Applied Harmonic Analysis and Sparse Approximation

Efficiently analyzing functions, in particular multivariate functions, is a key problem in applied mathematics. The area of applied harmonic analysis has a significant impact on this problem by providing methodologies both for theoretical questions and for a wide range of applications in technology and science, such as image processing. Approximation theory, in particular the branch of the theory of sparse approximations, is closely intertwined with this area with a lot of recent exciting developments in the intersection of both. Research topics typically also involve related areas such as convex optimization, probability theory, and Banach space geometry. The workshop was the continuation of a first event in 2012 and intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations

Exploiting Cross Domain Relationships for Target Recognition

Cross domain recognition extracts knowledge from one domain to recognize samples from another domain of interest. The key to solving problems under this umbrella is to find out the latent connections between different domains. In this dissertation, three different cross domain recognition problems are studied by exploiting the relationships between different domains explicitly according to the specific real problems. First, the problem of cross view action recognition is studied. The same action might seem quite different when observed from different viewpoints. Thus, how to use the training samples from a given camera view and perform recognition in another new view is the key point. In this work, reconstructable paths between different views are built to mirror labeled actions from one source view into one another target view for learning an adaptable classifier. The path learning takes advantage of the joint dictionary learning techniques with exploiting hidden information in the seemingly useless samples, making the recognition performance robust and effective. Second, the problem of person re-identification is studied, which tries to match pedestrian images in non-overlapping camera views based on appearance features. In this work, we propose to learn a random kernel forest to discriminatively assign a specific distance metric to each pair of local patches from the two images in matching. The forest is composed by multiple decision trees, which are designed to partition the overall space of local patch-pairs into substantial subspaces, where a simple but effective local metric kernel can be defined to minimize the distance of true matches. Third, the problem of multi-event detection and recognition in smart grid is studied. The signal of multi-event might not be a straightforward combination of some single-event signals because of the correlation among devices. In this work, a concept of ``root-pattern\u27\u27 is proposed that can be extracted from a collection of single-event signals, but also transferable to analyse the constituent components of multi-cascading-event signals based on an over-complete dictionary, which is designed according to the ``root-patterns\u27\u27 with temporal information subtly embedded. The correctness and effectiveness of the proposed approaches have been evaluated by extensive experiments

Sparse Representations & Compressed Sensing with application to the problem of Direction-of-Arrival estimation.

PhDThe significance of sparse representations has been highlighted in numerous signal processing applications ranging from denoising to source separation and the emerging field of compressed sensing has provided new theoretical insights into the problem of inverse systems with sparsity constraints. In this thesis, these advances are exploited in order to tackle the problem of direction-of-arrival (DOA) estimation in sensor arrays. Assuming spatial sparsity e.g. few sources impinging on the array, the problem of DOA estimation is formulated as a sparse representation problem in an overcomplete basis. The resulting inverse problem can be solved using typical sparse recovery methods based on convex optimization i.e. `1 minimization. However, in this work a suite of novel sparse recovery algorithms is initially developed, which reduce the computational cost and yield approximate solutions. Moreover, the proposed algorithms of Polytope Faces Pursuits (PFP) allow for the induction of structured sparsity models on the signal of interest, which can be quite beneficial when dealing with multi-channel data acquired by sensor arrays, as it further reduces the complexity and provides performance gain under certain conditions. Regarding the DOA estimation problem, experimental results demonstrate that the proposed methods outperform popular subspace based methods such as the multiple signal classification (MUSIC) algorithm in the case of rank-deficient data (e.g. presence of highly correlated sources or limited amount of data) for both narrowband and wideband sources. In the wideband scenario, they can also suppress the undesirable effects of spatial aliasing. However, DOA estimation with sparsity constraints has its limitations. The compressed sensing requirement of incoherent dictionaries for robust recovery sets limits to the resolution capabilities of the proposed method. On the other hand, the unknown parameters are continuous and therefore if the true DOAs do not belong to the predefined discrete set of potential locations the algorithms' performance will degrade due to errors caused by mismatches. To overcome this limitation, an iterative alternating descent algorithm for the problem of off-grid DOA estimation is proposed that alternates between sparse recovery and dictionary update estimates. Simulations clearly illustrate the performance gain of the algorithm over the conventional sparsity approach and other existing off-grid DOA estimation algorithms.EPSRC Leadership Fellowship EP/G007144/1; EU FET-Open Project FP7-ICT-225913

Graph Filters for Signal Processing and Machine Learning on Graphs

Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural networks. Increasingly, modern data also reside on networks and other irregular domains whose structure is better captured by a graph. To process and learn from such data, graph filters account for the structure of the underlying data domain. In this article, we provide a comprehensive overview of graph filters, including the different filtering categories, design strategies for each type, and trade-offs between different types of graph filters. We discuss how to extend graph filters into filter banks and graph neural networks to enhance the representational power; that is, to model a broader variety of signal classes, data patterns, and relationships. We also showcase the fundamental role of graph filters in signal processing and machine learning applications. Our aim is that this article provides a unifying framework for both beginner and experienced researchers, as well as a common understanding that promotes collaborations at the intersections of signal processing, machine learning, and application domains

