Leena Pasanen

Scale space multiresolution analysis of random signals

A method to capture the scale-dependent features in a random signal is proposed with the main focus on images and spatial fields defined on a regular grid. A technique based on scale space smoothing is used. However, while the usual scale space analysis approach is to suppress detail by increasing smoothing progressively, the proposed method instead considers differences of smooths at neighboring scales. A random signal can then be represented as a sum of such differences, a kind of a multiresolution analysis, each difference representing details relevant at a particular scale or resolution. Bayesian analysis is used to infer which details are credible and which are just artifacts of random variation. The applicability of the method is demonstrated using noisy digital images as well as global temperature change fields produced by numerical climate prediction models.

Bayesian Scale Space Analysis of Differences in Images

This article considers the detection of image features in different spatial scales. The main focus is on capturing the scale-dependent differences in a pair of noisy images, but the technique developed can also be applied to the analysis of single images. The approach proposed uses Bayesian statistical modeling and simulation-based inference, and it can be viewed as a further development of SiZer technology, originally designed for nonparametric curve fitting. Numerical examples include artificial test images and a preliminary analysis of a pair of Landsat images used in satellite-based forest inventory. This article has supplementary material online.

Bayesian LASSO, Scale Space and Decision Making in Association Genetics

Background LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection. Results We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

Bayesian scale space analysis of temporal changes in satellite images

We consider the detection of land cover changes using pairs of Landsat ETM+ satellite images. The images consist of eight spectral bands and to simplify the multidimensional change detection task, the image pair is first transformed to a one-dimensional image. When the transformation is non-linear, the true change in the images may be masked by complex noise. For example, when changes in the Normalized Difference Vegetation Index is considered, the variance of noise may not be constant over the image and methods based on image thresholding can be ineffective. To facilitate detection of change in such situations, we propose an approach that uses Bayesian statistical modeling and simulation-based inference. In order to detect both large and small scale changes, our method uses a scale space approach that employs multi-level smoothing. We demonstrate the technique using artificial test images and two pairs of real Landsat ETM+satellite images.

Extraction of sea temperature in the Barents Sea by a scale space multiresolution method – prospects for Atlantic salmon

ABSTRACT Variation of marine temperature at different time scales is a central environmental factor in the life cycle of marine organisms, and may have particular importance for various life stages of anadromous species, for example, Atlantic salmon. To understand the salient features of temperature variation we employ scale space multiresolution analysis, that uses differences of smooths of a time series to decompose it as a sum of scale-dependent components. The number of resolved components can be determined either automatically or by exploring a map that visualizes the structure of the time series. The statistical credibility of the features of the components is established with Bayesian inference. The method was applied to analyze a marine temperature time series measured from the Barents Sea and its correlation with the abundance of Atlantic salmon in three Barents Sea rivers. Besides the annual seasonal variation and a linear trend, the method revealed mid time-scale (∼10 years) and long time-scale (∼30 years) variation. The 10-year quasi-cyclical component of the temperature time series appears to be connected with a similar feature in Atlantic salmon abundance. These findings can provide information about the environmental factors affecting seasonal and periodic variation in survival and migrations of Atlantic salmon and other migratory fish.

Bayesian scale space analysis of images

Two new statistical scale space methodologies are discussed. The first method aims to detect differences between two images obtained from the same object at two different instants of time. Both small scale sharp changes and large scale average changes are detected. The second method detects features that differ in intensity from their surroundings and it produces a multiresolution analysis of an image as a sum of scale-dependent components. As images are usually noisy, Bayesian inference is used to separate real differences and features from artefacts caused by random noise. The use of the Bayesian paradigm facilitates application of flexible image models and it also allows one to take advantage of an experts prior knowledge about the images considered.