their Fourier transforms. An almost complete elimination of the distortions and complete deconvolution degree are achieved. The restrictions imposed by the noise enhancement are estimated.     

Spatial characterization of laser-induced plasmas by deconvolution of spatially resolved spectra

The spatial characterization of laser-induced plasmas, including their temperature, electron density, and relative atom density, has been carried out by emission spectroscopy. The plasmas were generated with iron samples in air and argon at atmospheric pressure. An imaging spectrometer equipped with an intensified CCD detector procured spectra with spatial resolution. The plasma characterization was made at three temporal gates (2-3, 5-6, and 9-11 micros) to permit the plasma's evolution to be studied. A deconvolution procedure was developed to transform the measured intensity, integrated along the line of sight, into the radial distribution of emissivity. Temperature and electron density distributions were obtained under the assumption of local thermodynamic equilibrium and Stark broadening of the emission lines. The relative atom density distributions in the plasma of the Fe atoms arising from the sample and of the Ar atoms arising from the ambient gas were determined and evidenced an important interaction between the plasma and the surrounding atmosphere.     

Application of superconductivity in the controlled thermonuclear research program

Applications of superconductivity will be needed in each of the three magnetic confinement systems being developed in the AEC controlled thermonuclear research program. Fusion plasmas must be confined by magnetic fields instead of solid walls. The tokamak and magnetic mirror confinement systems will need superconducting magnets to produce the confining magnetic field. The theta-pinch confinement system will need superconducting energy storage coils and homopolar machines to provide energy for pulsed magnetic fields. The AEC is supporting developments for these three systems but it is not yet known which magnetic confinement systems will be used in fusion power reactors. The technology problems associated with these applications of superconductivity are described in the paper.     

Comparison of direct blind deconvolution methods for motion-blurred images

Direct methods for restoration of images blurred by motion are analyzed and compared. The term direct means that the considered methods are performed in a one-step fashion without any iterative technique. The blurring point-spread function is assumed to be unknown, and therefore the image restoration process is called blind deconvolution. What is believed to be a new direct method, here called the whitening method, was recently developed. This method and other existing direct methods such as the homomorphic and the cepstral techniques are studied and compared for a variety of motion types. Various criteria such as quality of restoration, sensitivity to noise, and computation requirements are considered. It appears that the recently developed method shows some improvements over other older methods. The research presented here clarifies the differences among the direct methods and offers an experimental basis for choosing which blind deconvolution method to use. In addition, some improvements on the methods are suggested.     

Structural characterization of C-S-H gel through an improved deconvolution analysis of NMR spectra

The structure of the C-S-H gel in hydrated cement samples prepared with and without the addition of silica nanoparticles is studied in this work through the deconvolution of ²⁹Si MAS-NMR spectra. X-ray diffraction and energy dispersive X-ray microanalysis are also considered for the analysis. A method with improved sensitivity and reliability is proposed for the deconvolution of the spectra into elementary components involving a good fitting of both the spectral curve and its second derivative. The increased sensitivity of the deconvolution proves to be especially interesting for the characterization of low concentration components in the NMR spectra, and the high reliability allows properly defining the effect of nanosilica addition on the C-S-H gel nanostructure. In fact, the addition of nanosilica is found to produce a pozzolanic reaction that results in an increase of the mean silicate chain length and an enhancement of the aluminum incorporation into the C-S-H gel phase.     

A real-time instantaneous frequency estimator for rotating magneticislands in a tokamak thermonuclear plasma

The evolution of rotating magnetic islands is a limit for the regime of stable operation in tokamak plasma confinement systems for nuclear fusion research, working close to operating conditions required in a future reactor. It is possible to counteract the growth of the magnetic islands by applying an external magnetic field, provided that the rotating speed of the magnetic islands is measured. The rotating speed can be determined from the measurement of the frequency of the electromotive force induced on a set of magnetic detectors. This paper proposes a digital method for the estimation of this frequency. The results of some laboratory tests performed on a prototype device of the estimator are reported     

Deconvolution of Lorentzian broadened spectra part II: Stepped deconvolution and smooting filtration

A new method of numerical time domain deconvolution of Lorentzian broadened spectra is proposed. The new algorithm consist in convolution with a deconvoluting function accomplished by a preset step, so that an undersampling of the input spectra is performed. The main advantage of this method is the considerable reduction of the noise enhancement. A theoretical analysis of the possibilities, the restrictions and the errors is done. The results are confirmed by test investigations and by experimental examples.     

