Heimo Ihalainen

Tutorial on Univariate Autoregressive Spectral Analysis

In the present paper, the theoretical basis of autoregressive (AR) modelling in spectral analysis is explained in simple terms. Spectral analysis gives information about the frequency content and sources of variation in a time series. The AR method is an alternative to discrete Fourier transform, and the method of choice for high-resolution spectral estimation of a short time series. In biomedical engineering, AR modelling is used especially in the spectral analysis of heart rate variability and electroencephalogram tracings. In AR modelling, each value of a time series is regressed on its past values. The number of past values used is called the model order. An AR model or process may be used in either process synthesis or process analysis, each of which can be regarded as a filter. The AR analysis filter divides the time series into two additive components, the predictable time series and the prediction error sequence. When the prediction error sequence has been separated from the modelled time series, the AR model can be inverted, and the prediction error sequence can be regarded as an input and the measured time series as an output to the AR synthesis filter. When a time series passes through a filter, its amplitudes of frequencies are rescaled. The properties of the AR synthesis filter are used to determine the amplitude and frequency of the different components of a time series. Heart rate variability data are here used to illustrate the method of AR spectral analysis. Some basic definitions of discrete-time signals, necessary for understanding of the content of the paper, are also presented.

Practical systems thinking

System is a dynamic and complex whole, interacting as a structured functional unit. Systems thinking provides tools for understanding a such system structure and its dynamic behavior. Practical systems thinking course teaches first year bachelor students basics about systems and how open problem can be formulated to system task.

Tutorial on Multivariate Autoregressive Modelling

In the present paper, the theoretical background of multivariate autoregressive modelling (MAR) is explained. The motivation for MAR modelling is the need to study the linear relationships between signals. In biomedical engineering, MAR modelling is used especially in the analysis of cardiovascular dynamics and electroencephalographic signals, because it allows determination of physiologically relevant connections between the measured signals. In a MAR model, the value of each variable at each time instance is predicted from the values of the same series and those of all other time series. The number of past values used is called the model order. Because of the inter-signal connections, a MAR model can describe causality, delays, closed-loop effects and simultaneous phenomena. To provide a better insight into the subject matter, MAR modelling is here illustrated with a model between systolic blood pressure, RR interval and instantaneous lung volume.

Multivariate autoregressive modeling of autonomic cardiovascular control in neonatal lambs

The neonatal cardiovascular control system is a complicated interactive system which is under vigorous development at birth. From the measurement point of view the cardiovascular control is a closed-loop system. However, it can be examined on a beat-by-beat basis by analyzing circulatory-controlled variables with advanced signal analysis techniques. This paper proposes to use a multivariate autoregressive modeling technique in the analysis of several simultaneous physiological signals in order to examine interactions and inherent properties in the system. With the proposed multivariate autoregressive modeling technique, a signal is modeled as a linear combination of its own past and the past values of the other simultaneous signals plus a predictive error term of the model. The interactions in the system after the model identification are analyzed in frequency domain utilizing power spectrum estimates of the signals and signal contributions. The applicability of the proposed method was examined by a three-variable model between heart rate, blood pressure and respiration in the study of autonomic cardiovascular control in a chronic neonatal lamb model, in which the cardiovascular status was changed by using a beta-adrenergic autonomic nervous blockade. The study showed that the multivariate autoregressive modeling technique is a feasible technique in studying complicated interactions within the cardiovascular control system.

Adaptive autoregressive model for reduction of poisson noise in scintigraphic images.

In the present paper, a 2-dimensional adaptive autoregressive filter is proposed for noise reduction in images degraded with Poisson noise. In autoregressive models, each value of an image is regressed on its neighborhood pixel values, called the prediction region. The autoregressive models are linear prediction models that split an image into 2 additive components, a predictable image and a prediction error image. Methods: In this research, unfiltered images were split into smaller blocks, and best combinations of a prediction region and a block size for the image quality of predictable images were sought by using 3 Poisson noise–corrupted images with different image statistics. The images had dimensions of 128 × 128 pixels. Image quality was assessed by means of the mean squared error of the image. The adaptive autoregressive model was fitted into each block separately. Different degrees of overlapping of the image blocks were tested, and for each pixel the mean predictor coefficient of the different models was determined. The prediction error image was calculated for the entire image, and the filtered image was obtained by subtracting the prediction error image from the original image. The effect of the best adaptive autoregressive filter was illustrated using real scintigraphic data. Results: Generally, a prediction region of 4 orthogonal neighbors of the predicted pixel with a block size of 5 × 5 showed the best results. The use of 75% overlapping of the image blocks and 1 iteration of the filtering was found to improve prediction accuracy. The results were further improved when the 2 error term images were summed and subjected to adaptive autoregressive filtering and the resulting predictable image was added to the iteratively filtered image, allowing both noise reduction and edge preservation. Patient data illustrated effective noise reduction. Conclusion: The proposed method provided a convenient way to reduce Poisson noise in scintigraphic images on a pixel-by-pixel basis.

