Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Large Deformation Multiresolution Diffeomorphic Metric Mapping for Multiresolution Cortical Surfaces: A Coarse-to-Fine Approach

Abstract: Brain surface registration is an important tool for characterizing cortical anatomical variations and understanding their roles in normal cortical development and psychiatric diseases. However, surface registration remains challenging due to complicated cortical anatomy and its large differences across individuals. In this paper, we propose a fast coarse-to-fine algorithm for surface registration by adapting the large diffeomorphic deformation metric mapping (LDDMM) framework for surface mapping and show improvements in speed and accuracy via a multiresolution analysis of surface meshes and the construction of multiresolution diffeomorphic transformations. The proposed method constructs a family of multiresolution meshes that are used as natural sparse priors of the cortical morphology. At varying resolutions, these meshes act as anchor points where the parameterization of multiresolution deformation vector fields can be supported, allowing the construction of a bundle of multiresolution deformation fields, each originating from a different resolution. Using a coarse-to-fine approach, we show a potential reduction in computation cost along with improvements in sulcal alignment when compared with LDDMM surface mapping.

Maximum-likelihood multiresolution laser radar range imaging

Abstract: Maximum-likelihood range imaging is considered for pulsed-imager operation of a coherent laser radar. The expectation-maximization (EM) algorithm is used to develop an explicit procedure for maximum-likelihood fitting of a multiresolution (wavelet) basis-at a sequence of increasingly fine resolutions-to laser radar range data. Specialization to the Haar-wavelet basis yields a procedure that is both computationally efficient and numerically robust. Basic analytical properties of the estimation algorithm and its performance are presented, along with results based on simulated and real laser radar range data. It is shown that the weights associated with the expectation-maximization iterations provide a reliable indicator for terminating the coarse-to-fine resolution progression. At the weight-determined stopping point, estimation performance approaches the ultimate limit set by the complete-data bound.

Interest rate next-day variation prediction based on hybrid feedforward neural network, particle swarm optimization, and multiresolution techniques

Abstract: Multiresolution analysis techniques including continuous wavelet transform, empirical mode decomposition, and variational mode decomposition are tested in the context of interest rate next-day variation prediction. In particular, multiresolution analysis techniques are used to decompose interest rate actual variation and feedforward neural network for training and prediction. Particle swarm optimization technique is adopted to optimize its initial weights. For comparison purpose, autoregressive moving average model, random walk process and the naive model are used as main reference models. In order to show the feasibility of the presented hybrid models that combine multiresolution analysis techniques and feedforward neural network optimized by particle swarm optimization, we used a set of six illustrative interest rates; including Moody’s seasoned Aaa corporate bond yield, Moody’s seasoned Baa corporate bond yield, 3-Month, 6-Month and 1-Year treasury bills, and effective federal fund rate. The forecasting results show that all multiresolution-based prediction systems outperform the conventional reference models on the criteria of mean absolute error, mean absolute deviation, and root mean-squared error. Therefore, it is advantageous to adopt hybrid multiresolution techniques and soft computing models to forecast interest rate daily variations as they provide good forecasting performance.

Wavelet video denoising with regularized multiresolution motion estimation

Abstract: This paper develops a new approach to video denoising, in which motion estimation/compensation, temporal filtering, and spatial smoothing are all undertaken in the wavelet domain. The key to making this possible is the use of a shift-invariant, overcomplete wavelet transform, which allows motion between image frames to be manifested as an equivalent motion of coefficients in the wavelet domain. Our focus is on minimizing spatial blurring, restricting to temporal filtering when motion estimates are reliable, and spatially shrinking only insignificant coefficients when the motion is unreliable. Tests on standard video sequences show that our results yield comparable PSNR to the state of the art in the literature, but with considerably improved preservation of fine spatial details.

A Multiresolution Approach to Iterative Reconstruction Algorithms in X-Ray Computed Tomography

Abstract: In computed tomography, the application of iterative reconstruction methods in practical situations is impeded by their high computational demands. Especially in high resolution X-ray computed tomography, where reconstruction volumes contain a high number of volume elements (several giga voxels), this computational burden prevents their actual breakthrough. Besides the large amount of calculations, iterative algorithms require the entire volume to be kept in memory during reconstruction, which quickly becomes cumbersome for large data sets. To overcome this obstacle, we present a novel multiresolution reconstruction, which greatly reduces the required amount of memory without significantly affecting the reconstructed image quality. It is shown that, combined with an efficient implementation on a graphical processing unit, the multiresolution approach enables the application of iterative algorithms in the reconstruction of large volumes at an acceptable speed using only limited resources.