Damir Seršić

Wavelet packets approach to blind separation of statistically dependent sources

Sub-band decomposition independent component analysis (SDICA) assumes that wide-band source signals can be dependent but some of their sub-components are independent. Thus, it extends applicability of standard independent component analysis (ICA) through the relaxation of the independence assumption. In this paper, firstly, we introduce novel wavelet packets (WPs) based approach to SDICA obtaining adaptive sub-band decomposition of the wideband signals. Secondly, we introduce small cumulant based approximation of the mutual information (MI) as a criterion for the selection of the sub-band with the least-dependent components. Although MI is estimated for measured signals only, we have provided a proof that shows that index of the sub-band with least dependent components of the measured signals will correspond with the index of the sub-band with least dependent components of the sources. Unlike in the case of the competing methods, we demonstrate consistent performance in terms of accuracy and robustness as well as computational efficiency of WP SDICA algorithm.

Adaptive 2-D Wavelet Transform Based on the Lifting Scheme With Preserved Vanishing Moments

In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.

Adaptive spatio-temporal denoising of fluoroscopic X-ray sequences

Abstract Lowering the cumulative radiation dose to a patient undergoing fluoroscopic examination requires efficient denoising algorithms. We propose a method, which extensively utilizes temporal dimension in order to maximize denoising efficiency. A set of subsequent images is processed and two estimates of denoised images are calculated. One is based on a special implementation of an adaptive edge preserving wavelet transform, while the other is based on the statistical method intersection of confidence intervals (ICI) rule. Wavelet transform is thought to produce high quality denoised images and ICI estimate can be used to further improve denoising performance about object edges. The estimates are fused to produce the final denoised image. We show that the proposed method performs very well and do not suffer from blurring in clinically important parts of images. As a result, its application could allow for significant lowering of the fluoroscope single frame dose.

A Novel Approach to Wheeze Detection

Wheezing often accompanies pulmonary pathologies and its detection is considered of great importance for the diagnosis and management of respiratory diseases. Our aim was to develop a simple and robust algorithm for wheeze detection in respiratory sound spectra to be used for long-term monitoring and early stage assessment of asthma episode in children. The robustness of the algorithm enables wheezing detection in presence of noise and moving artifacts. Children cannot perform respiratory function tests such as peak-flow measurement and therefore we find continuous recording and processing of respiratory sounds as an alternative. The algorithm we used for wheeze detection is based on the idea of frequency domain peak detection proposed by Shabtai-Musih et al. because of its simplicity and scoring used for specifying the likelihood that the peaks in power spectra represent wheezes. In our algorithm, we have modified the way of searching peaks in the spectrogram. Before searching for peaks, wavelet denoising was used in order to remove the noise in spectrum without affecting the peaks that we were searching for. Using the scoring algorithm we were able to create a binary image of the spectrogram of the sounds - wheezes and score the length (duration) of connected components considered as wheezing. The components that did not meet length criterion were rejected and were not considered as wheezing. The algorithm was tested on respiratory sound signals from public signal databases and on our own signals recorded in a group of 26 asthmatic children. The algorithm successfully detected wheezes in all signals containing wheezing.

Image denoising based on adaptive quincunx wavelets

In this paper, we explore the use of nonseparable and adaptive wavelet decompositions for the purpose of image denoising. We apply the classical wavelet shrinkage methods on the wavelet coefficients obtained by using the adaptive wavelet transform defined on the quincunx grid. The wavelet transform is pixel-wise adaptive in all decomposition levels. While providing more compact representation of the analyzed image, the adaptive transform retains some useful properties of fixed transforms, such as numbers of vanishing moments of primal and dual wavelets. The adaptive wavelet decomposition is realized using the lifting scheme. For comparison purposes, the image denoising results are presented for both fixed and adaptive wavelet transforms.

Robust Blind Separation of Statistically Dependent Sources using Dual Tree Wavelets

Blind source separation (BSS) problem is commonly solved by means of independent component analysis (ICA) assuming statistically independent and non-Gaussian sources. The strict independence assumption can be relaxed to existence of subbands where signals are less dependent. In this paper, we use dual tree complex wavelets for the subband decomposition of observed signals and small cummulant based approximation of mutual information for finding the most independent subband(s). We compare the proposed method to previously reported shift invariant and decimated wavelet packet based approach, as well as to innovations based approach. We found proposed dual tree wavelets scheme as an efficient and robust solution of the BSS problem of statistically dependent sources. One important application of the proposed method is related to unsupervised segmentation of medical and remotely sensed multispectral images.

Wavelet filter banks with adaptive number of zero moments

An efficient realization of a two-channel wavelet filter bank with adaptive number of zero moments is proposed. The described time variant wavelet filter bank is more suitable for analysis of non-stationary signals then fixed banks. Filters with more zero moments result in a better representation of smooth parts of the analyzed signal, while less zero moments is better for transients and singularities. The proposed realization is based on the lifting scheme, derived from a method of fixed wavelet filter bank design, using Lagrange interpolation of samples in the time domain. Adaptation criterion is calculated from the wavelet coefficients, which is under some restrictions, reproducible on the reconstruction side. Wavelet filter banks with adaptive number of zero moments outperforms fixed banks in a number of applications.

Efficient Least Absolute Deviation Adaptive Wavelet Filter Bank

Compact representation of signals and images is a key for many applications. Compactness is often achieved through linear transforms with good energy concentration property. We present an adaptive wavelet filter bank with fixed number of vanishing moments, plus additional local adaptation. Proposed adaptation method is conducted at each sample according to the least absolute deviation (LAD) criterion. Fixed vanishing moments provide for polynomial annihilation. Adaptation is aimed to achieve maximum sparseness for a wider class of signals, such as sine waves. LAD criterion results in more accurate adaptation on sudden changes of signal statistics. In this paper, an efficient LAD realization is proposed, in spite of nonexistence of the closed form solution. Combining least squares and LAD criterion, we have achieved unbiased adaptation, robust to noise. Due to its simplicity and acceptable computational speed, the proposed scheme is a good candidate for the real-world applications. In this paper, advantages of the proposed scheme are shown in signal denoising and reconstruction.

Integer to integer mapping wavelet filter bank with adaptive number of zero moments

An efficient realization of a two-channel wavelet filter bank that maps integers to integers with an adaptive number of zero moments is presented. Filters with more zero moments result in a better representation of the smooth parts of the analyzed signal, while fewer zero moments are better for transients and singularities. The proposed realization is based on the lifting scheme that enables mapping integer signals to integer wavelet coefficients, preserving the perfect reconstruction property. The realization is derived from a method of fixed wavelet filter bank design, using Lagrange interpolation of samples in the time domain. The adaptation criterion is computed from integer wavelet coefficients, which is, under some restrictions, reproducible on the reconstruction side. Quantization introduces non-predictable components of the wavelet coefficients thus influencing the behavior of the adaptation algorithm. Adaptation on the interval is used to reduce the variance of the filter parameters.

Restoration of soft x-ray laser images of nanostructures

We present advanced techniques for the restoration of images obtained by soft x-ray laser microscopy. We show two methods. One method is based on adaptive thresholding, while the other uses local Wiener filtering in the wavelet domain to achieve high noise gains. These wavelet based denoising techniques are improved using spatial noise modeling. The accurate noise model is built up from two consecutive images of the object and respective background images. To our knowledge, the results of both proposed approaches over-perform competitive methods. The analysis is robust to enable image acquisition with significantly lower exposure times, which is critical in samples that are sensitive to radiation damage as is the case of biological samples imaged by SXR microscopy.