A novel algorithm for the adaptation of the pole of Laguerre filters

Published versio

Optimizing Laguerre expansion based deconvolution methods for analysing bi-exponential fluorescence lifetime images

Fast deconvolution is an essential step to calibrate instrument responses in big fluorescence lifetime imaging microscopy (FLIM) image analysis. This paper examined a computationally effective least squares deconvolution method based on Laguerre expansion (LSD-LE), recently developed for clinical diagnosis applications, and proposed new criteria for selecting Laguerre basis functions (LBFs) without considering the mutual orthonormalities between LBFs. Compared with the previously reported LSD-LE, the improved LSD-LE allows to use a higher laser repetition rate, reducing the acquisition time per measurement. Moreover, we extended it, for the first time, to analyze bi-exponential fluorescence decays for more general FLIM-FRET applications. The proposed method was tested on both synthesized bi-exponential and realistic FLIM data for studying the endocytosis of gold nanorods in Hek293 cells. Compared with the previously reported constrained LSD-LE, it shows promising results

Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems

This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO) systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples

New Laguerre Filter Approximators to the Grünwald-Letnikov Fractional Difference

This paper presents a series of new results in modeling of the Grünwald-Letnikov discrete-time fractional difference by means of discrete-time Laguerre filers. The introduced Laguerre-based difference (LD) and combined fractional/Laguerre-based difference (CFLD) are shown to perfectly approximate its fractional difference original, for fractional order . This paper is culminated with the presentation of finite (combined) fractional/Laguerre-based difference (FFLD), whose excellent approximation performance is illustrated in simulation examples