Search

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.

Most real world signals contain certain amount of noise, so, signal denoising algorithms are a topic of interest in many different applications. Wavelet transforms proved to perform very well in noise removal. Their success is based on the fact that, in the transform domain, crucial signal information is contained in a small number of larger magnitude wavelet coefficients. Also, white noise contained in a signal will map to a white noise in the transform domain. It will be represented by a large number of smaller magnitude wavelet coefficients, concentrated about zero. Noise removal can be efficiently carried out by thresholding wavelet coefficients before signal reconstruction. We proposed an adaptive lifting scheme with a goal of improving the transform performance about edges in a signal. The adaptive algorithm is based on the statistical method of intersection of confidence intervals (ICI). It is used on a point-by-point basis, and on each scale, to determine support of the lifting filter P. After deciding the support, filter P is selected from a predefined set of filters. Since the proposed lifting scheme uses filter U defined as: U = P/2, choosing the filter P is equivalent to selecting a wavelet from a predefined set of wavelets. As a final result, longer and smoother wavelets ares used in smooth signal regions, while shorter wavelets are used in higher frequency regions. The approach allows for efficient reconstruction of edges or, in general, higher signal frequencies. We compared the method efficiency to a number of conventional wavelets. It was shown that for the signal classes with prevailing low frequencies, the proposed method is at least comparable to the best performing conventional wavelet. For signal classes characterized by edges or abrupt changes in local signal properties, the method outperforms the conventional wavelets by a significant margin. The shortcoming of the proposed method is its reliance on the ICI gamma parameter, which defines the method sensitivity. Poorly chosen gamma parameter value can have a detrimental effect to a transform performance. As it is not possible to find the optimal Γ value analytically, we proposed a statistical method for its selection. It is based on a distribution of wavelet coefficients at the last decomposition level. Although there is still much room for improvement, it was shown that the method performs reasonably well across a range of signal classes, resolutions and noise levels. The adaptive algorithm was also tested in a real-world application of fluoroscopic image sequences denoising. It is the application in which edge preservation is an essential requirement. Original catheter insertion sequence was examined, as well as the sequence with artificially raised noise level. Set of subsequent images was converted to a 1-D signal and the proposed algorithm applied to it, as for any other native 1-D signal. Denoised 1-D signal is converted back to 3-D and fused with another estimate of denoised images, based on the basic ICI rule. The final result is a high quality denoised image with excellent edge preservation. The proposed adaptive edge preserving lifting scheme and accompanying Γ parameter selection method represent a well performing model of the second generation wavelets, i.e., wavelets which inherit all the benefits and good properties of the classical wavelet transforms, while in the same time introducing additional advantages and features.

In this thesis, we propose the novel adaptive wavelet filter bank structures that are used to obtain efficient representations of the analyzed images. We present the lifting scheme structures for building adaptive wavelet decompositions based on the nonseparable quincunx sampling scheme. The resulting wavelet decompositions are adaptive to the local properties of the analyzed image. Despite the introduced adaptation, a desired number of vanishing moments is still retained. The proposed adaptation is performed in order to minimize the energy of detail coefficients on a neighborhood of each pixel of the analyzed image. The appropriate neighborhood is determined for each pixel separately by using the intersection of confidence intervals (ICI) rule. The application of the ICI rule improves the estimation of the filter bank parameters and makes it more robust to noise. The image denoising results are presented for both synthetic and real-world images. It is shown that the adaptive wavelet decompositions outperform the existing fixed decompositions in terms of denoising quality of images that contain periodic components, and in general they give more compact image representations. U ovoj disertaciji predlažemo nove adaptivne valićne filtarske strukture koje se koriste za dobivanje efikasnih reprezentacija analiziranih slika. U radu prikazujemo filtarske slogove temeljene na shemi podizanja za konstrukciju adaptivnih valićnih razlaganja zasnovanih na neseparabilnom quincunx uzorkovanju. Rezultirajuća valićna razlaganja su prilagođena lokalnim svojstvima analizirane slike. Unatoč uvedenoj adaptaciji, zadržan je željeni broj nul-momenata pripadajućihih vali ćnih funkcija. Adaptacija se vrši sa ciljem minimizacije koeficijenata detalja na okolini svakog slikovnog elementa. Odabir odgovarajuće okoline za svaki slikovni element vrši se korištenjem metode presjecišta invervala pouzdanosti. Primjena dotične metode poboljšava adaptaciju parametara filtarskog sloga i čini je robusnijom na šum. Rezultati uklanjanja šuma iz slike prikazani su za primjere sintetičkih kao i realnih slika. Pokazano je da dobivena adaptivna valićna razlaganja nadmašuju postojeća fiksna razlaganja s obzirom na kvalitetu uklanjanja šuma iz slika koje sadrže periodičke komponente, te općenito daju kompaktniji zapis slike.

More efficient coding, modelling and image analysis generate the need for search for better methods of the multiresolution image analysis, i.e. for more efficient wavelet filter bank structures. This thesis is based on a previous research of one-dimensional filter bank structures that had the possibility to adapt filter parameters to the properties of the analyzed signal. In this thesis we present the construction of a two-dimensional adaptive wavelet filter bank that is based on a lifting scheme. The filter bank is nonseparable, based on a quincunx polyphase decomposition and nonseparable filters. The lifting scheme has been chosen since it allows for an easy construction of space varying filter banks with a perfect reconstruction property. The proposed filter bank adapts to the analyzed image for every pixel in all decomposition levels while still preserving the good properties of the wavelet decomposition. A number of vanishing moments is guaranteed by the fixed part of the filter bank. Without degrading the overall filter bank properties, the variable part can be changed in order to adapt to the analyzed image. The paper explores various one-dimensional and two-dimensional adaptation methods based on the least squares criterion. Adaptation results have been shown for a number of synthetic and real-world images. Effects of lossy image reconstruction and impact of filter coefcients' quantization to the efficiency of the image decomposition have been presented. Učinkovitije kodiranje, modeliranje i analiza slika stvaraju potrebu za traženjem boljih metoda višerezolucijskog razlaganja slika odnosno potrebu za učinkovitijim strukturama dvodimenzionalnih wavelet filtarskih slogova. Rad se temelji na prethodnom istraživanju struktura jednodimenzionalnih filtarskih slogova koji su imali mogućnost adaptacije filtarskih parametara svojstvima signala. U ovom radu prikazujemo izvedbu dvodimenzionalnog adaptivnog wavelet filtarskog sloga koji se temelji na shemi podizanja. Filtarski slog je neseparabilan, temelji se na quincunx polifaznom razlaganju i neseparabilnim filtrima. Shema podizanja je odabrana jer omogućava jednostavnu izvedbu prostorno promjenjivih filtarskih slogova sa svojstvima savršene rekonstrukcije. Predloženi filtarski slog se prilagođuje analiziranoj slici u svakom slikovnom elementu u svim razinama razlaganja u isto vrijeme zadržavajući dobra svojstva wavelet razlaganja. Dovoljan broj nul-momenata pridruženih wavelet funkcija zagarantiran je nepromjenjivim dijelom filtarskog sloga. Promjenjivi dio filtarskog sloga može se prilagođivati svojstvima slike bez narušavanja cjelokupnih svojstava filtarskog sloga. Istražene su razne jednodimenzionalne i dvodimenzionalne metode adaptacije zasnovane na kriteriju najmanjih kvadrata. Rezultati adaptacije prikazani su za razne sintetske i realne slike. Prezentirati su rezultati rekonstrukcije slike s gubicima i utjecaj kvantizacije filtarskih koeficijenata na učinkovitost adaptivnog razlaganja slike.

In this paper we have used a previously reported adaptive filter bank structure for image decomposition and lossy reconstruction. We used a robust 2D windowed LS (LSW) adaptation algorithm to change the filter parameters and to adapt them to the local image properties. To improve the coding gain of the lossy image compression scheme, quantization of the adapted filter parameters has been explored. We used a CDF-based method followed by an optimization procedure to find the best quantization values. The proposed method was applied to a number of synthetic and real world images. Reconstructed images were perceptually superior, achieving lower square error norm when compared to the well-known fixed wavelet scheme.

Wavelet transforms found widespread application in signal denoising. Many adaptive algorithms were proposed to improve their performance, especially about edges in a signal. In this study, the authors propose a novel denoising method based on adaptive edge-preserving lifting scheme - intersection of confidence intervals-edge preserving lifting scheme (ICI-EPL). By incorporating the statistical method of intersection of confidence intervals rule into the lifting scheme, the authors are able to select the most appropriate wavelet on a point-by-point basis. The resulting transform adapts very well to local signal properties and significantly improves denoising performance. Simulations on various signal classes show that the ICI-EPL in most cases easily outperforms other considered transforms, with the greatest improvement being about edges in a signal. Achieved results bring confidence that the ICI-EPL can be used to improve performance in a variety of denoising applications.

An adaptive lifting scheme is proposed, in which the intersection of confidence intervals (ICI) rule is used to determine the wavelet support. The adaptation is performed on a point-by-point basis and the ICI rule is used to prevent the support from spanning across the edges in a signal, in which the edge is considered to be any sudden change in the signal statistics. It is shown that the proposed method preserves the edges well, and the overall denoising performance is much better than in the other considered methods.