Adaptive Methods for Video Denoising Based on the ICI, FICI, and RICI Algorithms

In various applications, reducing noise from video sequence is of crucial importance. In this paper, we have presented performance analysis of the novel video denoising method based on the relative intersection of confidence intervals (RICI) rule, and compared it to the methods based on the intersection of confidence intervals (ICI) rule and the fast ICI (FICI) rule. Detailed comparisons, based on two test video signals, are provided for a range of noise levels and different noise types. The RICI video denoising method has shown to outperform the original ICI based method, both in the algorithms execution time, reducing it by up to 11 %, and in the level of noise suppression, improving it by up to 10 dB. It also outperforms the FICI based video denoising method by up to 12.7 dB for the two test videos

Algoritam za brzo uklanjanje šuma iz video signala temeljen na ICI postupku

In this paper, we have proposed a fast method for video denoising using the modified intersection of confidence intervals (ICI) rule, called fast ICI (FICI) method. The goal of the new FICI based video denoising method is to maintain an acceptable quality level of the denoised video estimate, and at the same time to significantly reduce denoising execution time when compared to the original ICI based method. The methods are tested on real-life video signals and their performances are analyzed and compared. It is shown that the FICI method outperforms the ICI method in terms of the execution time reduction by up to 96% (or up to 25 times). However, practical application demands dictate the choice of the video denoising method. If one wants fast denoising method with decent denoising results, the FICI based video denoising method is a better choice. The original ICI method, however, should be used in applications where significant noise suppression is an imperative regardless the computational complexity.U ovom smo radu predložili brzi postupak za uklanjanje šuma iz video signala koristeći modificirano pravilo presjecišta intervala pouzdanosti (eng. intersection of confidence intervals - ICI), nazvano brzim ICI (eng. fast ICI -- FICI) postupkom. Cilj novog FICI postupka za uklanjanje šuma iz video signala jest da se, uz zadržavanje prihvatljive razine kvalitete odšumljenog video signala, značajno smanji vrijeme izvršavanja algoritma u usporedbi s izvornim ICI postupkom. Postupci su testirani na realnim video signalima, a njihove su performanse analizirane i uspoređene.Pokazano je da FICI postupak ima do 96% kraće vrijeme izvršavanja (odnosno kraće i do 25 puta) u usporedi s izvornim ICI postupkom. Međutim, zahtjevi praktične primjene određuju izbor postupka za uklanjanje šuma iz video signala. Ukoliko je potrebno brzo izvršavanje s pristojnim performansama uklanjanja šuma, FICI postupak je bolji izbor. Međutim, u aplikacijama kojima je imperativ značajno suzbijanje šuma bez obzira na računsku složenost, trebao bi se koristiti izvorni ICI postupak

