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Images are often corrupted by noise which reduces their visual quality and interferes with analysis. Convolutional Neural Networks (CNNs) have become a popular method for denoising images, but their training typically relies on access to thousands of pairs of noisy and clean versions of the same underlying picture. Unsupervised methods lack this requirement and can instead be trained purely using noisy images. This thesis evaluated two different unsupervised denoising algorithms: Noise2Self (N2S) and Parametric Probabilistic Noise2Void (PPN2V), both of which train an internal CNN to denoise images. Four different CNNs were tested in order to investigate how the performance of these algorithms would be affected by different network architectures. The testing used two different datasets: one containing clean images corrupted by synthetic noise, and one containing images damaged by real noise originating from the camera used to capture them. Two of the networks, UNet and a CBAM-augmented UNet resulted in high performance competitive with the strong classical denoisers BM3D and NLM. The other two networks - GRDN and MultiResUNet - on the other hand generally caused poor performance.

Mass Spectrometry, especially matrix assisted laser desorption/ionization (MALDI) time of flight (TOF), is emerging as a leading technique in the proteomics revolution. It can be used to find disease-related protein patterns in mixtures of proteins derived from easily obtained samples. In this paper, a novel algorithm for MALDI-TOF MS data processing is developed. The software design includes the application of splines for data smoothing and baseline correction, wavelets for adaptive denoising, multivariable statistics techniques such as clustering analysis, and signal processing techniques to evaluate the complicated biological signals. A MatLab implementation shows the processing steps consecutively including step-interval unification, adaptive wavelet denoising, baseline correction, normalization, and peak detection and alignment for biomarker discovery.

This study evaluates noise robustness of convolutional autoencoders and neural networks for classification of Low Probability of Intercept (LPI) radar modulation type. Specifically, a number of different neural network architectures are tested in four different synthetic noise environments. Tests in Gaussian noise show that performance is decreasing with decreasing Signal to Noise Ratio (SNR). Training a network on all SNRs in the dataset achieved a peak performance of 70.8 % at SNR=-6 dB with a denoising autoencoder and convolutional classifier setup. Tests indicate that the models have a difficult time generalizing to SNRs lower than what is provided in training data, performing roughly 10-20% worse than when those SNRs are included in the training data. If intermediate SNRs are removed from the training data the models can generalize and perform similarly to tests where, intermediate noise levels are included in the training data. When testing data is generated with different parameters to training data performance is underwhelming, with a peak performance of 22.0 % at SNR=-6 dB. The last tests done use telecom signals as additive noise instead of Gaussian noise. These tests are performed when the LPI and telecom signals appear at different frequencies. The models preform well on such cases with a peak performance of 80.3 % at an intermidiate noise level. This study also contribute with a different, and more realistic, way of generating data than what is prevalent in literature as well as a network that performs well without the need for signal preprocessing. Without preprocessing a peak performance of 64.9 % was achieved at SNR=-6 dB. It is customary to generate data such that each sample always includes the start of its signals period which increases performance by around 20 % across all tests. In a real application however it is not certain that the start of a received signal can be determined. / Detta arbete studerar brustålighet hos neurala nätverk för klassificering av \textit{låg sannolikhet för avlyssning} (LPI) radars modulationstyp. Specifikt testas ett antal arkitekturer baserade på faltningsnätverk och evalueras i fyra olika syntetiska brusmiljöer. Tester genomförda på data med Gaussiskt brus visar att klasificeringsfelet är ökande med ett minskande signal-till-brusförhållande. Om man låter nätverken träna på alla brusnivåer som ingår i datan uppnås en högsta pricksäkerhet om 70.8 % vid ett signal-till-brusförhållande på -6 dB. Vidare tester tyder på att nätverken presterar sämre på låga signal-till-brusförhållanden om de inte finns med i träningsdata och ger i allmänhet mellan 10-20 % sämre pricksäkerhet. Om de mellersta brusnivåerna inte finns med i träningsdata presterar nätverken lika bra som när de finns med i träningsdata. Om träningsdata och testdata genereras med olika parameterar presterar nätverken dåligt. För dessa tester uppnås en högsta pricksäkerhet om 22.0 % vid ett signal-till-brusförhållande på -6 dB. Den sista brusmiljön som testades på använder sig av telekom signaler som om de vore brus istället för Gaussiskt brus. I detta fall är LPI och telekom signalerna väl skiljda i frekvens och nätverken presterar lika bra som tester i Gaussiskt brus med högt signal-till-brusförhållande. Högsta pricksäkerhet som uppnåts på dessa tester är 80.3 % i mellanhög brusnivå. Detta arbete bidrar även med nätverk som presterar bra utan att data behöver signalbehandlas innnan den kan klassificeras samt genererar data på ett mer realistiskt vis än tidigare litteratur inom detta område. Utan att signalbehandla data uppnåddes en högsta pricksäkerhet om 64.9 % vid ett signal-till-brusförhållande på -6 dB. Den mer realistiska datan genereras så att dess startpunkt är slumpmässig. I litteraturen brukar startpunkten inkluderas och uppnår på så vis överlag pricksäkerheter som är ungefär 20 % högre än de tester som genomförs i detta arbete. I verkliga applikationer är det sällan man kan identifera en signals startpunkt med säkerhet.

