Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels

In various signal-channel-estimation problems, the channel being estimated may be well approximated by a discrete finite impulse response (FIR) model with sparsely separated active or nonzero taps. A common approach to estimating such channels involves a discrete normalized least-mean-square (NLMS) adaptive FIR filter, every tap of which is adapted at each sample interval. Such an approach suffers from slow convergence rates and poor tracking when the required FIR filter is "long." Recently, NLMS-based algorithms have been proposed that employ least-squares-based structural detection techniques to exploit possible sparse channel structure and subsequently provide improved estimation performance. However, these algorithms perform poorly when there is a large dynamic range amongst the active taps. In this paper, we propose two modifications to the previous algorithms, which essentially remove this limitation. The modifications also significantly improve the applicability of the detection technique to structurally time varying channels. Importantly, for sparse channels, the computational cost of the newly proposed detection-guided NLMS estimator is only marginally greater than that of the standard NLMS estimator. Simulations demonstrate the favourable performance of the newly proposed algorithm. © 2006 IEEE.

A scalarization technique for computing the power and exponential moments of gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C are appropriately dimensioned constant matrices. We solve the problems by a matrix product scalarization technique and interpret the solutions in system-theoretic terms. The results of the paper are applicable to Bayesian prediction in multivariate autoregressive time series and mean-reverting diffusion processes.

Low density parity check codes: a statistical physics perspective

The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

Smart structure sensors based on embedded fibre Bragg grating arrays in aluminium alloy matrix by ultrasonic consolidation

Smart structure sensors based on embedded fibre Bragg grating (FBG) arrays in aluminium alloy matrix by ultrasonic consolidation (UC) technique have been proposed and demonstrated successfully. The temperature, loading and bending responses of the embedded FBG arrays have been systematically characterized. The embedded FBGs exhibit an average temperature sensitivity of ~36 pm °C-1, which is three times higher than that of normal FBGs, a bending sensitivity of 0.73 nm/m-1 and a loading responsivity of ~0.1 nm kg-1 within the dynamic range from 0 kg to 3 kg. These initial experimental results clearly demonstrate that the UC produced metal matrix structures can be embedded with FBG sensor arrays to become smart structures with capabilities to monitor the structure operation and health conditions in applications.

Embedded fibre Bragg grating array sensors in aluminium alloy matrix by ultrasonic consolidation

Fibre Bragg Grating (FBG) array sensors have been successfully embedded in aluminium alloy matrix by ultrasonic consolidation (UC) technique. The temperature and loading responses of the embedded FBG arrays have been systematically characterised. The embedded grating sensors exhibit an average temperature sensitivity of ~36pm/°C, which is three times higher than that of normal FBGs, and a loading responsivity of ~0.1nm/kg within the dynamic range from 0kg to 3kg. This initial experiment clearly demonstrates that FBG array sensors can be embedded in metal matrix together with other passive and active fibres to fabricate smart materials to monitor the operation and health of engineering structures.

Matrix-assisted diffusion-ordered spectroscopy:mixture resolution by NMR using SDSmicelles

Diffusion-ordered spectroscopy (DOSY) is a powerful technique for mixture analysis, but in its basic form it cannot separate the component spectra for species with very similar diffusion coefficients. It has been recently demonstrated that the component spectra of a mixture of isomers with nearly identical diffusion coefficients (the three dihydroxybenzenes) can be resolved using matrix-assisted DOSY (MAD), in which diffusion is perturbed by the addition of a co-solute such as a surfactant [R. Evans, S. Haiber, M. Nilsson, G. A. Morris, Anal. Chem. 2009, 81, 4548-4550]. However, little is known about the conditions required for such a separation, for example, the concentrations and concentration ratios of surfactant and solutes. The aim of this study was to explore the concentration range over whichmatrix-assisted DOSY using the surfactant SDS can achieve diffusion resolution of a simple model set of isomers, the monomethoxyphenols. The results show that the separation is remarkably robust with respect to both the concentrations and the concentration ratios of surfactant and solutes, supporting the idea that MAD may become a valuable tool formixture analysis. © 2010 John Wiley & Sons, Ltd.

Sparse representation of astronomical images

Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm (i) the effectiveness at producing sparse representations and (ii) competitiveness, with respect to the time required to process large images. The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks. This feature makes it possible to apply the effective greedy selection technique called orthogonal matching pursuit, up to some block size. For blocks exceeding that size, a refinement of the original matching pursuit approach is considered. The resulting method is termed "self-projected matching pursuit," because it is shown to be effective for implementing, via matching pursuit itself, the optional backprojection intermediate steps in that approach. © 2013 Optical Society of America.

