Denoising Two-Photon Calcium Imaging Data

Two-photon calcium imaging is now an important tool for in vivo imaging of biological systems. By enabling neuronal population imaging with subcellular resolution, this modality offers an approach for gaining a fundamental understanding of brain anatomy and physiology. Proper analysis of calcium imaging data requires denoising, that is separating the signal from complex physiological noise. To analyze two-photon brain imaging data, we present a signal plus colored noise model in which the signal is represented as harmonic regression and the correlated noise is represented as an order autoregressive process. We provide an efficient cyclic descent algorithm to compute approximate maximum likelihood parameter estimates by combing a weighted least-squares procedure with the Burg algorithm. We use Akaike information criterion to guide selection of the harmonic regression and the autoregressive model orders. Our flexible yet parsimonious modeling approach reliably separates stimulus-evoked fluorescence response from background activity and noise, assesses goodness of fit, and estimates confidence intervals and signal-to-noise ratio. This refined separation leads to appreciably enhanced image contrast for individual cells including clear delineation of subcellular details and network activity. The application of our approach to in vivo imaging data recorded in the ferret primary visual cortex demonstrates that our method yields substantially denoised signal estimates. We also provide a general Volterra series framework for deriving this and other signal plus correlated noise models for imaging. This approach to analyzing two-photon calcium imaging data may be readily adapted to other computational biology problems which apply correlated noise models.National Institutes of Health (U.S.) (DP1 OD003646-01)National Institutes of Health (U.S.) (R01EB006385-01)National Institutes of Health (U.S.) (EY07023)National Institutes of Health (U.S.) (EY017098

Efficient Multidimensional Regularization for Volterra Series Estimation

This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. To avoid the excessive memory needs in case of long measurements or large number of estimated parameters, a practical gradient-based estimation method is also provided, leading to the same numerical results as the proposed Volterra estimation method. Moreover, the transient effects in the simulated output are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Combining the proposed methodologies, the nonparametric Volterra models of the cascaded water tanks benchmark are presented in this paper. The results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series with and without transient removal are compared and studied. It is clear that the obtained models capture the system dynamics when tested on a validation dataset, and their performance is comparable with the white-box (physical) models

Whiteness and its transformations

The recent use of higher order statistics in signal processing allows us to extend the concept of' whiteness so far limited to the second order . This extension leads to define new kinds of white noises whose relationships are investigated. So, we might ask whether it is possible, using linear or non linear operations, to whiten a random process to an order higher than the second or at least to preserve its whiteness . Particularly we show that it is impossible to whiten with a linfeilatre,r, to an order higher thon the second and that the preservation of whiteness dépends on the gaussian property.L'usage récent des statistiques d'ordre supérieur en traitement du signal permet d'étendre le concept de blancheur, jusqu'alors limité à l'ordre deux . Cette extension conduit à définir de nouveaux types de bruits blancs dont les liens sont examinés en détail . On peut alors se demander si, au moyen d'opérations linéaires ou non linéaires, il est possible de blanchir à un ordre supérieur à deux un signal aléatoire ou tout au moins d'en conserver la blancheur . En particulier, on montre qu'il est impossible par filtrage linéaire de blanchir à un ordre supérieur à deux et que la conservation de la blancheur est liée au caractère gaussien

Hydrothermal modeling for optimum temperature control : an estimation-theoretic approach

