Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Sparse representation with multi-manifold analysis for texture classification from few training images

Texture classification is one of the most important tasks in computer vision field and it has been extensively investigated in the last several decades. Previous texture classification methods mainly used the template matching based methods such as Support Vector Machine and k-Nearest-Neighbour for classification. Given enough training images the state-of-the-art texture classification methods could achieve very high classification accuracies on some benchmark databases. However, when the number of training images is limited, which usually happens in real-world applications because of the high cost of obtaining labelled data, the classification accuracies of those state-of-the-art methods would deteriorate due to the overfitting effect. In this paper we aim to develop a novel framework that could correctly classify textural images with only a small number of training images. By taking into account the repetition and sparsity property of textures we propose a sparse representation based multi-manifold analysis framework for texture classification from few training images. A set of new training samples are generated from each training image by a scale and spatial pyramid, and then the training samples belonging to each class are modelled by a manifold based on sparse representation. We learn a dictionary of sparse representation and a projection matrix for each class and classify the test images based on the projected reconstruction errors. The framework provides a more compact model than the template matching based texture classification methods, and mitigates the overfitting effect. Experimental results show that the proposed method could achieve reasonably high generalization capability even with as few as 3 training images, and significantly outperforms the state-of-the-art texture classification approaches on three benchmark datasets. © 2014 Elsevier B.V. All rights reserved.

Reconstruction from image correspondences

A single picture provides a largely incomplete representation of the scene one is looking at. Usually it reproduces only a limited spatial portion of the scene according to the standpoint and the viewing angle, besides it contains only instantaneous information. Thus very little can be understood on the geometrical structure of the scene, the position and orientation of the observer with respect to it remaining also hard to guess. When multiple views, taken from different positions in space and time, observe the same scene, then a much deeper knowledge is potentially achievable. Understanding inter-views relations enables construction of a collective representation by fusing the information contained in every single image. Visual reconstruction methods confront with the formidable, and still unanswered, challenge of delivering a comprehensive representation of structure, motion and appearance of a scene from visual information. Multi-view visual reconstruction deals with the inference of relations among multiple views and the exploitation of revealed connections to attain the best possible representation. This thesis investigates novel methods and applications in the field of visual reconstruction from multiple views. Three main threads of research have been pursued: dense geometric reconstruction, camera pose reconstruction, sparse geometric reconstruction of deformable surfaces. Dense geometric reconstruction aims at delivering the appearance of a scene at every single point. The construction of a large panoramic image from a set of traditional pictures has been extensively studied in the context of image mosaicing techniques. An original algorithm for sequential registration suitable for real-time applications has been conceived. The integration of the algorithm into a visual surveillance system has lead to robust and efficient motion detection with Pan-Tilt-Zoom cameras. Moreover, an evaluation methodology for quantitatively assessing and comparing image mosaicing algorithms has been devised and made available to the community. Camera pose reconstruction deals with the recovery of the camera trajectory across an image sequence. A novel mosaic-based pose reconstruction algorithm has been conceived that exploit image-mosaics and traditional pose estimation algorithms to deliver more accurate estimates. An innovative markerless vision-based human-machine interface has also been proposed, so as to allow a user to interact with a gaming applications by moving a hand held consumer grade camera in unstructured environments. Finally, sparse geometric reconstruction refers to the computation of the coarse geometry of an object at few preset points. In this thesis, an innovative shape reconstruction algorithm for deformable objects has been designed. A cooperation with the Solar Impulse project allowed to deploy the algorithm in a very challenging real-world scenario, i.e. the accurate measurements of airplane wings deformations.

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization.

Reconstruction of sea-surface conditions at middle to high latitudes of the Northern Hemisphere