Sparse image representation with encryption

In this thesis we present an overview of sparse approximations of grey level images. The sparse representations are realized by classic, Matching Pursuit (MP) based, greedy selection strategies. One such technique, termed Orthogonal Matching Pursuit (OMP), is shown to be suitable for producing sparse approximations of images, if they are processed in small blocks. When the blocks are enlarged, the proposed Self Projected Matching Pursuit (SPMP) algorithm, successfully renders equivalent results to OMP. A simple coding algorithm is then proposed to store these sparse approximations. This is shown, under certain conditions, to be competitive with JPEG2000 image compression standard. An application termed image folding, which partially secures the approximated images is then proposed. This is extended to produce a self contained folded image, containing all the information required to perform image recovery. Finally a modified OMP selection technique is applied to produce sparse approximations of Red Green Blue (RGB) images. These RGB approximations are then folded with the self contained approach.

Nanoindentation measurement of surface residual stresses in particle-reinforced metal matrix composites

The surface residual stresses in SiC particle-reinforced Al matrix composites are measured using a recently developed nanoindentation technique. The tensile biaxial residual stress in Al is found to increase with the particle concentration. The stress magnitudes are in reasonable agreement with those from numerical modeling.

Embedded fibre Bragg grating array sensors in aluminium alloy matrix by ultrasonic consolidation

Fibre Bragg Grating (FBG) array sensors have been successfully embedded in aluminium alloy matrix by ultrasonic consolidation (UC) technique. The temperature and loading responses of the embedded FBG arrays have been systematically characterised. The embedded grating sensors exhibit an average temperature sensitivity of ~36pm/°C, which is three times higher than that of normal FBGs, and a loading responsivity of ~0.1nm/kg within the dynamic range from 0kg to 3kg. This initial experiment clearly demonstrates that FBG array sensors can be embedded in metal matrix together with other passive and active fibres to fabricate smart materials to monitor the operation and health of engineering structures.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Matrix-assisted diffusion-ordered spectroscopy

Diffusion NMR is a potentially routine tool in the analysis of mixtures, from industrial and synthetic outputs to natural products. However, the technique struggles to resolve species of similar size. Matrix-assisted DOSY offers a flexible approach to resolving such ambiguities on the basis of the chemical structures involved and on their interactions with a larger co-solute or matrix. The use of chromatographic supports, surfactants and polymers, in particular, is illustrated. The resolution of a wide range of different analyte mixtures, on the basis of differences in chemical structure and in stereochemistry, is demonstrated.

Hallux rigidus: Arthroplasty or arthrodesis. What technique produces better results?

Hallux rígidus (HR) affects the first metatarsophalangeal joint (MTPJ) between 35% and 60% of the population over 65 years and there are multiple ways of treatment. Depending on the radiological stage where you find the deformity determines the procedure to be performed; in the early stages cheilectomy techniques and corrective osteotomy is performed while the more advanced ratings, the surgeon chooses destructive techniques considered as arthrodesis and arthroplasty. This final of degree project aims to focus on 1 MTPJ destructive techniques to clarify which of the procedures generates better results by a number of parameters; outcomes of the American Orthopaedic Foot scale and Ankle Society Hallux metatarsophalangeal Interphalangeal-scale (AOFAS), range of motion (ROM) of the 1ºAMTF, radiological classification. As for the implant arthroplasty technique, this article offers information on material and design that generates better relating to patient characteristics such as age, inflammatory joint diseases, viability and durability of the implant results. The conclusion from this review is that the values obtained in the arthrodesis according AOFAS decrease due to loss of mobility, but both techniques have similar values of effectiveness and concludes with the decision that the technique used is determined taking into account various factors and patient characteristics. Keywords: Hallux rígidus; (Hallux Rígidus) and surgery treatment; Hallux Rígidus arthrodesis; Hallux Rígidus arthroplasty; Hallux Rígidus (arthroplasty and arthrodesis).

Voltage and current spectra for matrix power converters

Matrix power converters are used for transforming one alternating-current power supply to another, with different peak voltage and frequency. There are three input lines, with sinusoidally varying voltages which are 120◦ out of phase one from another, and the output is to be delivered as a similar three-phase supply. The matrix converter switches rapidly, to connect each output line in sequence to each of the input lines in an attempt to synthesize the prescribed output voltages. The switching is carried out at high frequency and it is of practical importance to know the frequency spectra of the output voltages and of the input and output currents. We determine in this paper these spectra using a new method, which has significant advantages over the prior default method (a multiple Fourier series technique), leading to a considerably more direct calculation. In particular, the determination of the input current spectrum is feasible here, whereas it would be a significantly more daunting procedure using the prior method instead.

Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.