Fred Godtliebsen

Edge-Preserving Smoothers for Image Processing

Abstract Classical smoothers have limited usefulness in image processing, because sharp “edges” tend to be blurred. There is a literature on edge-preserving smoothers, but these all require moderately large “smooth stretches.” Here we discuss an approach to this problem called “sigma filtering” and propose an improvement based on running M estimation. Both computational and theoretical aspects are developed. For image processing, the methods have a niche between standard filtering approaches and Bayes–Markov random-field analysis.

Significance in Scale Space for Bivariate Density Estimation

An important problem in the use of density estimation for data analysis is whether or not observed features, such as bumps, are “really there” as opposed to being artifacts of the natural sampling variability. Here we propose a solution to this problem, in the challenging two-dimensional case, using the graphical technique of significance in scale space. Color and dynamic graphics form an important part of the visualization method.

Combined Perfusion and Diffusion-Weighted Magnetic Resonance Imaging in a Rat Model of Reversible Middle Cerebral Artery Occlusion

BACKGROUND AND PURPOSE Diffusion-weighted imaging and dynamic first-pass bolus tracking of susceptibility contrast agents (perfusion imaging) are two new magnetic resonance imaging techniques that offer the possibility of early diagnosis of stroke. The present study was performed to evaluate the diagnostic information derived from these two methods in a rat model of temporary focal ischemia. METHODS Fifteen male Wistar rats were assigned to 45 (n = 7) or 120 minutes (n = 8) of middle cerebral artery occlusion followed by reperfusion using the intraluminal filament technique. The diffusion-weighted images were collected, and areas of hyperintensity were compared with histologically assessed areas of ischemic injury. The magnetic resonance perfusion image series were postprocessed to produce topographic maps reflecting the maximum reduction in the signal obtained during the first passage of the contrast agent and the time delay between the arrival of the bolus and the point of maximum contrast-agent effect. RESULTS Hyperintensity in diffusion-weighted images was demonstrated after 30 minutes of middle cerebral artery occlusion and was mainly expressed in the lateral caudoputamen and parts of the lower frontoparietal cortex. Reperfusion after 45 minutes of occlusion reduced the area of hyperintensity from 24.2% to 9.9% of hemispheric area. In the group with 120 minutes of occlusion, the hyperintense area increased from 24.4% to 29.1%. Relative to the nonischemic hemisphere, the changes in the topographic maps of maximum signal reduction occurred in the lateral caudoputamen and adjacent lower neocortical areas. Increased time delay to maximum effect, however, was seen also in the upper frontoparietal cortex. CONCLUSIONS Hyperintensity in diffusion-weighted images was reversible after 45 minutes but not after 120 minutes of middle cerebral artery occlusion. Analysis of the signal-reduction and time-delay parametric maps demonstrated regions of different perfusion changes in the ischemic hemisphere.

EM-estimation and modeling of heavy-tailed processes with the multivariate normal inverse Gaussian distribution

The heavy-tailed multivariate normal inverse Gaussian (MNIG) distribution is a recent variance-mean mixture of a multivariate Gaussian with a univariate inverse Gaussian distribution. Due to the complexity of the likelihood function, parameter estimation by direct maximization is exceedingly difficult. To overcome this problem, we propose a fast and accurate multivariate expectation-maximization (EM) algorithm for maximum likelihood estimation of the scalar, vector, and matrix parameters of the MNIG distribution. Important fundamental and attractive properties of the MNIG as a modeling tool for multivariate heavy-tailed processes are discussed. The modeling strength of the MNIG, and the feasibility of the proposed EM parameter estimation algorithm, are demonstrated by fitting the MNIG to real world hydrophone data, to wideband synthetic aperture sonar data, and to multichannel radar sea clutter data.

Thousand years of winter surface air temperature variations in Svalbard and northern Norway reconstructed from ice-core data

Two isotopic ice core records from western Svalbard are calibrated to reconstruct more than 1000 years of past winter surface air temperature variations in Longyearbyen, Svalbard, and Vardø, northern Norway. Analysis of the derived reconstructions suggests that the climate evolution of the last millennium in these study areas comprises three major sub-periods. The cooling stage in Svalbard (ca. 800–1800) is characterized by a progressive winter cooling of approximately 0.9 °C century−1 (0.3 °C century−1 for Vardø) and a lack of distinct signs of abrupt climate transitions. This makes it difficult to associate the onset of the Little Ice Age in Svalbard with any particular time period. During the 1800s, which according to our results was the coldest century in Svalbard, the winter cooling associated with the Little Ice Age was on the order of 4 °C (1.3 °C for Vardø) compared to the 1900s. The rapid warming that commenced at the beginning of the 20th century was accompanied by a parallel decline in sea-ice extent in the study area. However, both the reconstructed winter temperatures as well as indirect indicators of summer temperatures suggest the Medieval period before the 1200s was at least as warm as at the end of the 1990s in Svalbard.