Originally presented as part of the first author's thesis, (Environmental Engineer) in the M.I.T. Dept. of Civil EngineeringA short-term temperature forecasting (STF) system is proposed to predict and control plant intake and discharge temperatures at Salem Harbor Electric Generating Station. It is desired to minimize receiving-water (i.e., intake-water) temperatures during peak power demand periods, in order to minimize the cost of complying with the maximum discharge water temperature limit. This study addresses the hydrothermal modeling requirements of an STF system. An important element of an STF system is a predictive model of plant intake water temperatures. For application to Salem Harbor Station, strict model performance criteria exist, defining a model development problem: Develop a simple model to predict plant intake water temperatures 24 hours ahead, predicting daily peak intake temperatures within 10F on 90% of the days, and using only existing measurements. An estimation-theoretic approach to model development is used, which quantifies and minimizes the uncertainties in the model. The approach employs optimal filtering and full-information maximum- likelihood (FIML) estimation to obtain optimum parameter estimates. A two-basin, two-layer hydrothermal model of Salem Harbor is developed. The model computes hourly intake temperatures, incorporating tidal flushing, stratification, surface heat exchange, and wind advection of the plume. Twenty-eight model parameters and five noise statistics are estimated from intake-temperature data. Preliminary best-fit parameter values are obtained subjectively, followed by FIML parameter estimation using a data base of 96 hourly measurements (7/29 - 8/2/74). The model is tested for 106 days (5/17- 9/20/74) and various performance measures are computed, including sum- of-squares of measurement residuals (S), whiteness (P), percent of daily peak temperature predictions within 10F of actual (T), and others. Visual inspection of 24-hour intake temperature predictions shows that the two-basin, two-layer model performs qualitatively well. However, the model fails statistical tests on S and P, indicating structural weaknesses. FIML estimation yields physically unrealistic values for certain parameters, probably compensating for inadequate model structure. Despite structural flaws in the two-basin, two-layer model, FIML estimation yields parameters with consistently better performance than the preliminary estimates (by a small amount). It is concluded that the two-basin, two-layer model is presently unsuitable for STF use, largely due to structural weaknesses. Possible corrections are suggested; however, a statistical model of hourly temperatures appears to offer greater potential accuracy than physically-derived models. FIML parameter estimation is shown to be useful for water quality model development on a real system, particularly after subjective model development has been exhausted.New England Power Company under the MIT Energy Laboratory Electric Power Progra

Figure-ground responsive fields of monkey V4 neurons estimated from natural image patches

Neurons in visual area V4 modulate their responses depending on the figure-ground (FG) organization in natural images containing a variety of shapes and textures. To clarify whether the responses depend on the extents of the figure and ground regions in and around the classical receptive fields (CRFs) of the neurons, we estimated the spatial extent of local figure and ground regions that evoked FG-dependent responses (RF-FGs) in natural images and their variants. Specifically, we applied the framework of spike triggered averaging (STA) to the combinations of neural responses and human-marked segmentation images (FG labels) that represent the extents of the figure and ground regions in the corresponding natural image stimuli. FG labels were weighted by the spike counts in response to the corresponding stimuli and averaged over. The bias due to the nonuniformity of FG labels was compensated by subtracting the ensemble average of FG labels from the weighted average. Approximately 50% of the neurons showed effective RF-FGs, and a large number exhibited structures that were similar to those observed in virtual neurons with ideal FG-dependent responses. The structures of the RF-FGs exhibited a subregion responsive to a preferred side (figure or ground) around the CRF center and a subregion responsive to a non-preferred side in the surroundings. The extents of the subregions responsive to figure were smaller than those responsive to ground in agreement with the Gestalt rule. We also estimated RF-FG by an adaptive filtering (AF) method, which does not require spherical symmetry (whiteness) in stimuli. RF-FGs estimated by AF and STA exhibited similar structures, supporting the veridicality of the proposed STA. To estimate the contribution of nonlinear processing in addition to linear processing, we estimated nonlinear RF-FGs based on the framework of spike triggered covariance (STC). The analyses of the models based on STA and STC did not show inconsiderable contribution of nonlinearity, suggesting spatial variance of FG regions. The results lead to an understanding of the neural responses that underlie the segregation of figures and the construction of surfaces in intermediate-level visual areas.journal articl

Experimental characterization of the time correlation properties of nonlinear interference noise

We demonstrate a method for experimentally characterizing the time-evolution statistics of nonlinear interference noise (NLIN). Strong temporal correlations, beyond the phase-noise NLIN component, are measured experimentally, for the first time. The ability of measuring these correlation is imperative for designing effective NLIN mitigation schemes

Advanced Geoscience Remote Sensing

Nowadays, advanced remote sensing technology plays tremendous roles to build a quantitative and comprehensive understanding of how the Earth system operates. The advanced remote sensing technology is also used widely to monitor and survey the natural disasters and man-made pollution. Besides, telecommunication is considered as precise advanced remote sensing technology tool. Indeed precise usages of remote sensing and telecommunication without a comprehensive understanding of mathematics and physics. This book has three parts (i) microwave remote sensing applications, (ii) nuclear, geophysics and telecommunication; and (iii) environment remote sensing investigations