Adaptive Multiresolution Research Articles

Medical image registration based on fast and adaptive bidimensional empirical mode decomposition

Image registration plays a crucial role in several areas, yet iconic registration methods are more efficient than those in geometrical registration, but they require great execution time. Regarding reduction in the execution time of iconic registration, the authors have proposed a new method based on mutual information while exploiting adaptive multiresolution decomposition, bidimensional empirical mode decomposition (BEMD) in its fast and adaptive version fast and adaptive BEMD (FABEMD). The idea is that instead of registering two images, the authors proceed to registration of the bidimensional intrinsic mode functions (BIMFs) that results from the FABEMD decomposition. The BIMF selected by the authors' algorithm is characterised by preservation of the general form of the image, and it contains a tone of grey levels lower than that of the original image, thus the number of combinations of the grey levels, used while calculating entropy is reduced, which in turn reduces execution time of the registration.

Multi-dimensional hybrid Fourier continuation–WENO solvers for conservation laws

We introduce a multi-dimensional point-wise multi-domain hybrid Fourier-Continuation/WENO technique (FC–WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and essentially dispersionless, spectral, solution away from discontinuities, as well as mild CFL constraints for explicit time stepping schemes. The hybrid scheme conjugates the expensive, shock-capturing WENO method in small regions containing discontinuities with the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [A. Harten, Adaptive multiresolution schemes for shock computations, J. Comput. Phys. 115 (1994) 319–338]. We consider a WENO scheme of formal order nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws are investigated for problems with both smooth and non-smooth solutions. The Euler equations for gas dynamics are solved for the Mach 3 and Mach 1.25 shock wave interaction with a small, plain, oblique entropy wave using the hybrid FC–WENO, the pure WENO and the hybrid central difference–WENO (CD–WENO) schemes. We demonstrate considerable computational advantages of the new FC-based method over the two alternatives. Moreover, in solving a challenging two-dimensional Richtmyer–Meshkov instability (RMI), the hybrid solver results in seven-fold speedup over the pure WENO scheme. Thanks to the multi-domain formulation of the solver, the scheme is straightforwardly implemented on parallel processors using message passing interface as well as on Graphics Processing Units (GPUs) using CUDA programming language. The performance of the solver on parallel CPUs yields almost perfect scaling, illustrating the minimal communication requirements of the multi-domain strategy. For the same RMI test, the hybrid computations on a single GPU, in double precision arithmetics, displays five- to six-fold speedup over the hybrid computations on a single CPU. The relative speedup of the hybrid computation over the WENO computations on GPUs is similar to that on CPUs, demonstrating the advantage of hybrid schemes technique on both CPUs and GPUs.

Adaptive multiresolution discontinuous Galerkin schemes for conservation laws

A multiresolution-based adaptation concept is proposed that aims at accelerating Discontinuous Galerkin schemes applied to nonlinear hyperbolic conservation laws. Opposite to standard adaptation concepts no error estimates are needed to tag mesh elements for refinement. Instead of this, a multiresolution analysis is performed on a hierarchy of nested grids for the data given on a uniformly refined mesh. This provides difference information between successive refinement levels, that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. A central mathematical problem addressed in this work is then to show that the adaptive solution is of the same accuracy as the reference solution on a uniformly refined mesh. Numerical comparisons demonstrate the efficiency of the concept and provide reliable estimates of the actual error in the numerical solution.

A Fully Adaptive Multiresolution Algorithm for Atrial Arrhythmia Simulation on Anatomically Realistic Unstructured Meshes

Biophysically detailed and anatomically realistic atrial models are emerging as a valuable tool in the study of atrial arrhythmias, nevertheless clinical use of these models would be favored by a reduction of computational times. This paper introduces a novel adaptive mesh algorithm, based on multiresolution representation (MR), for the efficient integration of cardiac ordinary differential equation (ODE)-partial differential equation (PDE) systems on unstructured triangle meshes. The algorithm applies a dynamically adapted node-centered finite volume method (FVM) scheme for integration of diffusion. The method accuracy and efficiency were evaluated by simulating propagation scenarios of increasing complexity levels (pacing, stable spirals, atrial fibrillation) on tomography-derived three-dimensional monolayer atrial models, based on a monodomain reaction-diffusion formulation coupled with the Courtemanche atrial ionic model. All simulated propagation patterns were accurately reproduced with substantially reduced computational times (10%-30% of the full-resolution simulation time). The proposed algorithm, combining the MR computational efficiency with the geometrical flexibility of unstructured meshes, may favor the development of patient-specific multiscale models of atrial arrhythmias and their application in the clinical setting.

