Denoising and enhancement of mammographic images under the assumption of heteroscedastic additive noise by an optimal subband thresholding

Mammographic images suffer from low contrast and signal dependent noise, and a very small size of tumoral signs is not easily detected, especially for an early diagnosis of breast cancer. In this context, many methods proposed in literature fail for lack of generality. In particular, too weak assumptions on the noise model, e.g., stationary normal additive noise, and an inaccurate choice of the wavelet family that is applied, can lead to an information loss, noise emphasizing, unacceptable enhancement results, or in turn an unwanted distortion of the original image aspect. In this paper, we consider an optimal wavelet thresholding, in the context of Discrete Dyadic Wavelet Transforms, by directly relating all the parameters involved in both denoising and contrast enhancement to signal dependent noise variance (estimated by a robust algorithm) and to the size of cancer signs. Moreover, by performing a reconstruction from a zero-approximation in conjunction with a Gaussian smoothing filter, we are able to extract the background and the foreground of the image separately, as to compute suitable contrast improvement indexes. The whole procedure will be tested on high resolution X-ray mammographic images and compared with other techniques. Anyway, the visual assessment of the results by an expert radiologist will be also considered as a subjective evaluation

Multiscale copy number alteration analysis using wavelets

The need for multiscale modelling comes from the fact that it is rare for measured data to contain contributions at a single scale. For example, a typical signal from an experimental process may contain contributions from a variety of sources, such as noise and faults. These features usually occur with different localisation and at different locations in time and frequency. It is also inevitable for copy number DNA sequencing. Identifying Copy Number Alteration (CNA) from a sample cell faces difficulties due to errors, different sizes of reads being recorded, infiltration from normal cells, and different sizes of test and normal genomes. Thus, the representation of the measurements in terms of multiscale offers efficient feature extraction or noise removal from a typical process signal. One of the powerful tools used to extract the multiscale characteristics of the observed data is wavelets. Wavelets are mathematical expansions that are able to transform data from the time domain into different layers of frequency levels. In this thesis, wavelets are used, first, to segment the CNA data into regions of equal copy number and secondly, to extract useful information from the original data for a better prediction of tumour subtypes. For the first purpose, an approach called TGUHm method is presented which applies the tail-greedy unbalanced Haar (TGUH) wavelet transform to perform segmentation of CNA data. The `unbalanced' characteristic of the TGUH approach gives the advantage that the data length does not have to be a power of two as in the traditional discrete Haar wavelet method. An additional benefit is it can address the problem that commonly arises in Haar wavelet estimation where the estimator is more likely to detect jumps at dyadic locations which might not be the actual locations of the jumps/drops in the true underlying CNA pattern. The TGUHm method is then applied to the existing data-driven wavelet-Fisz methodology to deal with the heteroscedastic noise problem that we often find in CNA data. In practice, real CNA data deviate from homoscedastic noise assumption and indicate some dependencies of the variance on the mean value. The proposed method performs variance stabilisation to bring the problem into a homoscedastic model before applying a denoising procedure. The use of the unbalanced Haar wavelet also makes it possible to estimate short segments better than the balanced Haar wavelet-based segmentation methods. Moreover, our simulation study indicates that the proposed methodology has substantial advantages in estimating both short and long-altered segments in copy number data with heteroscedastic error variance. For the second purpose, a wavelet-based classification framework was proposed which employs non-decimated Haar wavelet transform to extract localised differences and means of the original data into several scales. The wavelet transformation decomposes the original data into detail (localised difference) and scaling (localised means) coefficients into different resolution levels. This would bring an advantage to discover hidden features or information which are difficult to find from original data only. Each resolution level corresponds to a different length of wavelet basis and by considering which levels are most useful in a model, the length of the region that is responsible for the prediction could be identified

Mammography

In this volume, the topics are constructed from a variety of contents: the bases of mammography systems, optimization of screening mammography with reference to evidence-based research, new technologies of image acquisition and its surrounding systems, and case reports with reference to up-to-date multimodality images of breast cancer. Mammography has been lagged in the transition to digital imaging systems because of the necessity of high resolution for diagnosis. However, in the past ten years, technical improvement has resolved the difficulties and boosted new diagnostic systems. We hope that the reader will learn the essentials of mammography and will be forward-looking for the new technologies. We want to express our sincere gratitude and appreciation?to all the co-authors who have contributed their work to this volume

