Jaakko Astola

Vector median filters

Two nonlinear algorithms for processing vector-valued signals are introduced. The algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum-likelihood-estimate approach. The underlying probability densities are exponential, and the resulting operations have properties very similar to those of the median filter. In the vector median approach, the samples of the vector-valued input signal are processed as vectors. The operation inherently utilizes the correlation between the signal components, giving the filters some desirable properties. General properties as well as the root signals of the vector median filters are studied. The vector median operation is combined with linear filtering, resulting in filters with improved noise attenuation and filters with very good edge response. An efficient algorithm for implementing long vector median filters is presented. The noise attenuation of the filters is discussed, and an application to velocity filtering is shown. >

Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation

The deterministic properties of weighted median (WM) filters are analyzed. Threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering. The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function. Because the cascade of WM filters can always be expressed as a single stack filter this allows expression of the cascade of WM filters as a single WM filter. A direct application is the computation of the output distribution of a cascade of WM filters. The same method is used to find a nonrecursive expansion of a recursive WM filter. As applications of theoretical results, several interesting deterministic and statistical properties of WM filters are derived. >

Analysis of the meter of acoustic musical signals

A method is described which analyzes the basic pattern of beats in a piece of music, the musical meter. The analysis is performed jointly at three different time scales: at the temporally atomic tatum pulse level, at the tactus pulse level which corresponds to the tempo of a piece, and at the musical measure level. Acoustic signals from arbitrary musical genres are considered. For the initial time-frequency analysis, a new technique is proposed which measures the degree of musical accent as a function of time at four different frequency ranges. This is followed by a bank of comb filter resonators which extracts features for estimating the periods and phases of the three pulses. The features are processed by a probabilistic model which represents primitive musical knowledge and uses the low-level observations to perform joint estimation of the tatum, tactus, and measure pulses. The model takes into account the temporal dependencies between successive estimates and enables both causal and noncausal analysis. The method is validated using a manually annotated database of 474 music signals from various genres. The method works robustly for different types of music and improves over two state-of-the-art reference methods in simulations.

From Local Kernel to Nonlocal Multiple-Model Image Denoising

We review the evolution of the nonparametric regression modeling in imaging from the local Nadaraya-Watson kernel estimate to the nonlocal means and further to transform-domain filtering based on nonlocal block-matching. The considered methods are classified mainly according to two main features: local/nonlocal and pointwise/multipoint. Here nonlocal is an alternative to local, and multipoint is an alternative to pointwise. These alternatives, though obvious simplifications, allow to impose a fruitful and transparent classification of the basic ideas in the advanced techniques. Within this framework, we introduce a novel single- and multiple-model transform domain nonlocal approach. The Block Matching and 3-D Filtering (BM3D) algorithm, which is currently one of the best performing denoising algorithms, is treated as a special case of the latter approach.

Systematic bioinformatic analysis of expression levels of 17,330 human genes across 9,783 samples from 175 types of healthy and pathological tissues

Our knowledge on tissue- and disease-specific functions of human genes is rather limited and highly context-specific. Here, we have developed a method for the comparison of mRNA expression levels of most human genes across 9,783 Affymetrix gene expression array experiments representing 43 normal human tissue types, 68 cancer types, and 64 other diseases. This database of gene expression patterns in normal human tissues and pathological conditions covers 113 million datapoints and is available from the GeneSapiens website.

Image database TID2013

This paper describes a recently created image database, TID2013, intended for evaluation of full-reference visual quality assessment metrics. With respect to TID2008, the new database contains a larger number (3000) of test images obtained from 25 reference images, 24 types of distortions for each reference image, and 5 levels for each type of distortion. Motivations for introducing 7 new types of distortions and one additional level of distortions are given; examples of distorted images are presented. Mean opinion scores (MOS) for the new database have been collected by performing 985 subjective experiments with volunteers (observers) from five countries (Finland, France, Italy, Ukraine, and USA). The availability of MOS allows the use of the designed database as a fundamental tool for assessing the effectiveness of visual quality. Furthermore, existing visual quality metrics have been tested with the proposed database and the collected results have been analyzed using rank order correlation coefficients between MOS and considered metrics. These correlation indices have been obtained both considering the full set of distorted images and specific image subsets, for highlighting advantages and drawbacks of existing, state of the art, quality metrics. Approaches to thorough performance analysis for a given metric are presented to detect practical situations or distortion types for which this metric is not adequate enough to human perception. The created image database and the collected MOS values are freely available for downloading and utilization for scientific purposes. We have created a new large database.This database contains larger number of distorted images and distortion types.MOS values for all images are obtained and provided.Analysis of correlation between MOS and a wide set of existing metrics is carried out.Methodology for determining drawbacks of existing visual quality metrics is described.

Optimal weighted median filtering under structural constraints

A new expression for the output moments of weighted median filtered data is derived. The noise attenuation capability of a weighted median filter can now be assessed using the L-vector and M-vector parameters in the new expression. The second major contribution of the paper is the development of a new optimality theory for weighted median filters. This theory is based on the new expression for the output moments, and combines the noise attenuation and some structural constraints on the filters behavior. In certain special cases, the optimal weighted median filter can be obtained by merely solving a set of linear inequalities. This leads in some cases to closed form solutions for optimal weighted median filters. Some applications of the theory developed in this paper, in 1-D signal processing and image processing are discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filters. >

Color image database for evaluation of image quality metrics

In this contribution, a new image database for testing full-reference image quality assessment metrics is presented. It is based on 1700 test images (25 reference images, 17 types of distortions for each reference image, 4 levels for each type of distortion). Using this image database, 654 observers from three different countries (Finland, Italy, and Ukraine) have carried out about 400000 individual human quality judgments (more than 200 judgments for each distorted image). The obtained mean opinion scores for the considered images can be used for evaluating the performances of visual quality metrics as well as for comparison and for the design of new metrics. The database, with testing results, is freely available.

Blur Identification by Multilayer Neural Network Based on Multivalued Neurons

A multilayer neural network based on multivalued neurons (MLMVN) is a neural network with a traditional feedforward architecture. At the same time, this network has a number of specific different features. Its backpropagation learning algorithm is derivative-free. The functionality of MLMVN is superior to that of the traditional feedforward neural networks and of a variety kernel-based networks. Its higher flexibility and faster adaptation to the target mapping enables to model complex problems using simpler networks. In this paper, the MLMVN is used to identify both type and parameters of the point spread function, whose precise identification is of crucial importance for the image deblurring. The simulation results show the high efficiency of the proposed approach. It is confirmed that the MLMVN is a powerful tool for solving classification problems, especially multiclass ones.

Nonlinear multivariate image filtering techniques

In this paper, nonlinear multivariate image filtering techniques are proposed to handle color images corrupted by noise. First, we briefly review the principle of reduced ordering (R-ordering) and then define three R-orderings by selecting different central locations. Considering noise attenuation, edge preservation, and detail retention, R-ordering based multivariate filters are designed by combining the R-ordering schemes. To implement color image filtering more effectively, we develop them into a locally adaptive version. The output of the adaptive filter is the closest sample to a central location that is a weighted linear combination of the mean, the marginal median, and the center sample. As a result, we study an adaptive hybrid multivariate (AHM) filter consisting of the mean filter, the marginal median filter, and the identity filter. The performance of the two adaptive filtering techniques is compared with that of some nonadaptive ones. The examples of color image filtering show that the adaptive multivariate image filtering gives a rather good performance improvement.