A denoising autoencoder is a type of neural network which excels at removingnoise from noisy input data. In this project, a denoising autoencoder isoptimized for removing noise from mobile positioning data. The mobilepositioning data with noise is generated specifically for this project. In orderto generate realistic noise, a study in how real world noise looks like is carriedout. The project aims to answer the question: can a denoising autoencoderbe used to remove noise from mobile positioning data? The results showthat using this method can effectively cut the noise in half. In this reportit is mainly analyzed how the amount of hidden layers and respective sizesaffected the performance. It was concluded that the most optimal design forthe autoencoder was a single hidden layer model with multiple more nodes inthe hidden layer than the input and output layer. / En brusreducerande autoencoder är ett sorts neuralt nätverk som är specialiserat för att ta bort brus från indata. I detta projekt optimeras en brusreducerande autoencoder för att ta bort brus från mobilpositioneringsdata. Till projektet skapades helt ny mobilpositioneringsdata med realistiskt brus. Detta gjordes genom att studera hur verkligt brus ser ut och skapa ett program som efterliknar detta. Projektets syfte var att undersöka om en brusreducerande autoencoder kan användas för att ta bort brus från mobilpositioneringsdata. Resultaten visar att metoden kan ta bort ungefär hälften av bruset. I rapporten undersöks och analyseras även hur antalet dolda lager och antalet noder i dessa lager påverkade mängden brus som autoencodern lyckades ta bort. Från de gjorda testerna drogs slutsatsen att den mest optimala designen var en enkel design med ett enda dolt lager som hade betydligt fler noder än input- och outputlagren.

Arterial spin labeling (ASL) perfusion Magnetic Resonance Imaging (MRI) is a noninvasive technique for measuring quantitative cerebral blood flow (CBF) but subject to an inherently low signal-to-noise-ratio (SNR), resulting in a big challenge for data processing. Traditional post-processing methods have been proposed to reduce artifacts, suppress non-local noise, and remove outliers. However, these methods are based on either implicit or explicit models of the data, which may not be accurate and may change across subjects. Deep learning (DL) is an emerging machine learning technique that can learn a transform function from acquired data without using any explicit hypothesis about that function. Such flexibility may be particularly beneficial for ASL denoising. In this dissertation, three different machine learning-based methods are proposed to improve the image quality of ASL MRI: 1) a learning-from-noise method, which does not require noise-free references for DL training, was proposed for DL-based ASL denoising and BOLD-to-ASL prediction; 2) a novel deep learning neural network that combines dilated convolution and wide activation residual blocks was proposed to improve the image quality of ASL CBF while reducing ASL acquisition time; 3) a prior-guided and slice-wise adaptive outlier cleaning algorithm was developed for ASL MRI. In the first part of this dissertation, a learning-from-noise method is proposed for DL-based method for ASL denoising. The proposed learning-from-noise method shows that DL-based ASL denoising models can be trained using only noisy image pairs, without any deliberate post-processing for obtaining the quasi-noise-free reference during the training process. This learning-from-noise method can also be applied to DL-based ASL perfusion prediction from BOLD fMRI as ASL references are extremely noisy in this BOLD-to-ASL prediction. Experimental results demonstrate that this learning-from-noise method can reliably denoise ASL MRI and predict ASL perfusion from BOLD fMRI, result in improved signal-to-noise-ration (SNR) of ASL MRI. Moreover, by using this method, more training data can be generated, as it requires fewer samples to generate quasi-noise-free references, which is particularly useful when ASL CBF data are limited. In the second part of this dissertation, we propose a novel deep learning neural network, i.e., Dilated Wide Activation Network (DWAN), that is optimized for ASL denoising. Our method presents two novelties: first, we incorporated the wide activation residual blocks with a dilated convolution neural network to achieve improved denoising performance in term of several quantitative and qualitative measurements; second, we evaluated our proposed model given different inputs and references to show that our denoising model can be generalized to input with different levels of SNR and yields images with better quality than other methods. In the final part of this dissertation, a prior-guided and slice-wise adaptive outlier cleaning (PAOCSL) method is proposed to improve the original Adaptive Outlier Cleaning (AOC) method. Prior information guided reference CBF maps are used to avoid bias from extreme outliers in the early iterations of outlier cleaning, ensuring correct identification of the true outliers. Slice-wise outlier rejection is adapted to reserve slices with CBF values in the reasonable range even they are within the outlier volumes. Experimental results show that the proposed outlier cleaning method improves both CBF quantification quality and CBF measurement stability. / Electrical and Computer Engineering

