Recent advances in adaptive filter theory and the hardware for signal acquisition have led to the realization that purely linear algorithms are often not adequate in these domains. Nonlinearities in the input space have become apparent with today's real world problems. Algorithms that process the data must keep pace with the advances in signal acquisition. Recently kernel adaptive (online) filtering algorithms have been proposed that make no assumptions regarding the linearity of the input space. Additionally, advances in wavelet data compression/dimension reduction have also led to new algorithms that are appropriate for producing a hybrid nonlinear filtering framework. In this paper we utilize a combination of wavelet dimension reduction and kernel adaptive filtering. We derive algorithms in which the dimension of the data is reduced by a wavelet transform. We follow this by kernel adaptive filtering algorithms on the reduced-domain data to find the appropriate model parameters demonstrating improved minimization of the mean-squared error (MSE). Another important feature of our methods is that the wavelet filter is also chosen based on the data, on-the-fly. In particular, it is shown that by using a few optimal wavelet coefficients from the constructed wavelet filter for both training and testing data sets as the input to the kernel adaptive filter, convergence to the near optimal learning curve (MSE) results. We demonstrate these algorithms on simulated and a real data set from food processing.

This paper introduces an image denoising procedure based on a 2D scale-mixing complex-valued wavelet transform. Both the minimal (unitary) and redundant (maximum overlap) versions of the transform are used. The covariance structure of white noise in wavelet domain is established. Estimation is performed via empirical Bayesian techniques, including versions that preserve the phase of the complex-valued wavelet coefficients and those that do not. The new procedure exhibits excellent quantitative and visual performance, which is demonstrated by simulation on standard test images.

The aim of this paper is to present results from a comparative investigation into the diagnostic performance of several wavelet-based estimators of scaling, some from published literature and some newly proposed. These estimators are evaluated based on their ability to classify digitized mammogram images from a clinical database, for which the true disease status is known by biopsy. We found that Abry-Veitch and modified weighted Theil-type estimators provided the best classification rates, while the standard wavelet-based OLS estimator performed worst. The results are robust with respect to choice of wavelets (Haar wavelet being an exception) and are of potential clinical value. The diagnostic is based on the properties of image backgrounds (which is an unused diagnostic modality in Mammograms) and the best correct classification rates achieve 90%, varying slightly with the choice of basis, levels used, and size of training set.

The current ubiquity of information technology has increased variability among users, creating a corresponding need to properly capture and understand these individual differences. This study introduces a novel application of multifractal statistical methods to distinguish users via patterns of variability within high frequency pupillary response behavior (PRB) data collected during computer-based interaction. PRB was measured from older adults, including two groups diagnosed with age-related macular degeneration (AMD) maintaining a range of visual acuities (n = 14), and one visually healthy control group (i.e., disease-free, 20/20--20/32 acuity) (n = 14). Three measures of the multifractal spectrum, the distribution of regularity indices extracted from time series data, distinguished the user groups, including: 1) Spectral Mode; 2) Broadness; and 3) Left Slope. The results demonstrate a clear relationship between the values of these measures and the level of visual capabilities. These analytical techniques leverage the inherent complexity and richness of this high frequency physiological response data, which can be used to meaningfully differentiate individuals whose sensory and cognitive capabilities may be affected by aging and visual impairment. Multifractality analysis provides an objective, quantifiable means of uncovering and examining the underlying signatures in physiological behavior that may account for individual differences in interaction needs and behaviors.