Proximal methods for structured group features and correlation matrix nearness

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de lectura: junio de 2014Optimization is ubiquitous in real life as many of the strategies followed both by nature and by humans aim to minimize a certain cost, or maximize a certain benefit. More specifically, numerous strategies in engineering are designed according to a minimization problem, although usually the problems tackled are convex with a di erentiable objective function, since these problems have no local minima and they can be solved with gradient-based techniques. Nevertheless, many interesting problems are not di erentiable, such as, for instance, projection problems or problems based on non-smooth norms. An approach to deal with them can be found in the theory of Proximal Methods (PMs), which are based on iterative local minimizations using the Proximity Operator (ProxOp) of the terms that compose the objective function. This thesis begins with a general introduction and a brief motivation of the work done. The state of the art in PMs is thoroughly reviewed, defining the basic concepts from the very beginning and describing the main algorithms, as far as possible, in a simple and self-contained way. After that, the PMs are employed in the field of supervised regression, where regularized models play a prominent role. In particular, some classical linear sparse models are reviewed and unified under the point of view of regularization, namely the Lasso, the Elastic–Network, the Group Lasso and the Group Elastic–Network. All these models are trained by minimizing an error term plus a regularization term, and thus they fit nicely in the domain of PMs, as the structure of the problem can be exploited by minimizing alternatively the di erent expressions that compose the objective function, in particular using the Fast Iterative Shrinkage–Thresholding Algorithm (FISTA). As a real-world application, it is shown how these models can be used to forecast wind energy, where they yield both good predictions in terms of the error and, more importantly, valuable information about the structure and distribution of the relevant features. Following with the regularized learning approach, a new regularizer is proposed, called the Group Total Variation, which is a group extension of the classical Total Variation regularizer and thus it imposes constancy over groups of features. In order to deal with it, an approach to compute its ProxOp is derived. Moreover, it is shown that this regularizer can be used directly to clean noisy multidimensional signals (such as colour images) or to define a new linear model, the Group Fused Lasso (GFL), which can be then trained using FISTA. It is also exemplified how this model, when applied to regression problems, is able to provide solutions that identify the underlying problem structure. As an additional result of this thesis, a public software implementation of the GFL model is provided. The PMs are also applied to the Nearest Correlation Matrix problem under observation uncertainty. The original problem consists in finding the correlation matrix which is nearest to the true empirical one. Some variants introduce weights to adapt the confidence given to each entry of the matrix; with a more general perspective, in this thesis the problem is explored directly considering uncertainty on the observations, which is formalized as a set of intervals where the measured matrices lie. Two di erent variants are defined under this framework: a robust approach called the Robust Nearest Correlation Matrix (which aims to minimize the worst-case scenario) and an exploratory approach, the Exploratory Nearest Correlation Matrix (which focuses on the best-case scenario). It is shown how both optimization problems can be solved using the Douglas–Rachford PM with a suitable splitting of the objective functions. The thesis ends with a brief overall discussion and pointers to further work.La optimización está presente en todas las facetas de la vida, de hecho muchas de las estrategias tanto de la naturaleza como del ser humano pretenden minimizar un cierto coste, o maximizar un cierto beneficio. En concreto, multitud de estrategias en ingeniería se diseñan según problemas de minimización, que habitualmente son problemas convexos con una función objetivo diferenciable, puesto que en ese caso no hay mínimos locales y los problemas pueden resolverse mediante técnicas basadas en gradiente. Sin embargo, hay muchos problemas interesantes que no son diferenciables, como por ejemplo problemas de proyección o basados en normas no suaves. Una aproximación para abordar estos problemas son los Métodos Proximales (PMs), que se basan en minimizaciones locales iterativas utilizando el Operador de Proximidad (ProxOp) de los términos de la función objetivo. La tesis comienza con una introducción general y una breve motivación del trabajo hecho. Se revisa en profundidad el estado del arte en PMs, definiendo los conceptos básicos y describiendo los algoritmos principales, dentro de lo posible, de forma simple y auto-contenida. Tras ello, se emplean los PMs en el campo de la regresión supervisada, donde los modelos regularizados tienen un papel prominente. En particular, se revisan y unifican bajo esta perspectiva de regularización algunos modelos lineales dispersos clásicos, a saber, Lasso, Elastic–Network, Lasso Grupal y Elastic–Network Grupal. Todos estos modelos se entrenan minimizando un término de error y uno de regularización, y por tanto encajan perfectamente en el dominio de los PMs, ya que la estructura del problema puede ser aprovechada minimizando alternativamente las diferentes expresiones que componen la función objetivo, en particular mediante el Algoritmo Fast Iterative Shrinkage–Thresholding (FISTA). Como aplicación al mundo real, se muestra que estos modelos pueden utilizarse para predecir energía eólica, donde proporcionan tanto buenos resultados en términos del error como información valiosa sobre la estructura y distribución de las características relevantes. Siguiendo con esta aproximación, se propone un nuevo regularizador, llamado Variación Total Grupal, que es una extensión grupal del regularizador clásico de Variación Total y que por tanto induce constancia sobre grupos de características. Para aplicarlo, se desarrolla una aproximación para calcular su ProxOp. Además, se muestra que este regularizador puede utilizarse directamente para limpiar señales multidimensionales ruidosas (como imágenes a color) o para definir un nuevo modelo lineal, el Fused Lasso Grupal (GFL), que se entrena con FISTA. Se ilustra cómo este modelo, cuando se aplica a problemas de regresión, es capaz de proporcionar soluciones que identifican la estructura subyacente del problema. Como resultado adicional de esta tesis, se publica una implementación software del modelo GFL. Asimismo, se aplican los PMs al problema de Matriz de Correlación Próxima (NCM) bajo incertidumbre. El problema original consiste en encontrar la matriz de correlación más cercana a la empírica verdadera. Algunas variantes introducen pesos para ajustar la confianza que se da a cada entrada de la matriz; con un carácter más general, en esta tesis se explora el problema considerando incertidumbre en las observaciones, que se formaliza como un conjunto de intervalos en el que se encuentran las matrices medidas. Bajo este marco se definen dos variantes: una aproximación robusta llamada NCM Robusta (que minimiza el caso peor) y una exploratoria, NCM Exploratoria (que se centra en el caso mejor). Ambos problemas de optimización pueden resolverse con el PM de Douglas–Rachford y una partición adecuada de las funciones objetivo. La tesis concluye con una discusión global y referencias a trabajo futur