Optical non-contact pH measurement in cell culture with sterilizable, modular parts

A non-contact real time pH measurement using fully modular optical parts is described for phenol-red medium cell cultures. The modular parts can be sterilized, and once the measurement is started at the beginning of culture, no recalibration or maintenance is needed till the end of the culture. Measurements can be carried out without any special manual attention. The modular assembly of LED and sensor cassettes is unique, robust, reusable and reproducible. pH is measured in an intact closed flow system, without wasting any culture medium. A special pump encapsulation enables the system to be effortlessly functional in extremely humid incubator environments. This avoids lengthy sample tubings in and out of the incubator, associated large temperature changes and CO2 buffering issues. A new correction model to compensate errors caused e.g. by biolayers in spectrometric pH measurement is put-forward, which improves the accuracy of pH estimation significantly. The method provides resolution down to 0.1 pH unit in physiological pH range with mean absolute error 0.02.

Adaptive Autoregressive Model for Reduction of Noise in SPECT.

This paper presents improved autoregressive modelling (AR) to reduce noise in SPECT images. An AR filter was applied to prefilter projection images and postfilter ordered subset expectation maximisation (OSEM) reconstruction images (AR-OSEM-AR method). The performance of this method was compared with filtered back projection (FBP) preceded by Butterworth filtering (BW-FBP method) and the OSEM reconstruction method followed by Butterworth filtering (OSEM-BW method). A mathematical cylinder phantom was used for the study. It consisted of hot and cold objects. The tests were performed using three simulated SPECT datasets. Image quality was assessed by means of the percentage contrast resolution (CR%) and the full width at half maximum (FWHM) of the line spread functions of the cylinders. The BW-FBP method showed the highest CR% values and the AR-OSEM-AR method gave the lowest CR% values for cold stacks. In the analysis of hot stacks, the BW-FBP method had higher CR% values than the OSEM-BW method. The BW-FBP method exhibited the lowest FWHM values for cold stacks and the AR-OSEM-AR method for hot stacks. In conclusion, the AR-OSEM-AR method is a feasible way to remove noise from SPECT images. It has good spatial resolution for hot objects.

Relating halftone dot quality to paper surface topography

Most printed material is produced by printing halftone dot patterns. One of the key issues that determine the attainable print quality is the structure of the paper surface, but the relation is non-deterministic in nature. We examine the halftone print quality and study the statistical dependence between the defects in printed dots and the topography measurement of the unprinted paper. The work concerns SC paper samples printed by an IGT gravure test printer. We have small-scale 2D measurements of the unprinted paper surface topography and the reflectance of the print result. The measurements before and after printing are aligned with subpixel resolution, and individual printed dots are detected. First, the quality of the printed dots is studied using Self Organizing Map and clustering and the properties of the corresponding areas in the unprinted topography are examined. The printed dots are divided into high and low print quality. Features from the unprinted paper surface topography are then used to classify the corresponding paper areas using Support Vector Machine classification. The results show that the topography of the paper can explain some of the print defects. However, there are many other factors that affect the print quality, and the topography alone is not adequate to predict the print quality.

Relating Halftone Dot Quality to Paper Surface Topography

Most printed material is produced by printing halftone dot patterns. One of the key issues that determine the attainable print quality is the structure of the paper surface but the relation is non-deterministic in nature. We examine the halftone print quality and study the statistical dependence between the defects in printed dots and the topography measurement of the unprinted paper. The work concerns SC paper samples printed by an IGT gravure test printer. We have small-scale 2D measurements of the unprinted paper surface topography and the reflectance of the print result. The measurements before and after printing are aligned with subpixel resolution and individual printed dots are detected. First, the quality of the printed dots is studied using Self Organizing Map and clustering and the properties of the corresponding areas in the unprinted topography are examined. The printed dots are divided into high and low print quality. Features from the unprinted paper surface topography are then used to classify the corresponding paper areas using Support Vector Machine classification. The results show that the topography of the paper can explain some of the print defects. However, there are many other factors that affect the print quality and the topography alone is not adequate to predict the print quality.

Measurement of annual ring width of log ends in forest machinery

The quality of wood is of increasing importance in wood industry. One important quality aspect is the average annual ring width and its standard deviation that is related to the wood strength and stiffness. We present a camera based measurement system for annual ring measurements. The camera system is designed for outdoor use in forest harvesters. Several challenges arise, such as the quality of cutting process, camera positioning and the light variations. In the freshly cut surface of log end the annual rings are somewhat unclear due to small splinters and saw marks. In the harvester the optical axis of camera cannot be set orthogonally to the log end causing non-constant resolution of the image. The amount of natural light in forest varies from total winter darkness to midsummer brightness. In our approach the image is first geometrically transformed to orthogonal geometry. The annual ring width is measured with two-dimensional power spectra. The two-dimensional power spectra combined with the transformation provide a robust method for estimating the mean and the standard deviation of annual ring width. With laser lighting the variability due to natural lighting can be minimized.