We explore the applicability of local polynomial approximation of signals for noise suppression. In the context of data regression, Savitzky and Golay showed that least-squares approximation of data with a polynomial of fixed order, together with a constant window length, is identical to convolution with a finite impulse response filter, whose characteristics depend entirely on two parameters, namely, the order and window length. Schafer’s recent article in IEEE Signal Processing Magazine provides a detailed account of one-dimensional Savitzky-Golay (SG) filters. Drawing motivation from this idea, we present an elaborate study of two-dimensional SG filters and employ them for image denoising by optimizing the filter response to minimize the mean-squared error (MSE) between the original image and the filtered output. The key contribution of this thesis is a method for optimal selection of order and window length of SG filters for denoising images. First, we apply the denoising technique for images contaminated by additive Gaussian noise. Owing to the absence of ground truth in practice, direct minimization of the MSE is infeasible. However, the classical work of C. Stein provides a statistical method to overcome the hurdle. Based on Stein’s lemma, an estimate of the MSE, namely Stein’s unbiased risk estimator (SURE), is derived, and the two critical parameters of the filter are optimized to minimize the cost. The performance of the technique improves when a regularization term, which penalizes fast variations in the estimate, is added to the optimization cost. In the next three chapters, we focus on non-Gaussian noise models. In Chapter 3, image degradation in the presence of a compound noise model, where images are corrupted by mixed Poisson-Gaussian noise, is addressed. Inspired by Hudson’s identity, an estimate of MSE, namely Poisson unbiased risk estimator (PURE), which is analogous to SURE, is developed. Combining both lemmas, Poisson-Gaussian unbiased risk estimator (PGURE) minimization is performed to obtain the optimal filter parameters. We also show that SG filtering provides better lowpass approximation for a multiresolution denoising framework. In Chapter 4, we employ SG filters for reducing multiplicative noise in images. The standard SG filter frequency response can be controlled along horizontal or vertical directions. This limits its ability to capture oriented features and texture that lie at other angles. Here, we introduce the idea of steering the SG filter kernel and perform mean-squared error minimization based on the new concept of multiplicative noise unbiased risk estimation (MURE). Finally, we propose a method to robustify SG filters, robustness to deviation from Gaussian noise statistics. SG filters work on the principle of least-squares error minimization, and are hence compatible with maximum-likelihood (ML) estimation in the context of Gaussian statistics. However, for heavily-tailed noise such as the Laplacian, where ML estimation requires mean-absolute error minimization in lieu of MSE minimization, standard SG filter performance deteriorates. `1 minimization is a challenge since there is no closed-form solution. We solve the problem by inducing the `1-norm criterion using the iteratively reweighted least-squares (IRLS) method. At every iteration, we solve an l`2 problem, which is equivalent to optimizing a weighted SG filter, but, as iterations progress, the solution converges to that corresponding to `1 minimization. The results thus obtained are superior to those obtained using the standard SG filter.

This dissertation explores the potential of EMD as analyzing tool for audio and speech processing. This signal expansion into IMFs is adaptive and without any prior assumptions (stationarity and linearity) on the signal to be analyzed. Salient properties of EMD such as dyadic filter bank structure, quasi-symmetry of IMF and fully description of IMF by its extrema, are exploited for denoising, coding and watermarking purposes. In speech signals denoising, we initially proposed a technique based on IMFs thresholding. A comparative analysis of performance of this technique compared to the denoising technique based on the wavelet. Then, to remedy the problem of the MMSE filters which requires an estimation of the spectral properties of noise, we introduced the ACWA filter in the denoising procedure. The proposed approach is consisted to filter all IMFs of the noisy signal by ACWA filter. This filtering approach is implemented in the time domain, and also applicable in the context of colored noise. Finally, to handle the case of hybrid speech frames, that is composed of voiced and unvoiced speech, we introduced a stationarity index in the denoising approach to detect the transition between the mixture of voiced and unvoiced sounds. In audio signals coding, we proposed four compression approaches. The first two approaches are based on the EMD, and the other two approaches exploit the EMD in association with Hilbert transform. In particular, we proposed to use a predictive coding of the instantaneous amplitude and frequency of the IMFs Finally, we studied the problem of audio signals watermarking in context of copyright protection. The number of IMFs can be variable depending on the attack type. The proposed approach involves inserting the mark in the extrema of last IMFs. In addition, we introduced a synchronization code in the procedure in order to facility the extraction of the mark. These contributions are illustrated on synthetic and real data and results compared to well established methods such as MMSE filter, wavelets approach, MP3 and AAC coders showing the good performances of EMD based signal processes. These findings demonstrate the real potential of EMD as analyzing tool (in adaptive way) in speech and audio processing.