A new calibration database of census counts of organic-walled dinoflagellate cyst (dinocyst) assemblages has been developed from the analyses of surface sediment samples collected at middle to high latitudes of the Northern Hemisphere after standardisation of taxonomy and laboratory procedures. The database comprises 940 reference data points from the North Atlantic, Arctic and North Pacific oceans and their adjacent seas, including the Mediterranean Sea, as well as epicontinental environments such as the Estuary and Gulf of St. Lawrence, the Bering Sea and the Hudson Bay. The relative abundance of taxa was analysed to describe the distribution of assemblages. The best analogue technique was used for the reconstruction of Last Glacial Maximum (LGM) sea-surface temperature and salinity during summer and winter, in addition to sea-ice cover extent, at sites from the North Atlantic (n=63), Mediterranean Sea (n=1) and eastern North Pacific (n=1). Three of the North Atlantic cores, from the continental margin of eastern Canada, revealed a barren LGM interval, probably because of quasi-permanent sea ice. Six other cores from the Greenland and Norwegian seas were excluded from the compilation because of too sparse assemblages and poor analogue situation. At the remaining sites (n= 54), relatively close modern analogues were found for most LGM samples, which allowed reconstructions. The new LGM results are consistent with previous reconstructions based on dinocyst data, which show much cooler conditions than at present along the continental margins of Canada and Europe, but sharp gradients of increasing temperature offshore. The results also suggest low salinity and larger than present contrasts in seasonal temperatures with colder winters and more extensive sea-ice cover, whereas relatively warm conditions may have prevailed offshore in summer. From these data, we hypothesise low thermal inertia in a shallow and low-density surface water layer.

Sea surface temperature reconstruction based on dinoflagellates from the North Atlantic

The application of quantitative and semiquantitative methods to assemblage data from dinoflagellate cysts shows potential for interpreting past environments, both in terms of paleotemperature estimates and in recognizing water masses and circulation patterns. Estimates of winter sea-surface temperature (WSST) were produced by using the Impagidinium Index (II) method, and by applying a winter-temperature transfer function (TFw). Estimates of summer sea-surface temperature (SSST) were produced by using a summer-temperature transfer function (TFs), two methods based on a temperature-distribution chart (ACT and ACTpo), and a method based on the ratio of gonyaulacoid:protoperidinioid specimens (G:P). WSST estimates from the II and TFw methods are in close agreement except where Impagidinium species are sparse. SSST estimates from TFs are more variable. The value of the G:P ratio for the Pliocene data in this paper is limited by the apparent sparsity of protoperidinioids, which results in monotonous SSST estimates of 14-26°C. The ACT methods show two biases for the Pliocene data set: taxonomic substitution may force 'matches' yielding incorrect temperature estimates, and the method is highly sensitive to the end-points of species distributions. Dinocyst assemblage data were applied to reconstruct Pliocene sea-surface temperatures between 3.5-2.5 Ma from DSDP Hole 552A, and ODP Holes 646B and 642B, which are presently located beneath cold and cool-temperate waters north of 56°N. Our initial results suggest that at 3.0 Ma, WSSTs were a few degrees C warmer than the present and that there was a somewhat reduced north-south temperature gradient. For all three sites, it is likely that SSSTs were also warmer, but by an unknown, perhaps large, amount. Past oceanic circulation in the North Atlantic was probably different from the present.

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Analysis and design of multirate synchronous sampling schemes for sparse multiband signals

We consider the problem of developing efficient sampling schemes for multiband sparse signals. Previous results on multicoset sampling implementations that lead to universal sampling patterns (which guarantee perfect reconstruction), are based on a set of appropriate interleaved analog to digital converters, all of them operating at the same sampling frequency. In this paper we propose an alternative multirate synchronous implementation of multicoset codes, that is, all the analog to digital converters in the sampling scheme operate at different sampling frequencies, without need of introducing any delay. The interleaving is achieved through the usage of different rates, whose sum is significantly lower than the Nyquist rate of the multiband signal. To obtain universal patterns the sampling matrix is formulated and analyzed. Appropriate choices of the parameters, that is the block length and the sampling rates, are also proposed.

Design of universal multicoset sampling patterns for compressed sensing of multiband sparse signals

Many problems in digital communications involve wideband radio signals. As the most recent example, the impressive advances in Cognitive Radio systems make even more necessary the development of sampling schemes for wideband radio signals with spectral holes. This is equivalent to considering a sparse multiband signal in the framework of Compressive Sampling theory. Starting from previous results on multicoset sampling and recent advances in compressive sampling, we analyze the matrix involved in the corresponding reconstruction equation and define a new method for the design of universal multicoset codes, that is, codes guaranteeing perfect reconstruction of the sparse multiband signal.

