Edge-preserving adaptive autoregressive model for Poisson noise reduction.

Autoregressive models in image processing are linear prediction models that split an image into a predicted (i.e. filtered) image and a prediction error image, which extracts data on the image edges. Edge separation is a crucial feature of an autoregressive model. Data on the edges can be processed in different ways and then added to the filtered image. Another basic feature of our method is spatially varying modelling. In this short article, we propose an improved autoregressive model that preserves image sharpness around the edges of the image and focus on the reduction of Poisson noise, which degrades nuclear medicine images and presents a special challenge in medical imaging.

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.

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

UNLABELLED: 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.

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.

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.