A nonlinear gaussian filter applied to images with discontinuities

We focus on a simple nonlinear filter with Gaussian weights for recovering the true underlying scene from images distorted by independent and identically distributed Gaussian noise. In some applications, like magnetic resonance (MR) brain scans, this model for the distortion is re-asonable. Apart from the good performance of this filter, the main advantage is that it is nearly instantaneous in processing time, which allows convenient interactive use. In this paper, we give a statistical justification of the filter by means of a weighted least squares interpretation and a Bayesian motivation. Furthermore, we describe how a smoothing parameter, which controls the degree of smoothness in the image, can be estimated from the observed image. Successful applications to both artificial and MR images are presented.

Multicentennial Variability of the Sea Surface Temperature Gradient across the Subpolar North Atlantic over the Last 2.8 kyr

A 2800-year-long August Sea Surface Temperature (aSST) record based on fossil diatom assemblages is generated from a marine sediment core from the northern subpolar North Atlantic. The record is compared with the aSST record from the Norwegian Sea to explore the variability of the aSST gradient between these areas during the late Holocene. The aSST records demonstrate the opposite climate tendencies towards a persistent warming in the core site in the subpolar North Atlantic and cooling in the Norwegian Sea. At the multicentennial scale of aSST variability of 600–900 years, the records are nearly in anti-phase with warmer (colder) periods in the subpolar North Atlantic corresponding to the colder (warmer) periods in the Norwegian Sea. At the shorter time scale of 200–450 years, the records display a phase-locked behaviour with a tendency for the positive aSST anomalies in the Norwegian Sea to lead by ~30 years the negative aSST anomalies in the subpolar North Atlantic. This apparent aSST seesaw might have an effect on two major anomalies of the European climate of the past Millennium: Medieval Warm Period (MWP) and the Little Ice Age (LIA). During the MWP warming of the sea surface in the Norwegian Sea occurred in parallel with cooling in the northern subpolar North Atlantic whereas the opposite pattern emerged during the LIA. The results suggest that the observed aSST seesaw between the subpolar North Atlantic and the Norwegian Sea could be a surface expression of the variability of the eastern and western branches of the Atlantic Meridional Circulation (AMOC) with a possible amplification through atmospheric feedback.

A visual display device for significant features in complicated signals

For many applications the significant features found in a data set depend on the level of resolution for which the data are considered. An excellent example of this is in climatology where the features found on scales of tens and hundreds of years, respectively, may be very different. A natural way to study such data sets is through the scale-space approach. In this paper a new scale-space method, which finds significant features in signals, is proposed. The new method, posterior smoothing, is formulated in a Bayesian framework and utilizes sampling from the posterior density. We compare the new methodology to a successful, existing scale-space technique entitled SiZer (Significant Zero crossings of derivatives). For smooth signals SiZer and the new method have similar performance. In signals containing complicated structures, posterior smoothing is preferable. This is demonstrated by applying the methods to simulated and real data sets. In particular, we show that posterior smoothing has better performance in applications taken from climatology, medical imaging, and fish industry.

Surface albedo in Ny-Ålesund, Svalbard: variability and trends during 1981–1997

Abstract Since 1981, hourly values of albedo have been measured routinely at Norwegian Polar Institutes research station in Ny-Alesund, Svalbard. We have undertaken statistical analysis of the time series 1981–1997 to investigate potential long-term variability and trends in the albedo data set. The following questions have been raised and answered by regression analysis: (i) Has the time of beginning of snow melt changed? (ii) Have melt rates changed? (iii) Has the time of snow arrival in fall changed? (iv) Has the period without snow cover changed? The period without snow on the ground is studied because of its importance for tundra characteristics as a habitat for biota, e.g. length of the growth season. Our data show that albedo varies seasonally, with large variations in spring and autumn and much smaller variations in winter and summer. The variability is reasonably constant within each season. Density estimates of the albedo data suggest that the dates with highest likelihood for (i) start of snow melt and (ii) start of snow formation are 5th of June and 17th of September, respectively. Highest probability for the length of snow-free season is 94 days. None of the tests indicated any significant trends (or indications of climate change) in the 17-year record of albedo, that means that the four questions above were all answered by “no.” Correlation with the North Atlantic Oscillation (NAO) index is also investigated. No correlation between the NAO index and albedo nor temperature or precipitation was found. Even so, because of the short duration that our data set spans, we cannot rule out that such a correlation exists on decadal time scales.

Noise reduction using Markov random fields

Abstract Today, averaging several measurements of the same slice is the only statistical technique in use for reducing noise in MR images. A problem with this approach is that is is very time-consuming. As a result, there is some risk that the patient will move during the image acquisition time (and thereby introduce noise) and the number of patients treated each day is rather small. The main purpose with this work was to find out whether statistical methods can be used to get the same image quality from fewer measurements of the same slice. Our empirical results indicate that a statistical method applied to a single measurement gives an image of about the same quality as an average of three single measurements.