Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

Accelerating FPGA-based evolution of wavelet transform filters by optimized task scheduling

Adaptive embedded systems are required in various applications. This work addresses these needs in the area of adaptive image compression in FPGA devices. A simplified version of an evolution strategy is utilized to optimize wavelet filters of a Discrete Wavelet Transform algorithm. We propose an adaptive image compression system in FPGA where optimized memory architecture, parallel processing and optimized task scheduling allow reducing the time of evolution. The proposed solution has been extensively evaluated in terms of the quality of compression as well as the processing time. The proposed architecture reduces the time of evolution by 44% compared to our previous reports while maintaining the quality of compression unchanged with respect to existing implementations. The system is able to find an optimized set of wavelet filters in less than 2 min whenever the input type of data changes.

On the use of discrete cosine transforms for multicarrier communications

In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redun-dancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.

Toward reduction of artifacts in fused images

Most fusion satellite image methodologies at pixel-level introduce false spatial details, i.e.artifacts, in the resulting fusedimages. In many cases, these artifacts appears because image fusion methods do not consider the differences in roughness or textural characteristics between different land covers. They only consider the digital values associated with single pixels. This effect increases as the spatial resolution image increases. To minimize this problem, we propose a new paradigm based on local measurements of the fractal dimension (FD). Fractal dimension maps (FDMs) are generated for each of the source images (panchromatic and each band of the multi-spectral images) with the box-counting algorithm and by applying a windowing process. The average of source image FDMs, previously indexed between 0 and 1, has been used for discrimination of different land covers present in satellite images. This paradigm has been applied through the fusion methodology based on the discrete wavelet transform (DWT), using the à trous algorithm (WAT). Two different scenes registered by optical sensors on board FORMOSAT-2 and IKONOS satellites were used to study the behaviour of the proposed methodology. The implementation of this approach, using the WAT method, allows adapting the fusion process to the roughness and shape of the regions present in the image to be fused. This improves the quality of the fusedimages and their classification results when compared with the original WAT method

Quality assessment by region in spot images fused by means dual-tree complex wavelet transform

This work is motivated in providing and evaluating a fusion algorithm of remotely sensed images, i.e. the fusion of a high spatial resolution panchromatic image with a multi-spectral image (also known as pansharpening) using the dual-tree complex wavelet transform (DT-CWT), an effective approach for conducting an analytic and oversampled wavelet transform to reduce aliasing, and in turn reduce shift dependence of the wavelet transform. The proposed scheme includes the definition of a model to establish how information will be extracted from the PAN band and how that information will be injected into the MS bands with low spatial resolution. The approach was applied to Spot 5 images where there are bands falling outside PAN’s spectrum. We propose an optional step in the quality evaluation protocol, which is to study the quality of the merger by regions, where each region represents a specific feature of the image. The results show that DT-CWT based approach offers good spatial quality while retaining the spectral information of original images, case SPOT 5. The additional step facilitates the identification of the most affected regions by the fusion process.

Two Different Approaches of Feature Extraction for Classifying the EEG Signals

The electroencephalograph (EEG) signal is one of the most widely used signals in the biomedicine field due to its rich information about human tasks. This research study describes a new approach based on i) build reference models from a set of time series, based on the analysis of the events that they contain, is suitable for domains where the relevant information is concentrated in specific regions of the time series, known as events. In order to deal with events, each event is characterized by a set of attributes. ii) Discrete wavelet transform to the EEG data in order to extract temporal information in the form of changes in the frequency domain over time- that is they are able to extract non-stationary signals embedded in the noisy background of the human brain. The performance of the model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed scheme has potential in classifying the EEG signals.

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics.

A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermo-visco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermo dynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

Thermodinamically consistent dynamic formulation of discrete thermoviscoelastic elements

Metodología para integrar numéricamente de forma termodinámicamente consistente las ecuaciones del problema termomecánico acoplado de un elemento discreto viscoso.

The flexibility matrix o timber composite beams with a discrete connection system

This work presents a method for the analysis of timber composite beams which considers the slip in the connection system, based on assembling the flexibility matrix of the whole structure. This method is based on one proposed by Tommola and Jutila (2001). This paper extends the method to the case of a gap between two pieces with an arbitrary location at the first connector, which notably broadens its practical application. The addition of the gap makes it possible to model a cracked zone in concrete topping, as well as the case in which forming produces the gap. The consideration of induced stresses due to changes in temperature and moisture content is also described, while the concept of equivalent eccentricity is generalized. This method has important advantages in connection with the current European Standard EN 1995-1-1: 2004, as it is able to deal with any type of load, variable section, discrete and non-regular connection systems, a gap between the two pieces, and variations in temperature and moisture content. Although it could be applied to any structural system, it is specially suited for the case of simple supported and continuous beams. Working examples are presented at the end, showing that the arrangement of the connection notably modifies shear force distribution. A first interpretation of the results is made on the basis of the strut and tie theory. The examples prove that the use of EC-5 is unsafe when, as a rule of thumb, the strut or compression field between the support and the first connector is at an angle with the axis of the beam of less than 60º.

The DLMT. An alternative to the DCT

In the last recent years, with the popularity of image compression techniques, many architectures have been proposed. Those have been generally based on the Forward and Inverse Discrete Cosine Transform (FDCT, IDCT). Alternatively, compression schemes based on discrete “wavelets” transform (DWT), used, both, in JPEG2000 coding standard and in the next H264-SVC (Scalable Video Coding), do not need to divide the image into non-overlapping blocks or macroblocks. This paper discusses the DLMT (Discrete Lopez-Moreno Transform). It proposes a new scheme intermediate between the DCT and the DWT (Discrete Wavelet Transform). The DLMT is computationally very similar to the DCT and uses quasi-sinusoidal functions, so the emergence of artifact blocks and their effects have a relative low importance. The use of quasi-sinusoidal functions has allowed achieving a multiresolution control quite close to that obtained by a DWT, but without increasing the computational complexity of the transformation. The DLMT can also be applied over a whole image, but this does not involve increasing computational complexity. Simulation results in MATLAB show that the proposed DLMT has significant performance benefits and improvements comparing with the DCT

DCT Type-III for Multicarrier Modulation

In this paper we propose the use of Discrete Cosine Transform Type-III (DCT3) for multicarrier modulation. There are two DCT3 (even and odd) and, for each of them, we derive the expressions for both prefix and suffix to be appended into each data symbol to be transmitted. Moreover, DCT3 are closely related to the corresponding inverse DCT Type-II even and odd. Furthermore, we give explicit expressions for the 1-tap per subcarrier equalizers that must be implemented at the receiver to perform the channel equalization in the frequency-domain. As a result, the proposed DCT3-based multicarrier modulator can be used as an alternative to DFT-based systems to perform Orthogonal Frequency-Division Multiplexing or Discrete Multitone Modulation

Extreme temperature events analyzed with Fast Fourier Transform

Extreme weather and climate events have received increased attention in the last few years, due to the often large loss of agriculture business and exponentially increasing costs associated with them and insurance planning. This increased attention raises the question as to whether extreme weather and climate events are truly increasing, whether this is only a perceived increase exacerbated by enhanced media coverage, or both. There are a number of ways extreme climate events can be defined, such as extreme daily temperatures, extreme daily rainfall amounts, and large areas experiencing unusually warm monthly temperatures, among others. In this study, we will focus our attention in frost and heatstroke events measuring it as the number of days under 0 ºC and number of days with daily maximum over 30ºC monthly respectively. We have studied the trends in these extreme events applying a Fast Fourier Transform to the series to clarify the tendency. Lack of long-term climate data suitable for analysis of extremes is the single biggest obstacle to quantifying whether extreme events have changed over the twentieth century, including high temporal and spatial resolution observations of temperatures. However, several series have been grouped in different ways: chosen the longest series independently, by provinces, by main watersheds and altitude. On the other hand, synthetic series generated by Luna and Balairón (AEMet) were also analyzed. The results obtained by different pooling data are discussed concluding the difficulties to assess the extreme events tendencies and high regional variation in the trends.

Glottal Parameter Estimation by Wavelet Transform for Voice Biometry

Voice biometry is classically based on the parameterization and patterning of speech features mainly. The present approach is based on the characterization of phonation features instead (glottal features). The intention is to reduce intra-speaker variability due to the `text'. Through the study of larynx biomechanics it may be seen that the glottal correlates constitute a family of 2-nd order gaussian wavelets. The methodology relies in the extraction of glottal correlates (the glottal source) which are parameterized using wavelet techniques. Classification and pattern matching was carried out using Gaussian Mixture Models. Data of speakers from a balanced database and NIST SRE HASR2 were used in verification experiments. Preliminary results are given and discussed.

3D Wavelet-based Fusion Techniques for Biomedical Imaging

Hoy en día las técnicas de adquisición de imágenes tridimensionales son comunes en diversas áreas, pero cabe destacar la relevancia que han adquirido en el ámbito de la imagen biomédica, dentro del cual encontramos una amplia gama de técnicas como la microscopía confocal, microscopía de dos fotones, microscopía de fluorescencia mediante lámina de luz, resonancia magnética nuclear, tomografía por emisión de positrones, tomografía de coherencia óptica, ecografía 3D y un largo etcétera. Un denominador común de todas esas aplicaciones es la constante necesidad por aumentar la resolución y la calidad de las imágenes adquiridas. En algunas de dichas técnicas de imagen tridimensional se da una interesante situación: aunque que cada volumen adquirido no contiene información suficiente para representar el objeto bajo estudio dentro de los parámetros de calidad requeridos por algunas aplicaciones finales, el esquema de adquisición permite la obtención de varios volúmenes que representan diferentes vistas de dicho objeto, de tal forma que cada una de las vistas proporciona información complementaria acerca del mismo. En este tipo de situación es posible, mediante la combinación de varias de esas vistas, obtener una mejor comprensión del objeto que a partir de cada una de ellas por separado. En el contexto de esta Tesis Doctoral se ha propuesto, desarrollado y validado una nueva metodología de proceso de imágenes basada en la transformada wavelet disc¬reta para la combinación, o fusión, de varias vistas con información complementaria de un mismo objeto. El método de fusión propuesto aprovecha la capacidad de descom¬posición en escalas y orientaciones de la transformada wavelet discreta para integrar en un solo volumen toda la información distribuida entre el conjunto de vistas adquiridas. El trabajo se centra en dos modalidades diferentes de imagen biomédica que per¬miten obtener tales adquisiciones multi-vista. La primera es una variante de la micro¬scopía de fluorescencia, la microscopía de fluorescencia mediante lámina de luz, que se utiliza para el estudio del desarrollo temprano de embriones vivos en diferentes modelos animales, como el pez cebra o el erizo de mar. La segunda modalidad es la resonancia magnética nuclear con realce tardío, que constituye una valiosa herramienta para evaluar la viabilidad del tejido miocárdico en pacientes con diversas miocardiopatías. Como parte de este trabajo, el método propuesto ha sido aplicado y validado en am¬bas modalidades de imagen. En el caso de la aplicación a microscopía de fluorescencia, los resultados de la fusión muestran un mejor contraste y nivel de detalle en comparación con cualquiera de las vistas individuales y el método no requiere de conocimiento previo acerca la función de dispersión puntual del sistema de imagen. Además, los resultados se han comparado con otros métodos existentes. Con respecto a la aplicación a imagen de resonancia magnética con realce tardío, los volúmenes fusionados resultantes pre-sentan una mejora cuantitativa en la nitidez de las estructuras relevantes y permiten una interpretación más sencilla y completa de la compleja estructura tridimensional del tejido miocárdico en pacientes con cardiopatía isquémica. Para ambas aplicaciones los resultados de esta tesis se encuentran actualmente en uso en los centros clínicos y de investigación con los que el autor ha colaborado durante este trabajo. Además se ha puesto a libre disposición de la comunidad científica la implementación del método de fusión propuesto. Por último, se ha tramitado también una solicitud de patente internacional que cubre el método de visualización desarrollado para la aplicación de Resonancia Magnética Nuclear. Abstract Nowadays three dimensional imaging techniques are common in several fields, but es-pecially in biomedical imaging, where we can find a wide range of techniques including: Laser Scanning Confocal Microscopy, Laser Scanning Two Photon Microscopy, Light Sheet Fluorescence Microscopy, Magnetic Resonance Imaging, Positron Emission To-mography, Optical Coherence Tomography, 3D Ultrasound Imaging, etc. A common denominator of all those applications being the constant need for further increasing resolution and quality of the acquired images. Interestingly, in some of the mentioned three-dimensional imaging techniques a remarkable situation arises: while a single volume does not contain enough information to represent the object being imaged within the quality parameters required by the final application, the acquisition scheme allows recording several volumes which represent different views of a given object, with each of the views providing complementary information. In this kind of situation one can get a better understanding of the object by combining several views instead of looking at each of them separately. Within such context, in this PhD Thesis we propose, develop and test new image processing methodologies based on the discrete wavelet transform for the combination, or fusion, of several views containing complementary information of a given object. The proposed fusion method exploits the scale and orientation decomposition capabil¬ities of the discrete wavelet transform to integrate in a single volume all the available information distributed among the set of acquired views. The work focuses in two different biomedical imaging modalities which provide such multi-view datasets. The first one is a particular fluorescence microscopy technique, Light-Sheet Fluorescence Microscopy, used for imaging and gaining understanding of the early development of live embryos from different animal models (like zebrafish or sea urchin). The second is Delayed Enhancement Magnetic Resonance Imaging, which is a valuable tool for assessing the viability of myocardial tissue on patients suffering from different cardiomyopathies. As part of this work, the proposed method was implemented and then validated on both imaging modalities. For the fluorescence microscopy application, the fusion results show improved contrast and detail discrimination when compared to any of the individual views and the method does not rely on prior knowledge of the system’s point spread function (PSF). Moreover, the results have shown improved performance with respect to previous PSF independent methods. With respect to its application to Delayed Enhancement Magnetic Resonance Imaging, the resulting fused volumes show a quantitative sharpness improvement and enable an easier and more complete interpretation of complex three-dimensional scar and heterogeneous tissue information in ischemic cardiomyopathy patients. In both applications, the results of this thesis are currently in use in the clinical and research centers with which the author collaborated during his work. An imple¬mentation of the fusion method has also been made freely available to the scientific community. Finally, an international patent application has been filed covering the visualization method developed for the Magnetic Resonance Imaging application.

Classification of discrete systems on a square lattice

We consider the classification up to a Möbius transformation of real linearizable and integrable partial difference equations with dispersion defined on a square lattice by the multiscale reduction around their harmonic solution. We show that the A1, A2, and A3 linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions are insufficient for a complete characterization of the subclass of multilinear equations on a square lattice.