Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Binary sparse nonnegative matrix factorization

This paper presents a fast part-based subspace selection algorithm, termed the binary sparse nonnegative matrix factorization (B-SNMF). Both the training process and the testing process of B-SNMF are much faster than those of binary principal component analysis (B-PCA). Besides, B-SNMF is more robust to occlusions in images. Experimental results on face images demonstrate the effectiveness and the efficiency of the proposed B-SNMF.

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.

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.