Algorithms for super-resolution of images based on Sparse Representation and Manifolds

lmage super-resolution is defined as a class of techniques that enhance the spatial resolution of images. Super-resolution methods can be subdivided in single and multi image methods. This thesis focuses on developing algorithms based on mathematical theories for single image super­ resolution problems. lndeed, in arder to estimate an output image, we adopta mixed approach: i.e., we use both a dictionary of patches with sparsity constraints (typical of learning-based methods) and regularization terms (typical of reconstruction-based methods). Although the existing methods already per- form well, they do not take into account the geometry of the data to: regularize the solution, cluster data samples (samples are often clustered using algorithms with the Euclidean distance as a dissimilarity metric), learn dictionaries (they are often learned using PCA or K-SVD). Thus, state-of-the-art methods still suffer from shortcomings. In this work, we proposed three new methods to overcome these deficiencies. First, we developed SE-ASDS (a structure tensor based regularization term) in arder to improve the sharpness of edges. SE-ASDS achieves much better results than many state-of-the- art algorithms. Then, we proposed AGNN and GOC algorithms for determining a local subset of training samples from which a good local model can be computed for recon- structing a given input test sample, where we take into account the underlying geometry of the data. AGNN and GOC methods outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings. Next, we proposed aSOB strategy which takes into account the geometry of the data and the dictionary size. The aSOB strategy outperforms both PCA and PGA methods. Finally, we combine all our methods in a unique algorithm, named G2SR. Our proposed G2SR algorithm shows better visual and quantitative results when compared to the results of state-of-the-art methods.

Sparse Signal Representation in Digital and Biological Systems

Theories of sparse signal representation, wherein a signal is decomposed as the sum of a small number of constituent elements, play increasing roles in both mathematical signal processing and neuroscience. This happens despite the differences between signal models in the two domains. After reviewing preliminary material on sparse signal models, I use work on compressed sensing for the electron tomography of biological structures as a target for exploring the efficacy of sparse signal reconstruction in a challenging application domain. My research in this area addresses a topic of keen interest to the biological microscopy community, and has resulted in the development of tomographic reconstruction software which is competitive with the state of the art in its field. Moving from the linear signal domain into the nonlinear dynamics of neural encoding, I explain the sparse coding hypothesis in neuroscience and its relationship with olfaction in locusts. I implement a numerical ODE model of the activity of neural populations responsible for sparse odor coding in locusts as part of a project involving offset spiking in the Kenyon cells. I also explain the validation procedures we have devised to help assess the model's similarity to the biology. The thesis concludes with the development of a new, simplified model of locust olfactory network activity, which seeks with some success to explain statistical properties of the sparse coding processes carried out in the network.

Towards automatic tree crown detection and delineation in spectral feature space using PCNN and morphological reconstruction

The application of object-based approaches to the problem of extracting vegetation information from images requires accurate delineation of individual tree crowns. This paper presents an automated method for individual tree crown detection and delineation by applying a simplified PCNN model in spectral feature space followed by post-processing using morphological reconstruction. The algorithm was tested on high resolution multi-spectral aerial images and the results are compared with two existing image segmentation algorithms. The results demonstrate that our algorithm outperforms the other two solutions with the average accuracy of 81.8%.

Fast reconstruction of aerodynamic shapes using evolutionary algorithms and virtual Nash strategies in a CFD design environment

This paper compares the performances of two different optimisation techniques for solving inverse problems; the first one deals with the Hierarchical Asynchronous Parallel Evolutionary Algorithms software (HAPEA) and the second is implemented with a game strategy named Nash-EA. The HAPEA software is based on a hierarchical topology and asynchronous parallel computation. The Nash-EA methodology is introduced as a distributed virtual game and consists of splitting the wing design variables - aerofoil sections - supervised by players optimising their own strategy. The HAPEA and Nash-EA software methodologies are applied to a single objective aerodynamic ONERA M6 wing reconstruction. Numerical results from the two approaches are compared in terms of the quality of model and computational expense and demonstrate the superiority of the distributed Nash-EA methodology in a parallel environment for a similar design quality.

3-D reconstruction of an ancient Egyptian mummy using X-ray computer tomography

Computer tomography has been used to image and reconstruct in 3-D an Egyptian mummy from the collection of the British Museum. This study of Tjentmutengebtiu, a priestess from the 22nd dynasty (945-715 BC) revealed invaluable information of a scientific, Egyptological and palaeopathological nature without mutilation and destruction of the painted cartonnage case or linen wrappings. Precise details on the removal of the brain through the nasal cavity and the viscera from the abdominal cavity were obtained. The nature and composition of the false eyes were investigated. The detailed analysis of the teeth provided a much closer approximation of age at death. The identification of materials used for the various amulets including that of the figures placed in the viscera was graphically demonstrated using this technique.