[pt] Nos últimos anos, vários mecanismos permitem medir campos vetoriais reais, provendo uma compreensão melhor de fenômenos importantes, tais como dinâmica de fluidos ou movimentos de fluido cerebral. Isso abre um leque de novos desafios a visualização e análise de campos vetoriais em muitas aplicações de engenharia e de medicina por exemplo. Em particular, dados reais são geralmente corrompidos por ruído, dificultando a compreensão na hora da visualização. Esta informação necessita de uma etapa de remoção de ruído como pré-processamento, no entanto remoção de ruído normalmente remove as descontinuidades e singularidades, que são fundamentais para a análise do campo vetorial. Nesta dissertação é proposto um método inovador para remoção de ruído em campo vetorial baseado em caminhadas aleatórias que preservam certas descontinuidades. O método funciona em um ambiente desestruturado, sendo rápido, simples de implementar e mostra um desempenho melhor do que a tradicional técnica Gaussiana de remoção de ruído. Esta tese propõe também uma metodologia semi-automática para remover ruído, onde o usuário controla a escala visual da filtragem, levando em consideração as mudanças topológicas que ocorrem por causa da filtragem. / [en] In recent years, several devices allow to measure real vector fields, leading to a better understanding of fundamental phenomena such as fluid dynamics or brain water movements. This gives vector field visualization and analysis new challenges in many applications in engineering and in medicine. In particular real data is generally corrupted by noise, puzzling the understanding provided by visualization tools. This data needs a denoising step as preprocessing, however usual denoising removes discontinuities and singularities, which are fundamental for vector field analysis. In this dissertation a novel method for vector field denoising based on random walks is proposed which preserves certain discontinuities. It works in a unstructured setting; being fast, simple to implement, and shows a better performance than the traditional Gaussian denoising technique. This dissertation also proposes a semi-automatic vector field denoising methodology, where the user visually controls the filtering scale by validating topological changes caused by classical vector field filtering.

O objetivo deste trabalho é apresentar um novo método para a remoção do ruído Poisson em imagens de mamografia digital adquiridas com baixa dosagem de radiação. Sabe-se que a mamografia por raios X é o exame mais eficiente para a detecção precoce do câncer de mama, aumentando consideravelmente as chances de cura da doença. No entanto, a radiação absorvida pela paciente durante o exame ainda é um problema a ser tratado. Estudos indicam que a exposição à radiação pode induzir a formação do câncer em algumas mulheres radiografadas. Apesar desse número ser significativamente baixo em relação ao número de mulheres que são salvas pelo exame, existe a necessidade do desenvolvimento de meios que viabilizem a diminuição da dose de radiação empregada. No entanto, uma redução na dose de radiação piora a qualidade da imagem pela diminuição da relação sinal-ruído, prejudicando o diagnóstico médico e a detecção precoce da doença. Nesse sentido, a proposta deste trabalho é apresentar um método para a filtragem do ruído Poisson que é adicionado às das imagens mamográficas quando adquiridas com baixa dosagem de radiação, fazendo com que ela apresente qualidade equivalente àquela adquirida com a dose padrão de radiação. O algoritmo proposto foi desenvolvido baseado em adaptações de algoritmos bem estabelecidos na literatura, como a filtragem no domínio Wavelet, aqui usando o Shrink-thresholding (WTST), e o Block-matching and 3D Filtering (BM3D). Os resultados obtidos com imagens mamográficas adquiridas com phantom e também imagens clínicas, mostraram que o método proposto é capaz de filtrar o ruído adicional incorporado nas imagens sem perda aparente de informação. / The aim of this work is to present a novel method for removing the Poisson noise in digital mammography images acquired with reduced radiation dose. It is known that the X-ray mammography is the most effective exam for early detection of breast cancer, greatly increasing the chances of healing the disease. However, the radiation absorbed by the patient during the exam is still a problem to be treated. Some studies showed that mammography can induce breast cancer in a few women. Although this number is significantly low compared to the number of women who are saved by the exam, it is important to develop methods to enable the reduction of the radiation dose used in the exam. However, dose reduction led to a decrease in image quality by means of the signal to noise ratio, impairing medical diagnosis and the early detection of the disease. In this sense, the purpose of this study is to propose a new method to reduce Poisson noise in mammographic images acquired with low radiation dose, in order to achive the same quality as those acquired with the standard dose. The method is based on well established algorithms in the literature as the filtering in Wavelet domain, here using Shrink-thresholding (WTST) and the Block-matching and 3D Filtering (BM3D). Results using phantom and clinical images showed that the proposed algorithm is capable of filtering the additional noise in images without apparent loss of information.