Electrical and Computer Engineering

The time consuming part of the encoding step is the search for an appropriate domain for each range. Several methods have been devised to accelerate the search and reduce the encoding complexity. In this paper we implement both quadtree and diamond partitioning. Quadtree partitioning uses horizontally and vertically oriented domains that are twice as large as the ranges. This works extremely well for images that has horizontal and vertical block structure. Many images also possess block structures oriented in other directions. Thus it makes sense to add domains that are of diamond or other kinds of shapes so that a large range block may find a "close" domain counterpart to avoid being further partitioned. . The diamond is well suited for our needs because it is already in a square shape on only rotational transformations of 45 degrees are needed to related them to our square ranges.

The main problem of all fractal compression implementations is the execution time. The algorithms can spend hours and hours to compress a single image. So the major variants of the standard algorithm were proposed to speed up computation time. But most of them lead to a bad quality, or a lower compression ratio. For example, the Fisher's proposed classification pattern has greatly accelerated the algorithm, but image quality was poor, due to the search space reduction imposed by the classification, which eliminates a lot of good solutions. By using genetic algorithms to address the problem, we want to optimize the domain blocks search, we explore all domain blocks presents in the image, but not in exhaustive way (like standard algorithm), and without omitting any possible block (solution) like does classification pattern. A genetic algorithm is the unique method to satisfy theses constraints. And it is away to be a random search, because the genetic one is directed by fitness selection which produce optimal solutions. Our goal in this work is to use genetic algorithm to solve the IFS inverse problem, and build a fractal compression algorithm based on genetic optimization of domain blocks search. We have also implemented Barnsley standard algorithm, Y. Fisher algorithm based on classification and the genetic compression algorithm with quadtree partitioning. A population of transformations was evolved for each range block and the result is compared with standard Barnsley algorithm, and Yuval fisher algorithm based classification. We deduced an optimal set of values for the best parameters combination, and we can also specify the best combination for each desired criteria: best compression ratio, best image quality or quick compression process. By running many test images ,we experimentally found the following set of optimal values of all the algorithm parameters which ensure compromise between execution time and solutions optimality : Population Size=100 ; Maximum generations = 20 ; Crossover rate = 0.7 ;Mutation rate = 0.1 ;RMS limit = 5 ; Decomposition error limit = 10 ;Flips and isometrics count = 8. In our proposed algorithm, results were much better than those obtained in both Vences & Rudomin and Marc M. Lankhorst [46] approaches.

This document demonstrates how a face recognition system can be designed with artificial neural network. Note that the training process did not consist of a single call to a training function. Instead, the network was trained several times on various input ideal and noisy images, the images which contents faces. In this case training a network on different sets of noisy images forced the network to learn how to deal with noise, a common problem in the real world.

The paper describes a new approach of classification using genetic programming. The proposed technique consists of genetically coevolving a population of non-linear transformations on the input data to be classified, and map them to a new space with a reduced dimension, in order to get maximum inter-classes discrimination. The classification of new samples is then performed on the transformed data, and so becomes much easier. Contrary to the existing GP-classification techniques, the proposed one uses a dynamic repartition of the transformed data in separated intervals, the efficacy of a given interval repartition is handled by the fitness criterion, with maximum classes discrimination. Experiments were first performed using the Fisher's Iris dataset, and the KDD'99 Cup dataset was used to study the intrusion detection and classification problem. Obtained results demonstrate that the proposed genetic approach outperforms the existing GP-classification methods, and gives accepted results compared to other existing techniques.

We denoise HARDI (High Angular Resolution Diffusion Imaging) data arising in medical imaging. Diffusion imaging is a relatively new and powerful method to measure the 3D profile of water diffusion at each point. This can be used to reconstruct fiber directions and pathways in the living brain, providing detailed maps of fiber integrity and connectivity. HARDI is a powerful new extension of diffusion imaging, which goes beyond the diffusion tensor imaging (DTI) model: mathematically, intensity data is given at every voxel and at any direction on the sphere. However, HARDI data is usually highly contaminated with noise, depending on the b-value which is a tuning parameter pre-selected to collect the data. Larger b-values help to collect more accurate information in terms of measuring diffusivity, but more noise is generated by many factors as well. So large b-values are preferred, if we can satisfactorily reduce the noise without losing the data structure. We propose a variational method to denoise HARDI data by denoising the spherical Apparent Diffusion Coefficient (sADC), a field of radial functions derived from the data. We use vectorial total variation regularization, an L 1 data fidelity term and the logarithmic barrier function in the minimization. We present experiments of denoising synthetic and real HARDI data.

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 ≤ N ≤ 94) that optimized a spherical angular distribution energy, we created SNR plots (versus gradient numbers) for seven common diffusion anisotropy indices: fractional and relative anisotropy (FA, RA), mean diffusivity (MD), volume ratio (VR), geodesic anisotropy (GA), its hyperbolic tangent (tGA), and generalized fractional anisotropy (GFA). SNR, defined in a region of interest in the corpus callosum, was near-maximal with 58, 66, and 62 gradients for MD, FA, and RA, respectively, and with about 55 gradients for GA and tGA. For VR and GFA, SNR increased rapidly with more gradients. SNR was optimized when the ratio of diffusion-sensitized to non-sensitized images was 9.13 for GA and tGA, 10.57 for FA, 9.17 for RA, and 26 for MD and VR. In orientation density functions modeling the HARDI signal as a continuous mixture of tensors, the diffusion profile reconstruction accuracy rose rapidly with additional gradients. These plots may help in making trade-off decisions when designing diffusion imaging protocols.