Image Blind Separation Based on Adaptive Multi-Resolution Independent Component Analysis

In this paper, a novel image blind separation using adaptive multi-resolution independent component analysis is presented.This method separates mixed images based on quadratic function. The quadratic function can be interpreted as the time-frequency function or time-scale function, or other. According to the signal characteristics, we can choose the frequency resolution or scale resolution. The argorithm extends the separate technology from one dimensional domain to two dimensional domain,and it’s implement by adaptive procedure. The experimental result showed the method can be effective separation of mixed images. And it shows that the method is feasible.

Simulation of human ischemic stroke in realistic 3D geometry

In silico research in medicine is thought to reduce the need for expensive clinical trials under the condition of reliable mathematical models and accurate and efficient numerical methods. In the present work, we tackle the numerical simulation of reaction–diffusion equations modeling human ischemic stroke. This problem induces peculiar difficulties like potentially large stiffness which stems from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of steep spatial gradients in the reaction fronts, spatially very localized. Furthermore, simulations on realistic 3D geometries are mandatory in order to describe correctly this type of phenomenon. The main goal of this article is to obtain, for the first time, 3D simulations on realistic geometries and to show that the simulation results are consistent with those obtain in experimental studies or observed on MRI images in stroke patients.For this purpose, we introduce a new resolution strategy based mainly on time operator splitting that takes into account complex geometry coupled with a well-conceived parallelization strategy for shared memory architectures. We consider then a high order implicit time integration for the reaction and an explicit one for the diffusion term in order to build a time operator splitting scheme that exploits efficiently the special features of each problem. Thus, we aim at solving complete and realistic models including all time and space scales with conventional computing resources, that is on a reasonably powerful workstation. Consequently and as expected, 2D and also fully 3D numerical simulations of ischemic strokes for a realistic brain geometry, are conducted for the first time and shown to reproduce the dynamics observed on MRI images in stroke patients. Beyond this major step, in order to improve accuracy and computational efficiency of the simulations, we indicate how the present numerical strategy can be coupled with spatial adaptive multiresolution schemes. Preliminary results in the framework of simple geometries allow to assess the proposed strategy for further developments.

Numerical simulation of cooling gas injection using adaptive multiresolution techniques

The interaction of a jet of cooling gas injected through single boreholes or slots with a supersonic flow field plays an essential role in the design of innovative cooling systems. For a reliable validation of this technological concept thorough experimental and numerical investigations are necessary. A key inherent problem is the large bandwidth of scales that are relevant for the highly complex processes. Therefore, a sufficiently accurate resolution of all these scales at affordable computational cost requires accordingly advanced mathematical and algorithmic concepts. For that purpose we employ here an effective multiresolution grid adaptation technique based on advanced multiscale methods. In particular, it is shown that computations based on these concepts reveal features of the flow field that cannot be resolved by current experimental techniques.The underlying mathematical concept and its algorithmic realization is briefly summarized and thoroughly validated for the application at hand. To characterize the efficiency of cooling injection techniques, two- and three-dimensional simulations for slots of infinite and finite length are carried out with varying rates of cooling gas and a certain range of injection angles. The results of these simulations are compared with experimental data. In particular, we discover three-dimensional effects, occurring at the tips of a finite slot, that are not resolved by experiments and thus reveal new insight into the technical usability.

Wavelet-Based Adaptive Multiresolution Inversion for Quantitative Microwave Imaging of Breast Tissues

Microwave imaging is a feasible tool for medical imaging owing to the different electric properties of tissues. To this end, it is important to devise inversion procedures capable of achieving a reliable quantitative estimate of the tissues under test. With respect to breast screening, we propose a full-wave inversion method, which takes advantage of the adaptive multiresolution features of the wavelet basis to accommodate the trade off between spatial resolution and inversion stability. As shown through a preliminary numerical assessment on 2D anthropomorphic breast phantoms, the proposed approach is capable of achieving satisfying results without any a priori knowledge of breast shape, as well as of thickness and electric properties of the skin layer.

Improving multiresolution topology optimization via multiple discretizations

SUMMARYUnlike the traditional topology optimization approach that uses the same discretization for finite element analysis and design optimization, this paper proposes a framework for improving multiresolution topology optimization (iMTOP) via multiple distinct discretizations for: (1) finite elements; (2) design variables; and (3) density. This approach leads to high fidelity resolution with a relatively low computational cost. In addition, an adaptive multiresolution topology optimization (AMTOP) procedure is introduced, which consists of selective adjustment and refinement of design variable and density fields. Various two‐dimensional and three‐dimensional numerical examples demonstrate that the proposed schemes can significantly reduce computational cost in comparison to the existing element‐based approach. Copyright © 2012 John Wiley & Sons, Ltd.

