Analytic signal | EPFL Graph Search

In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform. The analytic representation of a real-valued function is an analytic signal, comprising the original function and its Hilbert transform. This representation facilitates many mathematical manipulations. The basic idea is that the negative frequency components of the Fourier transform (or spectrum) of a real-valued function are superfluous, due to the Hermitian symmetry of such a spectrum. These negative frequency components can be discarded with no loss of information, provided one is willing to deal with a complex-valued function instead. That makes certain attributes of the function more accessible and facilitates the derivation of modulation and demodulation techniques, such as single-sideband. As long as the manipulated f

High resolution eddy current inspection and eddy current testing for additive manufacturing

David Florian Hippert

Non-destructive testing (NDT) is one of the key method developed for the safety mechanism of many industrial fields, e.g. aerospace, oil and gas and power industries. Among the NDT techniques, eddy current testing belongs to the well-established ones and has been used since the 1940s. Eddy current testing is widely used to detect defects in electrically conducting materials, especially surface breaking ones. Many devices and developments push the eddy current testing to a highly technical level. Eddy current testing applied to NDT is a normalized technique that is performed by certified inspectors. These have received a specific training to interpret the complex signals produced by the eddy current equipment. One key challenge of the interpretation of the eddy current signals is caused by variations of the conditions and material properties that affect the response. Nowadays, the inspectors need a deep understanding of physics and in some cases years of experience for an accurate defect identification. The field of rapid prototyping is one of the most growing and successful areas in the industrial world in the past years. News topics show that this technique is becoming more and more rapid manufacturing. Already nowadays, parts are built with rapid prototyping and used for demonstrations and functional concept studies. But the failure rate of built objects with rapid prototyping, especially metallic ones, is still high. There is therefore a demand for so called "quality machines" able to control the quality of the manufactured components, if possible in situ and to generate the corresponding documentation. Industries and universities are undertaking projects and research in that direction and the eddy current technique has been identified as a potential candidate to reach this goal. In this context, we identified three specific needs for the eddy current non-destructive testing. Firstly, for many applications the accurate size and dimensions of the defects are necessary to estimate the remaining lifetime of a subject. The crack depth of fatigue cracks that is not accessible with standard eddy current instruments should be estimated accurately. Another special need that we observe is the development of an assisting device tool that will help the operators to identify cracks and defects easier. Finally, additive manufacturing of metallic objects has a high potential for improvements and eddy current testing would be an added value for lower failure rates during the manufacturing. In this work, we will demonstrate how eddy current non-destructive testing meets the above mentioned needs. To this end, â¢ we measure the local magnetic field of the induced eddy currents with a special sensor array. We measure and calibrate our system on artificial defects and use a model to estimate the crack depth of fatigue defects. Finally we open these defects and compare the estimation with the actual defect; â¢ we show the development of a 2D hand scanning eddy current system which provides images, and we will give a practical approach towards scanning devices. This 2D hand scanning device does not change the operatorsâ hand scanning habits and provides; â¢ we took into account delamination and porosity changes, which are two of the fundamental problems of additive manufactured parts, in order to demonstrate the performance of eddy current testing for additive manufacturing.

EPFL2016

Phase retrieval in high dimensions: Statistical and computational phase transitions

Florent Gérard Krzakala, Bruno Loureiro, Lenka Zdeborová

We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , in a high-dimensional setting where m , n → ∞ while α = m / n = Θ ( 1 ) . First, we derive sharp asymptotics for the lowest possible estimation error achievable statistically and we unveil the existence of sharp phase transitions for the weak- and full-recovery thresholds as a function of the singular values of the matrix Φ . This is achieved by providing a rigorous proof of a result first obtained by the replica method from statistical mechanics. In particular, the information-theoretic transition to perfect recovery for full-rank matrices appears at α = 1 (real case) and α = 2 (complex case). Secondly, we analyze the performance of the best-known polynomial time algorithm for this problem --- approximate message-passing--- establishing the existence of statistical-to-algorithmic gap depending, again, on the spectral properties of Φ . Our work provides an extensive classification of the statistical and algorithmic thresholds in high-dimensional phase retrieval for a broad class of random matrices.

Curran Associates, Inc.2020

Multimodal feature extraction and fusion for audio-visual speech recognition

Mihai Gurban

Multimodal signal processing analyzes a physical phenomenon through several types of measures, or modalities. This leads to the extraction of higher-quality and more reliable information than that obtained from single-modality signals. The advantage is two-fold. First, as the modalities are usually complementary, the end-result of multimodal processing is more informative than for each of the modalities individually, which represents the first advantage. This is true in all application domains: human-machine interaction, multimodal identification or multimodal image processing. The second advantage is that, as modalities are not always reliable, it is possible, when one modality becomes corrupted, to extract the missing information from the other one. There are two essential challenges in multimodal signal processing. First, the features used from each modality need to be as relevant and as few as possible. The fact that multimodal systems have to process more than just one modality means that they can run into errors caused by the curse of dimensionality much more easily than mono-modal ones. The curse of dimensionality is a term used essentially to say that the number of equally-distributed samples required to cover a region of space grows exponentially with the dimensionality of the space. This has important implications in the classification domain, since accurate models can only be obtained if an adequate number of samples is available, and obviously this required number of samples grows with the dimensionality of the features. Dimensionality reduction is thus a necessary step in any application dealing with complex signals, and this is achieved through selection, transforms or the combination of the two. The second essential challenge is multimodal integration. Since the signals involved do not necessarily have the same data rate, range or even dimensionality, combining information coming from such different sources is not straightforward. This can be done at different levels, starting from the basic signal level by combining the signals themselves, if they are compatible, up to the highest decision level, where only the individual decisions taken based on the signals are combined. Ideally, the fusion method should allow temporal variations in the relative importance of the two streams, to account for possible changes in their quality. However, this can only be done with methods operating at a high decision level. The aim of this thesis is to offer solutions to both these challenges, in the context of audio-visual speech recognition and speaker localization. Both these applications are from the field of human-machine interaction. Audio-visual speech recognition aims to improve the accuracy of speech recognizers by augmenting the audio with information extracted from the video, more particularly, the movement of the speaker's lips. This works well especially when the audio is corrupted, leading in this case to significant gains in accuracy. Speaker localization means detecting who is the active speaker in a audio-video sequence containing several persons, something that is useful for videoconferencing and the automated annotation of meetings. These two applications are the context in which we present our solutions to both feature selection and multimodal integration. First, we show how informative features can be extracted from the visual modality, using an information-theoretic framework which gives us a quantitative measure of the relevance of individual features. We also prove that reducing redundancy between these features is important for avoiding the curse of dimensionality and improving recognition results. The methods that we present are novel in the field of audio-visual speech recognition and we found that their use leads to significant improvements compared to the state of the art. Second, we present a method of multimodal fusion at the level of intermediate decisions using a weight for each of the streams. The weights are adaptive, changing according to the estimated reliability of each stream. This makes the system tolerant to changes in the quality of either stream, and even to the temporary interruption of one of the streams. The reliability estimate is based on the entropy of the posterior probability distributions of each stream at the intermediate decision level. Our results are superior to those obtained with a state of the art method based on maximizing the same posteriors. Moreover, we analyze the effect of a constraint typically imposed on stream weights in the literature, the constraint that they should sum to one. Our results show that removing this constraint can lead to improvements in recognition accuracy. Finally, we develop a method for audio-visual speaker localization, based on the correlation between audio energy and the movement of the speaker's lips. Our method is based on a joint probability model of the audio and video which is used to build a likelihood map showing the likely positions of the speaker's mouth. We show that our novel method performs better than a similar method from the literature. In conclusion, we analyze two different challenges of multimodal signal processing for two audio-visual problems, and offer innovative approaches for solving them.

EPFL2009