Cloud removal from optical remote sensing images

Optical remote sensing images used for Earth surface observations are constantly contaminated by cloud cover. Clouds dynamically affect the applications of optical data and increase the difficulty of image analysis. Therefore, cloud is considered as one of the sources of noise in optical image data, and its detection and removal need to be operated as a pre-processing step in most remote sensing image processing applications. This thesis investigates the current cloud detection and removal algorithms and develops three new cloud removal methods to improve the accuracy of the results. A thin cloud removal method based on signal transmission principles and spectral mixture analysis (ST-SMA) for pixel correction is developed in the first contribution. This method considers not only the additive reflectance from the clouds but also the energy absorption when solar radiation passes through them. Data correction is achieved by subtracting the product of the cloud endmember signature and the cloud abundance and rescaling according to the cloud thickness. The proposed method has no requirement for meteorological data and does not rely on reference images. The experimental results indicate that the proposed approach is able to perform effective removal of thin clouds in different scenarios. In the second study, an effective cloud removal method is proposed by taking advantage of the noise-adjusted principal components transform (CR-NAPCT). It is found that the signal-to-noise ratio (S/N) of cloud data is higher than data without cloud contamination, when spatial correlation is considered and are shown in the first NAPCT component (NAPC1) in the NAPCT data. An inverse transformation with a modified first component is then applied to generate the cloud free image. The effectiveness of the proposed method is assessed by performing experiments on simulated and real data to compare the quantitative and qualitative performance of the proposed approach. The third study of this thesis deals with both cloud and cloud shadow problems with the aid of an auxiliary image in a clear sky condition. A new cloud removal approach called multitemporal dictionary learning (MDL) is proposed. Dictionaries of the cloudy areas (target data) and the cloud free areas (reference data) are learned separately in the spectral domain. An online dictionary learning method is then applied to obtain the two dictionaries in this method. The removal process is conducted by using the coefficients from the reference image and the dictionary learned from the target image. This method is able to recover the data contaminated by thin and thick clouds or cloud shadows. The experimental results show that the MDL method is effective from both quantitative and qualitative viewpoints

From spline wavelet to sampling theory on circulant graphs and beyond– conceiving sparsity in graph signal processing

Graph Signal Processing (GSP), as the field concerned with the extension of classical signal processing concepts to the graph domain, is still at the beginning on the path toward providing a generalized theory of signal processing. As such, this thesis aspires to conceive the theory of sparse representations on graphs by traversing the cornerstones of wavelet and sampling theory on graphs. Beginning with the novel topic of graph spline wavelet theory, we introduce families of spline and e-spline wavelets, and associated filterbanks on circulant graphs, which lever- age an inherent vanishing moment property of circulant graph Laplacian matrices (and their parameterized generalizations), for the reproduction and annihilation of (exponen- tial) polynomial signals. Further, these families are shown to provide a stepping stone to generalized graph wavelet designs with adaptive (annihilation) properties. Circulant graphs, which serve as building blocks, facilitate intuitively equivalent signal processing concepts and operations, such that insights can be leveraged for and extended to more complex scenarios, including arbitrary undirected graphs, time-varying graphs, as well as associated signals with space- and time-variant properties, all the while retaining the focus on inducing sparse representations. Further, we shift from sparsity-inducing to sparsity-leveraging theory and present a novel sampling and graph coarsening framework for (wavelet-)sparse graph signals, inspired by Finite Rate of Innovation (FRI) theory and directly building upon (graph) spline wavelet theory. At its core, the introduced Graph-FRI-framework states that any K-sparse signal residing on the vertices of a circulant graph can be sampled and perfectly reconstructed from its dimensionality-reduced graph spectral representation of minimum size 2K, while the structure of an associated coarsened graph is simultaneously inferred. Extensions to arbitrary graphs can be enforced via suitable approximation schemes. Eventually, gained insights are unified in a graph-based image approximation framework which further leverages graph partitioning and re-labelling techniques for a maximally sparse graph wavelet representation.Open Acces

Signal and data processing for machine olfaction and chemical sensing: A review

Signal and data processing are essential elements in electronic noses as well as in most chemical sensing instruments. The multivariate responses obtained by chemical sensor arrays require signal and data processing to carry out the fundamental tasks of odor identification (classification), concentration estimation (regression), and grouping of similar odors (clustering). In the last decade, important advances have shown that proper processing can improve the robustness of the instruments against diverse perturbations, namely, environmental variables, background changes, drift, etc. This article reviews the advances made in recent years in signal and data processing for machine olfaction and chemical sensing

Intelligent Biosignal Processing in Wearable and Implantable Sensors

This reprint provides a collection of papers illustrating the state-of-the-art of smart processing of data coming from wearable, implantable or portable sensors. Each paper presents the design, databases used, methodological background, obtained results, and their interpretation for biomedical applications. Revealing examples are brain–machine interfaces for medical rehabilitation, the evaluation of sympathetic nerve activity, a novel automated diagnostic tool based on ECG data to diagnose COVID-19, machine learning-based hypertension risk assessment by means of photoplethysmography and electrocardiography signals, Parkinsonian gait assessment using machine learning tools, thorough analysis of compressive sensing of ECG signals, development of a nanotechnology application for decoding vagus-nerve activity, detection of liver dysfunction using a wearable electronic nose system, prosthetic hand control using surface electromyography, epileptic seizure detection using a CNN, and premature ventricular contraction detection using deep metric learning. Thus, this reprint presents significant clinical applications as well as valuable new research issues, providing current illustrations of this new field of research by addressing the promises, challenges, and hurdles associated with the synergy of biosignal processing and AI through 16 different pertinent studies. Covering a wide range of research and application areas, this book is an excellent resource for researchers, physicians, academics, and PhD or master students working on (bio)signal and image processing, AI, biomaterials, biomechanics, and biotechnology with applications in medicine

Application of sound source separation methods to advanced spatial audio systems

This thesis is related to the field of Sound Source Separation (SSS). It addresses the development and evaluation of these techniques for their application in the resynthesis of high-realism sound scenes by means of Wave Field Synthesis (WFS). Because the vast majority of audio recordings are preserved in twochannel stereo format, special up-converters are required to use advanced spatial audio reproduction formats, such as WFS. This is due to the fact that WFS needs the original source signals to be available, in order to accurately synthesize the acoustic field inside an extended listening area. Thus, an object-based mixing is required. Source separation problems in digital signal processing are those in which several signals have been mixed together and the objective is to find out what the original signals were. Therefore, SSS algorithms can be applied to existing two-channel mixtures to extract the different objects that compose the stereo scene. Unfortunately, most stereo mixtures are underdetermined, i.e., there are more sound sources than audio channels. This condition makes the SSS problem especially difficult and stronger assumptions have to be taken, often related to the sparsity of the sources under some signal transformation. This thesis is focused on the application of SSS techniques to the spatial sound reproduction field. As a result, its contributions can be categorized within these two areas. First, two underdetermined SSS methods are proposed to deal efficiently with the separation of stereo sound mixtures. These techniques are based on a multi-level thresholding segmentation approach, which enables to perform a fast and unsupervised separation of sound sources in the time-frequency domain. Although both techniques rely on the same clustering type, the features considered by each of them are related to different localization cues that enable to perform separation of either instantaneous or real mixtures.Additionally, two post-processing techniques aimed at improving the isolation of the separated sources are proposed. The performance achieved by several SSS methods in the resynthesis of WFS sound scenes is afterwards evaluated by means of listening tests, paying special attention to the change observed in the perceived spatial attributes. Although the estimated sources are distorted versions of the original ones, the masking effects involved in their spatial remixing make artifacts less perceptible, which improves the overall assessed quality. Finally, some novel developments related to the application of time-frequency processing to source localization and enhanced sound reproduction are presented.Cobos Serrano, M. (2009). Application of sound source separation methods to advanced spatial audio systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8969Palanci

Bayesian image restoration and bacteria detection in optical endomicroscopy

Optical microscopy systems can be used to obtain high-resolution microscopic images of tissue cultures and ex vivo tissue samples. This imaging technique can be translated for in vivo, in situ applications by using optical fibres and miniature optics. Fibred optical endomicroscopy (OEM) can enable optical biopsy in organs inaccessible by any other imaging systems, and hence can provide rapid and accurate diagnosis in a short time. The raw data the system produce is difficult to interpret as it is modulated by a fibre bundle pattern, producing what is called the “honeycomb effect”. Moreover, the data is further degraded due to the fibre core cross coupling problem. On the other hand, there is an unmet clinical need for automatic tools that can help the clinicians to detect fluorescently labelled bacteria in distal lung images. The aim of this thesis is to develop advanced image processing algorithms that can address the above mentioned problems. First, we provide a statistical model for the fibre core cross coupling problem and the sparse sampling by imaging fibre bundles (honeycomb artefact), which are formulated here as a restoration problem for the first time in the literature. We then introduce a non-linear interpolation method, based on Gaussian processes regression, in order to recover an interpretable scene from the deconvolved data. Second, we develop two bacteria detection algorithms, each of which provides different characteristics. The first approach considers joint formulation to the sparse coding and anomaly detection problems. The anomalies here are considered as candidate bacteria, which are annotated with the help of a trained clinician. Although this approach provides good detection performance and outperforms existing methods in the literature, the user has to carefully tune some crucial model parameters. Hence, we propose a more adaptive approach, for which a Bayesian framework is adopted. This approach not only outperforms the proposed supervised approach and existing methods in the literature but also provides computation time that competes with optimization-based methods