Adaptive MultireSolution Modulation for Multimedia Traffic over Nakagami Fading Channels

Future wireless communications networks will be required to support a multitude of services with different reliability and latency requirements. However, achieving such flexible systems are challenging in Mobile Ad-hoc Networks (MANET) due to limited battery resources, node mobility, changes in path attenuation, and fluctuations in interference. By employing adaptive signaling techniques with Unequal Error Protection (UEP) to take advantage of the differences in the quality of service (QoS) requirements among different types of multimedia traffic, energy efficiency can be improved and also increase the data rate (spectral efficiency) over a fading channel, especially at low and moderate Carrier-to-Noise Ratio (CNR). This paper proposed a combination of curve fitting techniques that derives an exponential approximation to the average packet error rate (PER) probabilities as well as individual PER probabilities for asymmetrical phase-shift keying (PSK) and asymmetrical Quadrature Amplitude Modulation (QAM). Our design is both simpler and more robust than existing schemes.

Prototype development and field-test results of an adaptive multiresolution PANOPTES imaging architecture

The design, development, and field-test results of a visible-band, folded, multiresolution, adaptive computational imaging system based on the Processing Arrays of Nyquist-limited Observations to Produce a Thin Electro-optic Sensor (PANOPTES) concept is presented. The architectural layout that enables this imager to be adaptive is described, and the control system that ensures reliable field-of-view steering for precision and accuracy in subpixel target registration is explained. A digital superresolution algorithm introduced to obtain high-resolution imagery from field tests conducted in both nighttime and daytime imaging conditions is discussed. The digital superresolution capability of this adaptive PANOPTES architecture is demonstrated via results in which resolution enhancement by a factor of 4 over the detector Nyquist limit is achieved.

Adaptive multiresolution non-local means filter for three-dimensional magnetic resonance image denoising

In this study, an adaptive multiresolution version of the blockwise non-local (NL)-means filter is presented for three-dimensional (3D) magnetic resonance (MR) images. On the basis of an adaptive soft wavelet coefficient mixing, the proposed filter implicitly adapts the amount of denoising according to the spatial and frequency information contained in the image. Two versions of the filter are described for Gaussian and Rician noise. Quantitative validation was carried out on BrainWeb datasets by using several quality metrics. The results show that the proposed multiresolution filter obtained competitive performance compared with recently proposed Rician NL-means filters. Finally, qualitative experiments on anatomical and diffusion-weighted MR images show that the proposed filter efficiently removes noise while preserving fine structures in classical and very noisy cases. The impact of the proposed denoising method on fibre tracking is also presented on a HARDI dataset.

Adaptive multiresolution methods

These lecture notes present adaptive multiresolution schemes for evolutionary PDEs in Cartesian geometries. The discretization schemes are based either on finite volume or finite difference schemes. The concept of multiresolution analyses including Harten's approach for point and cell aver- ages is described in some detail. Then the sparse point representation method is discussed. Different strategies for adaptive time-stepping, like local scale dependent time stepping and time step control are presented. Numerous numerical examples in one, two and three space dimensions validate the adaptive schemes and illustrate the accuracy and the gain in computational efficiency in terms of CPU time and memory requirements. Another aspect, modeling of turbulent flows using multiresolution decompositions, the so-called Coherent Vortex Simulation ansatz is also described and examples are given for computations of three-dimensional weakly compressible mixing layers. Most of the material is assembled and adapted from previous publications (21,23-25,57,58).

Adaptive Multiresolution Methods: Practical issues on Data Structures, Implementation and Parallelization

The concept of fully adaptive multiresolution finite volume schemes has been developed and investigated during the past decade. Here grid adaptation is realized by performing a multiscale decomposition of the discrete data at hand. By means of hard thresholding the resulting multiscale data are compressed. From the remaining data a locally refined grid is constructed. The aim of the present work is to give a self-contained overview on the construction of an appropriate multiresolution analysis using biorthogonal wavelets, its efficient realization by means of hash maps using global cell identifiers and the parallelization of the multiresolution-based grid adaptation via MPI using space-filling curves.

New Resolution Strategy for Multi-scale Reaction Waves using Time Operator Splitting and Space Adaptive Multiresolution: Application to Human Ischemic Stroke

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts, spatially very localized. In this paper, we introduce a new resolution strategy based on time operator splitting and space adaptive multiresolution in the context of very localized and stiff reaction fronts. Based on recent theoretical studies of numerical analysis, such a strategy leads to a splitting time step which is not restricted neither by the fastest scales in the source term nor by restrictive diffusive step stability limits, but only by the physics of the phenomenon. We aim thus at solving accurately complete models including all time and space scales of the phenomenon, considering large simulation domains with conventional computing resources. The efficiency of the method is evaluated through 2D and 3D numerical simulations of a human ischemic stroke model, conducted on a simplified brain geometry, for which a simple parallelization strategy for shared memory architectures was implemented, in order to reduce computing costs related to detailed chemistry features of the model.

Tutorials on Adaptive multiresolution for mesh refinement applied to fluid dynamics and reactive media problems

This work aims at evaluating in practical situations the capability of the mesh renement technique based on the multiresolution adaptive method coupled with high resolution spatial and temporal approximations, to recover elementary physical mechanisms by achieving gains in both CPU time and memory use compared to single grid computations. We rst present a summary of the multiresolution procedure. We then describe MR algorithms. Finally, the evaluation of the method is presented on several well known numerical test cases in 1D and multi-D congurations. R esum e. Ce travail a pour objectif d' evaluer dans des situations pratiques, la capacit e d'une m ethode

Adaptive multiresolution analysis based on synchronization

We propose an adaptive multiscale approach to data analysis based on synchronization. The approach is nonlinear, data driven in the sense that it does not rely on a priori chosen basis, and automatically determines the data scale. Numerical results for one- and two-dimensional cases illustrate that the method works effectively for the usual modulated signals such as chirps, etc., as well as for more complicated data with multiple scales. The method extends straightforwardly to functions defined on weighted graphs and grids in high dimensions. Connections with some other recent approaches to multiscale analysis are briefly discussed.

New Resolution Strategy for Multiscale Reaction Waves using Time Operator Splitting, Space Adaptive Multiresolution, and Dedicated High Order Implicit/Explicit Time Integrators

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problem induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of steep spatial gradients in the reaction fronts, spatially very localized. In this paper, we introduce a new resolution strategy based on time operator splitting and space adaptive multiresolution in the context of very localized and stiff reaction fronts. The paper considers a high order implicit time integration of the reaction and an explicit one for the diffusion term in order to build a time operator splitting scheme that exploits efficiently the special features of each problem. Based on recent theoretical studies of numerical analysis such a strategy leads to a splitting time step which is restricted by neither the fastest scales in the source term nor by stability constraints of the diffusive steps but only by the physics of the phenomenon. We aim thus at solving complete models including all time and space scales within a prescribed accuracy, considering large simulation domains with conventional computing resources. The efficiency is evaluated through the numerical simulation of configurations which were so far out of reach of standard methods in the field of nonlinear chemical dynamics for two-dimensional spiral waves and three-dimensional scroll waves, as an illustration. Future extensions of the proposed strategy to more complex configurations involving other physical phenomena as well as optimization capability on new computer architectures are discussed.

Adaptive multiresolution analysis based on anisotropic triangulations

A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations on these triangulations. The refinement procedure consists in bisecting a triangle T in a direction which is chosen so as to minimize the local approximation error in some prescribed norm between the approximated function and its piecewise polynomial approximation after T is bisected. The hierarchical structure allows us to derive various approximation tools such as multiresolution analysis, wavelet bases, adaptive triangulations based either on greedy or optimal CART trees, as well as a simple encoding of the corresponding triangulations. We give a general proof of convergence in the Lp norm of all these approximations. Numerical tests performed in the case of piecewise linear approximation of functions with analytic expressions or of numerical images illustrate the fact that the refinement procedure generates triangles with an optimal aspect ratio (which is dictated by the local Hessian of of the approximated function in case of C2 functions).

Scalable Video Compression Framework With Adaptive Orientational Multiresolution Transform and Nonuniform Directional Filterbank Design

Although wavelet-based scalable video coding becomes the state-of-the-art video compression engine for its adaptability to heterogeneous networks and clients, a large number of attempts have been made to integrate local directionality onto discrete wavelet transform to explore the intrinsic geometrical structures. Taking into consideration that the contours and textures scattered in different scales change their directional resolutions as their curvatures change, we investigate adaptive directional resolutions along scales to achieve the dual (scale and orientation) multiresolution transform. This paper proposes nonuniform directional frequency decompositions for video representation and approximation, and exploits the nonuniformity of orientation multiresolution distribution and designs nonuniform directional filter banks to make the geometrical transform more sparse and efficient. The nonuniform directional frequency decomposition under arbitrary scales is fulfilled by a non-symmetric binary tree (NSBT) topology structure with nonuniform directional filterbank design. In turn, the proposed scalable video coding framework, called DMSVC, is enriched with the dual multiresolution transform. Each temporal subband through motion compensated temporal filtering is further decomposed into multiscale subbands, and the highpass wavelet subspaces are divided into an arbitrary number of directional subspaces in alignment with the orientation distribution via phase congruency to establish NSBT. The paraunitary perfect reconstruction condition is provided through a polyphase identical form of filter bank. Comparing with the isolated wavelet basis, our transform provides a greater correlated set of localized and anisotropic basis functions. The spatio-temporal subband coefficients are coded by a 3-D ESCOT entropy coding algorithm which is adopted to match the structure of NSBT. Experimental results show that the reconstructed video frames DMSVC in the proposed DMSVC scheme have better visual quality than existing scalable video coding schemes. It could produce higher compression ratio on video sequences full of directional edges and textures.