Classification with Asymmetric Label Noise: Consistency and Maximal Denoising

In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are "mutually irreducible," a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. Our results are facilitated by a connection to "mixture proportion estimation," which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach

Line-Field Based Adaptive Image Model for Blind Deblurring

Ph.DDOCTOR OF PHILOSOPH

3D Segmentation & Measurement of Macular Holes

Macular holes are blinding conditions where a hole develops in the central part of retina, resulting in reduced central vision. The prognosis and treatment options are related to a number of variables including the macular hole size and shape. In this work we introduce a method to segment and measure macular holes in three-dimensional (3D) data. High-resolution spectral domain optical coherence tomography (SD-OCT) allows precise imaging of the macular hole geometry in three dimensions, but the measurement of these by human observers is time consuming and prone to high inter- and intra-observer variability, being characteristically measured in 2D rather than 3D. This work introduces several novel techniques to automatically retrieve accurate 3D measurements of the macular hole, including surface area, base area, base diameter, top area, top diameter, height, and minimum diameter. Specifically, it is introducing a multi-scale 3D level set segmentation approach based on a state-of-the-art level set method, and introducing novel curvature-based cutting and 3D measurement procedures. The algorithm is fully automatic, and we validate the extracted measurements both qualitatively and quantitatively, where the results show the method to be robust across a variety of scenarios. A segmentation software package is presented for targeting medical and biological applications, with a high level of visual feedback and several usability enhancements over existing packages. Specifically, it is providing a substantially faster graphics processing unit (GPU) implementation of the local Gaussian distribution fitting (LGDF) energy model, which can segment inhomogeneous objects with poorly defined boundaries as often encountered in biomedical images. It also provides interactive brushes to guide the segmentation process in a semi-automated framework. The speed of implementation allows us to visualise the active surface in real-time with a built-in ray tracer, where users may halt evolution at any timestep to correct implausible segmentation by painting new blocking regions or new seeds. Quantitative and qualitative validation is presented, demonstrating the practical efficacy of the interactive elements for a variety of real-world datasets. The size of macular holes is known to be one of the strongest predictors of surgical success both anatomically and functionally. Furthermore, it is used to guide the choice of treatment, the optimum surgical approach and to predict outcome. Our automated 3D image segmentation algorithm has extracted 3D shape-based macular hole measurements and described the dimensions and morphology. Our approach is able to robustly and accurately measure macular hole dimensions. This thesis is considered as a significant contribution for clinical applications particularly in the field of macular hole segmentation and shape analysis

Joint 1D and 2D Neural Networks for Automatic Modulation Recognition

The digital communication and radar community has recently manifested more interest in using data-driven approaches for tasks such as modulation recognition, channel estimation and distortion correction. In this research we seek to apply an object detector for parameter estimation to perform waveform separation in the time and frequency domain prior to classification. This enables the full automation of detecting and classifying simultaneously occurring waveforms. We leverage a lD ResNet implemented by O\u27Shea et al. in [1] and the YOLO v3 object detector designed by Redmon et al. in [2]. We conducted an in depth study of the performance of these architectures and integrated the models to perform joint detection and classification. To our knowledge, the present research is the first to study and successfully combine a lD ResNet classifier and Yolo v3 object detector to fully automate the process of AMR for parameter estimation, pulse extraction and waveform classification for non-cooperative scenarios. The overall performance of the joint detector/ classifier is 90 at 10 dB signal to noise ratio for 24 digital and analog modulations

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition