Luís B. Almeida

The fractional Fourier transform and time-frequency representations

The functional Fourier transform (FRFT), which is a generalization of the classical Fourier transform, was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community, to which it may, however, be potentially useful. The FRFT depends on a parameter /spl alpha/ and can be interpreted as a rotation by an angle /spl alpha/ in the time-frequency plane. An FRFT with /spl alpha/=/spl pi//2 corresponds to the classical Fourier transform, and an FRFT with /spl alpha/=0 corresponds to the identity operator. On the other hand, the angles of successively performed FRFTs simply add up, as do the angles of successive rotations. The FRFT of a signal can also be interpreted as a decomposition of the signal in terms of chirps. The authors briefly introduce the FRFT and a number of its properties and then present some new results: the interpretation as a rotation in the time-frequency plane, and the FRFTs relationships with time-frequency representations such as the Wigner distribution, the ambiguity function, the short-time Fourier transform and the spectrogram. These relationships have a very simple and natural form and support the FRFTs interpretation as a rotation operator. Examples of FRFTs of some simple signals are given. An example of the application of the FRFT is also given. >

Blind and Semi-Blind Deblurring of Natural Images

A method for blind image deblurring is presented. The method only makes weak assumptions about the blurring filter and is able to undo a wide variety of blurring degradations. To overcome the ill-posedness of the blind image deblurring problem, the method includes a learning technique which initially focuses on the main edges of the image and gradually takes details into account. A new image prior, which includes a new edge detector, is used. The method is able to handle unconstrained blurs, but also allows the use of constraints or of prior information on the blurring filter, as well as the use of filters defined in a parametric manner. Furthermore, it works in both single-frame and multiframe scenarios. The use of constrained blur models appropriate to the problem at hand, and/or of multiframe scenarios, generally improves the deblurring results. Tests performed on monochrome and color images, with various synthetic and real-life degradations, without and with noise, in single-frame and multiframe scenarios, showed good results, both in subjective terms and in terms of the increase of signal to noise ratio (ISNR) measure. In comparisons with other state of the art methods, our method yields better results, and shows to be applicable to a much wider range of blurs.

Speeding up Backpropagation

Backpropagation is probably the best known, and most widely used learning algorithm for neural networks. It is a gradient based optimization procedure, and it suffers from the common limitations of this kind of algorithms, namely in what concerns convergence speed. In this paper, we present an improvement to the backpropagation algorithm, based on the use of an independent, adaptive learning rate parameter for each weight. We discuss the reasons for using this modification to the basic algorithm, and we give experimental results showing the improvement in learning speed obtained with this method.

Acceleration Techniques for the Backpropagation Algorithm

Like other gradient descent techniques, backpropagation converges slowly, even for medium sized network problems. This fact results from the usually large dimension of the weight space and from the particular shape of the error surface in each iteration point. Oscillation between the sides of deep and narrow valleys, for example, is a well known case where gradient descent provides poor convergence rates.

Hyperspectral Pansharpening: A Review

Pansharpening aims at fusing a panchromatic image with a multispectral one, to generate an image with the high spatial resolution of the former and the high spectral resolution of the latter. In the last decade, many algorithms have been presented in the literatures for pansharpening using multispectral data. With the increasing availability of hyperspectral systems, these methods are now being adapted to hyperspectral images. In this work, we compare new pansharpening techniques designed for hyperspectral data with some of the state-of-the-art methods for multispectral pansharpening, which have been adapted for hyperspectral data. Eleven methods from different classes (component substitution, multiresolution analysis, hybrid, Bayesian and matrix factorization) are analyzed. These methods are applied to three datasets and their effectiveness and robustness are evaluated with widely used performance indicators. In addition, all the pansharpening techniques considered in this paper have been implemented in a MATLAB toolbox that is made available to the community.

Polymer Nanocomposites for Multifunctional Finishing of Textiles – A Review

Improvement of existing properties and the creation of new material properties are the most important reasons for the functionalization of textiles. Polymer nanocomposites offer the possibility of developing a new class of nanofinishing materials for textiles with their own manifold of structure property relationship only indirectly related to their components and their micron and macro-scale composite counterparts. Though polymer nanocomposites with inorganic filler of different dimensionality and chemistry are possible, efforts have only begun to uncover the wealth of possibilities of these new materials. Approaches to modify the polymer nanocomposite system by various inorganic or organic substances can lead to a huge number of additional functionalities which are increasingly demanded by the textile industries. In this review, we have compiled the current research in polymer nanocomposite-based nanofinishes for multifunctional textiles which provides a snapshot of the current experimental and theoretical tools being used to advance our understanding of polymer nanocomposites and their applications in textiles.

A Convex Formulation for Hyperspectral Image Superresolution via Subspace-Based Regularization

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images that combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector total variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the nonquadratic and nonsmooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally “live” in a low-dimensional subspace and by tailoring the split augmented Lagrangian shrinkage algorithm (SALSA), which is an instance of the alternating direction method of multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state of the art, as illustrated in a series of experiments with simulated and real-life data.

Effects of Agitation and Endoglucanase Pretreatment on the Hydrolysis of Cotton Fabrics by a Total Cellulase

We have attempted to clarify the effects of low and high levels of mechanical agitation on the cellulolytic activity of a pure endoglucanase ( EG ) and a total cellulase mixture (TC) on scoured and bleached cotton fabric, along with the effect of EG pretreatment on subsequent treatments with TC. Methods used to follow the progress of fabric treatments include weight loss, breaking load loss, bending hysteresis, and the pro duction of soluble reducing sugars and reducing end groups in the fibers. The results show that agitation rate affects the mechanism of cellulolytic attack, and that this has implications for delivering desired finishing effects.

Nonstationary spectral modeling of voiced speech

The main purpose of this paper is to present a novel model for voiced speech. The classical model, which is being used in many applications, assumes local stationarity, and consequently imposes a simple and well known line structure to the short-time spectrum of voiced speech. The model derived in this paper allows for local non-stationarities not only in terms of pitch perturbations, but in terms of vocal tract variations as well. The resulting structure of the short-time spectrum becomes more complex, but can still be interpreted in terms of generalized lines. The proposed model supports new forms of spectral prediction, which can be put to advantage in speech coding applications. Experimental results are presented supporting the validity of both the model itself and the prediction relationships. Finally, a new class of speech coders, denoted harmonic coders, based on the presented model, is proposed, and a specific implementation is presented.

An introduction to the angular Fourier transform

The author introduces the angular Fourier transform (AFT), a generalization of the classical Fourier transform. The AFT can be interpreted as a rotation on the time-frequency plane. An AFT with an angle of alpha = pi /2 corresponds to the classical Fourier transform, and an AFT with alpha =0 corresponds to the identity operator. The angles of successively performed AFTs simply add up, as do the angles of successive rotations. A number of properties of the AFT are given. Most important among these are the AFTs relationships with time-frequency representations such as the Wigner distribution, the ambiguity function, the short-time Fourier transform, and the spectrogram. These relationships have a very simple and natural form, which further enhances the AFTs interpretation as a rotation operator. An example of the application of the AFT to the study of swept-frequency filters is given.<<ETX>>