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber’s anisotropy, and partial volume effects from neighboring gray matter. With High-angular resolution diffusion imaging (HARDI) and the tensor distribution function (TDF), one can reconstruct multiple underlying fibers per voxel and their individual anisotropy measures by representing the diffusion profile as a probabilistic mixture of tensors. We found that FA, when compared with TDF-derived anisotropy measures, correlates poorly with individual fiber anisotropy, and may sub-optimally detect disease processes that affect myelination. By contrast, mean diffusivity (MD) as defined in standard DTI appears to be more accurate. Overall, we argue that novel measures derived from the TDF approach may yield more sensitive and accurate information than DTI-derived measures.

Diffusion tensor imaging (DTI) is sensitive to the directionally-constrained flow of water, which diffuses preferentially along axons. Tractography programs may be used to infer matrices of connectivity (anatomical networks) between pairs of brain regions. Little is known about how these computed connectivity measures depend on the scans' spatial and angular resolutions. To determine this, we scanned 8 young adults with DTI at 2.5 and 3mm resolutions, and an additional subject at 4 resolutions between 2-4 mm. We computed 70×70 connectivity matrices, using whole-brain tractography to measure fiber density between all pairs of 70 cortical and subcortical regions. Spatial and angular resolution affected the computed connectivity for narrower tracts (internal capsule and cerebellum), but also for the corticospinal tract. Data resolution affected the apparent role of some key structures in cortical anatomic networks. Care is needed when comparing network data across studies, and interpreting apparent disagreements among findings.

Diffusion tensor imaging has accelerated the study of brain connectivity, but single-tensor diffusion models are too simplistic to model fiber crossing and mixing. Hybrid diffusion imaging (HYDI) samples the radial and angular structure of local diffusion on multiple spherical shells in q-space, combining the high SNR and CNR achievable at low and high b-values, respectively. We acquired and analyzed human multi-shell HARDI at ultra-high field-strength (7 Tesla; b=1000, 2000, 3000 s/mm2). In experiments with the tensor distribution function (TDF), the b-value affected the intrinsic uncertainty for estimating component fiber orientations and their diffusion eigenvalues. We computed orientation density functions by least-squares fitting in multiple HARDI shells simultaneously. Within the range examined, higher b-values gave improved orientation estimates but poorer eigenvalue estimates; lower b-values showed opposite strengths and weaknesses. Combining these strengths, multiple-shell HARDI, especially with staggered angular sampling, outperformed single-shell scanning protocols, even when overall scanning time was held constant.

Previous findings suggested the role of the prefrontal cortex, hippocampus, and cingulate gyrus in major depressive disorders (MDD), but the white matter microstructural abnormalities of the fibers connecting these brain structures are not known. The purpose of this study was to test the hypothesis that white matter abnormalities are present in association fibers of the uncinate fasciculus (UF) and cingulum bundle (CB) among MDD subjects. A total of 21 MDD subjects aged between 30 and 65 years and 21 age-matched healthy controls (HC) were recruited. All subjects were right-handed and without history of diabetes or other cardiac diseases. We extracted quantitative tract-specific measures based on diffusion tensor imaging tractography to examine both diffusivity and geometric properties of the UF and CB. Significantly decreased fractional anisotropy (FA) and increased radial diffusivity of the right UF were observed in MDD patients compared with HC (po0.05), while their geometric characteristics remained relatively unchanged. Among MDD subjects, depression severity had a significant negative correlation with normalized number of fibers (NNF) in the right UF (r ¼ À0.53, p ¼ 0.02). We also found significant age effect (oldoyoung) in HC group and laterality effect (L4R) in both groups in the FA measure of the CB. Our study demonstrates novel findings of white matter microstructural abnormalities of the right UF in MDD. In the MDD group, the severity of depression is associated with reduced NNF in the right UF. These findings have implications for both clinical manifestations of depression as well as its pathophysiology.

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. High-angular resolution diffusion imaging (HARDI) can resolve more complex diffusion geometries than standard DTI, including fibers crossing or mixing. The tensor distribution function (TDF) can be used to reconstruct multiple underlying fibers per voxel, representing the diffusion profile as a probabilistic mixture of tensors. Here we found that DTIderived mean diffusivity (MD) correlates well with actual individual fiber MD, but DTI-derived FA correlates poorly with actual individual fiber anisotropy, and may be suboptimal when used to detect disease processes that affect myelination. Analysis of the TDFs revealed that almost 40% of voxels in the white matter had more than one dominant fiber present. To more accurately assess fiber integrity in these cases, we here propose the differential diffusivity (DD), which measures the average anisotropy based on all dominant directions in each voxel.

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

We introduce a fluid mechanics based tractography method that estimates the most likely connection path between points in a tensor distribution function (TDF) dataset. We simulated the flow of an artificial fluid whose properties are related to the underlying TDF dataset. The resulting fluid velocity was used as a metric of connection strength. We validated our algorithm using a digital phantom dataset based on a pattern with two intersecting tracts. When compared to a TDF streamline method and our single tensor fluid mechanics tractography algorithm, our method was able to segment intersecting tracts at a finer spatial resolution. Our method was successfully applied to human control data to segment a major fiber pathway, the corpus callosum, even in problematic regions with crossing fiber geometries.