Traitement d'images de radiographie à faible dose : Débruitage et rehaussement de contraste conjoints et détection automatique de points de repère anatomiques pour l'estimation de la qualité des images

We aim at reducing the ALARA (As Low As Reasonably Achievable) dose limits for images acquired with EOS full-body system by means of image processing techniques. Two complementary approaches are studied. First, we define a post-processing method that optimizes the trade-off between acquired image quality and X-ray dose. The Non-Local means filter is extended to restore EOS images. We then study how to combine it with a multi-scale contrast enhancement technique. The image quality for the diagnosis is optimized by defining non-parametric noise containment maps that limit the increase of noise depending on the amount of local redundant information captured by the filter. Secondly, we estimate exposure index (EI) values on EOS images which give an immediate feedback on image quality to help radiographers to verify the correct exposure level of the X-ray examination. We propose a landmark detection based approach that is more robust to potential outliers than existing methods as it exploits the redundancy of local estimates. Finally, the proposed joint denoising and contrast enhancement technique significantly increases the image quality with respect to an algorithm used in clinical routine. Robust image quality indicators can be automatically associated with clinical EOS images. Given the consistency of the measures assessed on preview images, these indices could be used to drive an exposure management system in charge of defining the optimal radiation exposure.Nos travaux portent sur la réduction de la dose de rayonnement lors d'examens réalisés avec le Système de radiologie EOS. Deux approches complémentaires sont étudiées. Dans un premier temps, nous proposons une méthode de débruitage et de rehaussement de contraste conjoints pour optimiser le compromis entre la qualité des images et la dose de rayons X. Nous étendons le filtre à moyennes non locales pour restaurer les images EOS. Nous étudions ensuite comment combiner ce filtre à une méthode de rehaussement de contraste multi-échelles. La qualité des images cliniques est optimisée grâce à des fonctions limitant l'augmentation du bruit selon la quantité d’information locale redondante captée par le filtre. Dans un deuxième temps, nous estimons des indices d’exposition (EI) sur les images EOS afin de donner aux utilisateurs un retour immédiat sur la qualité de l'image acquise. Nous proposons ainsi une méthode reposant sur la détection de points de repère qui, grâce à l'exploitation de la redondance de mesures locales, est plus robuste à la présence de données aberrantes que les méthodes existantes. En conclusion, la méthode de débruitage et de rehaussement de contraste conjoints donne des meilleurs résultats que ceux obtenus par un algorithme exploité en routine clinique. La qualité des images EOS peut être quantifiée de manière robuste par des indices calculés automatiquement. Étant donnée la cohérence des mesures sur des images de pré-affichage, ces indices pourraient être utilisés en entrée d'un système de gestion automatique des expositions

Subband variance computation of homoscedastic additive noise in discrete dyadic wavelet transform

The paper deals with noise power variation that occurs when Discrete Dyadic Wavelet Transform (DDWT) is applied to signals affected by Wide Sense Stationary (WSS) additive white noise owing to the use of a non orthonormal expansion. An exact relationship between the noise variance in the original signal and the noise variance in the wavelet coefficients at a generic level is derived. This relationship is crucial in the application of wavelet thresholding for signal denoising to properly select the threshold in each subband.The paper deals with noise power variation that occurs when Discrete Dyadic Wavelet Transform (DDWT) is applied to signals affected by Wide Sense Stationary (WSS) additive white noise owing to the use of a non orthonormal expansion. An exact relationship between the noise variance in the original signal and the noise variance in the wavelet coefficients at a generic level is derived. This relationship is crucial in the application of wavelet thresholding for signal denoising to properly select the threshold in each subband

GPS Stochastic Modelling - Signal Quality Measures and ARMA Processes

This work extends the GPS stochastic model using SNR measurements and time series analysis of observation residuals. The proposed SNR-based observation weighting model significantly improves the results of GPS data analysis, while the temporal correlation of GPS observation noise can be efficiently described by means of ARMA processes. Furthermore, this work includes an up-to-date overview of the GPS error effects and a comprehensive description of various mathematical methods