Charge ratio analysis method: approach for the deconvolution of electrospray mass spectra

A new method to interpret electrospray mass spectral data based on calculating the ratio of mass-to-charge (m/z) values of multiply charged ions is described. The mass-to-charge ratios of any two multiply charged ions corresponding to a single compound are unique numbers that enable the charge states for each ion to be unequivocally identified. The multiply charged ions in electrospray mass spectra originate from the addition or abstraction of protons, cations, or anions to and from a compound under analysis. In contrast to existing deconvolution processes, the charge ratio analysis method (CRAM), identifies the charge states of multiply charged ions without any prior knowledge of the nature of the charge-carrying species. In the case of high-resolution electrospray mass spectral data, in which multiply charged ions are resolved to their isotopic components, the CRAM is capable of correlating the isotope peaks of different multiply charged ions that share the same isotopic composition. This relative ratio method is illustrated here for electrospray mass spectral data of lysozyme and oxidized ubiquitin recorded at low- to high-mass resolution on quadrupole ion trap and Fourier transform ion cyclotron mass spectrometers, and theoretical data for the protein calmodulin based upon a reported spectrum recorded on the latter.     

Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra: reply to comment

Partial correction in adaptive optics (AO) is well understood now. This partial correction is due to the limitations of the AO system performance, which leaves residual phase fluctuations in the instrument pupil. Knowledge of these residuals allows the optical transfer function (OTF) of the high-angular-resolution imaging system to be estimated accurately. Therefore, light scattering by aerosols cannot be invoked to justify the shape of an AO partial-correction OTF in astronomical conditions. The light scattering does not modify the high-angular-resolution OTF but merely contributes to a slight increase of the sky background.     

一种改进的盲解卷积算法在轴承声学诊断中的应用

针对时域盲解卷积算法滤波器长度估计困难的缺点,提出一种基于遗传算法优化的改进算法。该算法利用遗传算法搜索最佳时延,解决了盲解卷积结果不确定问题,并改进了信号分量的聚类指标,采用峭度作为独立分量间距离测度,提高了信号分量聚类的准确性,获得了可靠的估计信号。计算机仿真和实际环境中故障轴承声信号提取实验验证了该算法的有效性。     

Automatic deconvolution of isotope-resolved mass spectra using variable selection and quantized peptide mass distribution

We present an algorithm for the deconvolution of isotope-resolved mass spectra of complex peptide mixtures where peaks and isotope series often overlap. The algorithm formulates the problem of mass spectrum deconvolution as a classical statistical problem of variable selection, which aims to interpret the spectrum with the least number of peptides. The LASSO method is used to perform automatic variable selection. The algorithm also makes use of the quantized distribution of peptide masses in the NCBInr database after in silico trypsin digestion as filters to aid the deconvolution process. Errors in the expected isotope pattern are accounted for to avoid spurious isotope series. The effectiveness of the algorithm is demonstrated with annotated ESI spectrum of known peptides for which the peaks and isotope series are highly overlapping. The algorithm successfully finds all correct masses in the experimental spectrum, except for one spectrum where an additional refinement procedure is required to obtain the correct results. Our results compare favorably to those from a widely used commercial program.     

Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra

Adaptive optics systems provide a real-time compensation for atmospheric turbulence. However, the correction is often only partial, and a deconvolution is required for reaching the diffraction limit. The need for a regularized deconvolution is discussed, and such a deconvolution technique is presented. This technique incorporates a positivity constraint and some a priori knowledge of the object (an estimate of its local mean and a model for its power spectral density). This method is then extended to the case of an unknown point-spread function, still taking advantage of similar a priori information on the point-spread function. Deconvolution results are presented for both simulated and experimental data.     

