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

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248301
Author(s):  
Daniel U. Campos-Delgado ◽  
Omar Gutierrez-Navarro ◽  
Ricardo Salinas-Martinez ◽  
Elvis Duran ◽  
Aldo R. Mejia-Rodriguez ◽  
...  
Keyword(s):  
Least Squares ◽  
Fluorescent Dyes ◽  
Blind Deconvolution ◽  
Global Perspective ◽  
Free Form ◽  
Fluorescence Lifetime Imaging ◽  
Exponential Functions ◽  
Spatial Point ◽  
Laguerre Basis ◽  
Deconvolution Techniques

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.

scholarly journals Fluorescence background discrimination by prebleaching.

1979 ◽  
Vol 27 (1) ◽  
pp. 96-101 ◽  
Author(s):  
T Hirschfeld
Keyword(s):  
Fluorescent Dyes ◽  
Fluorescence Decay ◽  
Free Form ◽  
Alternative Procedure ◽  
Background Fluorescence ◽  
Decay Lifetime ◽  
Fluorescent Molecules ◽  
Background Contrast

A number of electrooptical techniques are described that discriminate against background fluorescence in biologic staining, whether from sample background or unbound excess stain. These techniques are based on the fluorescent decay lifetime difference between bound stain and the sample background or between the bound stain its free form. The fluorescence decay lifetimes may be measured either directly or in a combination gated photometry scheme to substantially enhance the sample background contrast. An alternative procedure uses the photochemical bleaching of fluorescent dyes under intense exposure to time discriminate with higher selectivity, sensitivity and in a more convenient fashion between diverse fluorescent molecules.

NURBS Surface Reconstruction From a Large Set of Image and World Data Points

1993 ◽  
Author(s):  
Vassilios E. Theodoracatos ◽  
Vasudeva Bobba
Keyword(s):  
Least Squares ◽  
Vision System ◽  
Physical Object ◽  
Free Form ◽  
Approximation Technique ◽  
Global Coordinate System ◽  
Large Set ◽  
Affine Invariant ◽  
Nurbs Surface ◽  
Data Points

Abstract In this paper an approach is presented for the generation of a NURBS (Non-Uniform Rational B-splines) surface from a large set of 3D data points. The main advantage of NURBS surface representation is the ability to analytically describe both, precise quadratic primitives and free-form curves and surfaces. An existing three dimensional laser-based vision system is used to obtain the spatial point coordinates of an object surface with respect to a global coordinate system. The least-squares approximation technique is applied in both the image and world space of the digitized physical object to calculate the homogeneous vector and the control net of the NURBS surface. A new non-uniform knot vectorization process is developed based on five data parametrization techniques including four existing techniques, viz., uniform, chord length, centripetal, and affine invariant angle and a new technique based on surface area developed in this study. Least-squares error distribution and surface interrogation are used to evaluate the quality of surface fairness for a minimum number of NURBS control points.

Automatic blind deconvolution with Toeplitz-structured sparse total least squares

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. V345-V357 ◽  
Author(s):  
Nasser Kazemi
Keyword(s):  
Least Squares ◽  
Cross Validation ◽  
Blind Deconvolution ◽  
Real Data ◽  
Total Least Squares ◽  
Data Matrix ◽  
Seismic Survey ◽  
Structural Constraints ◽  
Generalized Cross Validation ◽  
Free Data

Given the noise-corrupted seismic recordings, blind deconvolution simultaneously solves for the reflectivity series and the wavelet. Blind deconvolution can be formulated as a fully perturbed linear regression model and solved by the total least-squares (TLS) algorithm. However, this algorithm performs poorly when the data matrix is a structured matrix and ill-conditioned. In blind deconvolution, the data matrix has a Toeplitz structure and is ill-conditioned. Accordingly, we develop a fully automatic single-channel blind-deconvolution algorithm to improve the performance of the TLS method. The proposed algorithm, called Toeplitz-structured sparse TLS, has no assumptions about the phase of the wavelet. However, it assumes that the reflectivity series is sparse. In addition, to reduce the model space and the number of unknowns, the algorithm benefits from the structural constraints on the data matrix. Our algorithm is an alternating minimization method and uses a generalized cross validation function to define the optimum regularization parameter automatically. Because the generalized cross validation function does not require any prior information about the noise level of the data, our approach is suitable for real-world applications. We validate the proposed technique using synthetic examples. In noise-free data, we achieve a near-optimal recovery of the wavelet and the reflectivity series. For noise-corrupted data with a moderate signal-to-noise ratio (S/N), we found that the algorithm successfully accounts for the noise in its model, resulting in a satisfactory performance. However, the results deteriorate as the S/N and the sparsity level of the data are decreased. We also successfully apply the algorithm to real data. The real-data examples come from 2D and 3D data sets of the Teapot Dome seismic survey.

scholarly journals Exponential Polynomial Fitting for Fibre Spectrum CCD Profiles

2010 ◽  
Vol 27 (3) ◽  
pp. 290-295 ◽  
Author(s):  
Zhangqin Zhu ◽  
Jia Zhu ◽  
Hanqin Qin ◽  
Chong Wang ◽  
Zhongfu Ye
Keyword(s):  
Least Squares ◽  
Spatial Orientation ◽  
Least Squares Method ◽  
Exponential Polynomial ◽  
Exponential Functions ◽  
Polynomial Fitting ◽  
Gaussian Functions ◽  
Profile Fitting ◽  
Fitting Method

AbstractA fibre spectrum profile fitting method based on the least-squares method is presented in this article. For each spectrum of one fibre in spatial orientation, two exponential functions are employed to approximate the profile. Experiments are performed with both simulated profiles and observed profiles to demonstrate the effectiveness of the algorithm. Specially, the proposed method has a better performance for profiles that are asymmetric or composed of multi-Gaussian functions.

Fitting of radioactivity data to exponential functions by weighted least squares analysis

1984 ◽  
Vol 9 (4) ◽  
Author(s):  
P. Dimitriou ◽  
J. Giamouris ◽  
A. Kasfiki ◽  
T. Karpathios ◽  
S.E. Antipas
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Exponential Functions

Blind Deconvolution of SEM Images

2007 ◽  
Author(s):  
William E. Vanderlinde ◽  
James N. Caron
Keyword(s):  
Cross Section ◽  
Integrated Circuit ◽  
Blind Deconvolution ◽  
Signal To Noise Ratio ◽  
Image Resolution ◽  
Reference Standard ◽  
Signal To Noise ◽  
Sem Images ◽  
Resolution Improvement ◽  
Deconvolution Techniques

Abstract Blind deconvolution techniques were used to enhance scanning electron microscope (SEM) images in the range of 200,000x to 500,000x magnification. Typical SEM samples were imaged including a gold island reference standard, a plasma delayered integrated circuit, and an integrated circuit cross section. Image resolution improvement up to 40% was observed. However, it was necessary to use 16-bit TIFF images with greater than 120:1 signal to noise ratio, which required 10 minute frame times.

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