Stress-induced plasma volume change determined using plasma FT-IR spectra

Our purpose was to determine the plasma-volume (PV) change induced by a physical stress independent of the metabolic events that may interfere with physiological fluid shifts in to and out of the intravascular space. Our methods included using 178 exercise tests of varying duration and intensity for determination of PV change during exercise. Plasma Fourier transform infrared (FT-IR) spectra were used to compare hematocrit change to the total spectral area (4000-500 cm(-1)) and the protein and albumin concentration changes induced by exercise. Our results showed that exercise induced a raise in protein (+10.4 +/- 3.1%) and albumin (+9.8 +/- 3.3%) concentrations that significantly correlated with PV change (14.1 +/- 5.2% of plasma volume; P = 0.05 with protein and albumin concentration changes). However, evolution of the total spectral area obtained from rest-plasma (524 +/- 21 a.u.) and exercise-plasma (611 +/- 26 a.u.; +14.1 +/- 4.8%) FT-IR spectra showed a higher correlation level with PV change (r = 0.98; P = 0.005; S(x/y) = 1.26 a.u.). It is our conclusion that although exercise-induced changes in protein and albumin concentrations were found to correlate with PV change, the use of the total spectral area of the plasma FT-IR spectra allowed a more precise measurement of PV change.     

Development of 2D band-target entropy minimization and application to the deconvolution of multicomponent 2D nuclear magnetic resonance spectra

Spectral reconstruction from multicomponent spectroscopic data is the frequent primary goal in chemical system identification and exploratory chemometric studies. Various methods and techniques have been reported in the literature. However, few algorithms/methods have been devised for spectral recovery without the use of any a priori information. In the present studies, a higher dimensional entropy minimization method based on the BTEM algorithm (Widjaja, E.; Li, C.; Garland, M. Organometallics 2002, 21, 1991-1997.) and related techniques were extended to large-scale arrays, namely, 2D NMR spectroscopy. The performance of this novel method had been successfully verified on various real experimental mixture spectra from a series of randomized 2D NMR mixtures (COSY NMR and HSQC NMR). With the new algorithm and raw multicomponent NMR alone, it was possible to reconstruct the pure spectroscopic patterns and calculate the relative concentration of each species without recourse to any libraries or any other a priori information. The potential advantages of this novel algorithm and its implications for general chemical system identification of unknown mixtures are discussed.     

Maximum entropy deconvolution of infrared spectra: use of a novel entropy expression without sign restriction

Absorbance and difference infrared spectra are often acquired aiming to characterize protein structure and structural changes of proteins upon ligand binding, as well as for many other chemical and biochemical studies. Their analysis requires as a first step the identification of the component bands (number, position, and area) and as a second step their assignment. The first step of the analysis is challenged by the habitually strong band overlap in infrared spectra. Therefore, it is useful to make use of a mathematical method able to narrow the component bands to the extent to eliminate, or at least reduce, the band overlap. Additionally, to be of general applicability this method should permit negative values for the solution. We present a maximum entropy deconvolution approach for the band-narrowing of absorbance and difference spectra showing the required characteristics, which uses the generalized negative Burg-entropy (Itakura-Saito discrepancy) generalized for difference spectra. We present results on synthetic noisy absorbance and difference spectra, as well as on experimental infrared spectra from the membrane protein bacteriorhodopsin.     

Application of deconvolution to the analysis of univalent ion-exchange isotherms in zeolites X and Y

A numerical method of regularization has been used to effect the deconvolution of isotherms obtained from the literature describing the exchange of Li⁺ K⁺, and Rb⁺ into the synthetic faujasites NaX and NaY. The obtained selectivity coefficient distributions fit the univalent isotherms used for deconvolution. The relative number of K⁺ cations undergoing exchange with the obtained selectivity coefficients has been compared with published cation-site populations in K-X and K-Y, determined crystallographically.     

Iterative statistical approach to blind image deconvolution

Image deblurring has long been modeled as a deconvolution problem. In the literature, the point-spread function (PSF) is often assumed to be known exactly. However, in practical situations such as image acquisition in cameras, we may have incomplete knowledge of the PSF. This deblurring problem is referred to as blind deconvolution. We employ a statistical point of view of the data and use a modified maximum a posteriori approach to identify the most probable object and blur given the observed image. To facilitate computation we use an iterative method, which is an extension of the traditional expectation-maximization method, instead of direct optimization. We derive separate formulas for the updates of the estimates in each iteration to enhance the deconvolution results, which are based on the specific nature of our a priori knowledge available about the object and the blur.