Semi-local scaling exponent estimation with box-penalty constraints and total-variation regularisation

We here establish and exploit the result that 2-D isotropic self-similar fields beget quasi-decorrelated wavelet coefficients and that the resulting localised log sample second moment statistic is asymptotically normal. This leads to the development of a semi-local scaling exponent estimation framework with optimally modified weights. Furthermore, recent interest in penalty methods for least squares problems and generalised Lasso for scaling exponent estimation inspires the simultaneous incorporation of both bounding box constraints and total variation smoothing into an iteratively reweighted least-squares estimator framework. Numerical results on fractional Brownian fields with global and piecewise constant, semi-local Hurst parameters illustrate the benefits of the new estimators

Noise Covariance Properties in Dual-Tree Wavelet Decompositions

Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is performed -- which occurs in particular when an additive noise is corrupting the signal to be analyzed -- it is useful to characterize the statistical properties of the dual-tree wavelet coefficients of this process. As dual-tree decompositions constitute overcomplete frame expansions, correlation structures are introduced among the coefficients, even when a white noise is analyzed. In this paper, we show that it is possible to provide an accurate description of the covariance properties of the dual-tree coefficients of a wide-sense stationary process. The expressions of the (cross-)covariance sequences of the coefficients are derived in the one and two-dimensional cases. Asymptotic results are also provided, allowing to predict the behaviour of the second-order moments for large lag values or at coarse resolution. In addition, the cross-correlations between the primal and dual wavelets, which play a primary role in our theoretical analysis, are calculated for a number of classical wavelet families. Simulation results are finally provided to validate these results

Methods for characterising microphysical processes in plasmas

Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geospace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.Comment: Space Science Reviews (2013), in pres

Multi-Modal Enhancement Techniques for Visibility Improvement of Digital Images

Image enhancement techniques for visibility improvement of 8-bit color digital images based on spatial domain, wavelet transform domain, and multiple image fusion approaches are investigated in this dissertation research. In the category of spatial domain approach, two enhancement algorithms are developed to deal with problems associated with images captured from scenes with high dynamic ranges. The first technique is based on an illuminance-reflectance (I-R) model of the scene irradiance. The dynamic range compression of the input image is achieved by a nonlinear transformation of the estimated illuminance based on a windowed inverse sigmoid transfer function. A single-scale neighborhood dependent contrast enhancement process is proposed to enhance the high frequency components of the illuminance, which compensates for the contrast degradation of the mid-tone frequency components caused by dynamic range compression. The intensity image obtained by integrating the enhanced illuminance and the extracted reflectance is then converted to a RGB color image through linear color restoration utilizing the color components of the original image. The second technique, named AINDANE, is a two step approach comprised of adaptive luminance enhancement and adaptive contrast enhancement. An image dependent nonlinear transfer function is designed for dynamic range compression and a multiscale image dependent neighborhood approach is developed for contrast enhancement. Real time processing of video streams is realized with the I-R model based technique due to its high speed processing capability while AINDANE produces higher quality enhanced images due to its multi-scale contrast enhancement property. Both the algorithms exhibit balanced luminance, contrast enhancement, higher robustness, and better color consistency when compared with conventional techniques. In the transform domain approach, wavelet transform based image denoising and contrast enhancement algorithms are developed. The denoising is treated as a maximum a posteriori (MAP) estimator problem; a Bivariate probability density function model is introduced to explore the interlevel dependency among the wavelet coefficients. In addition, an approximate solution to the MAP estimation problem is proposed to avoid the use of complex iterative computations to find a numerical solution. This relatively low complexity image denoising algorithm implemented with dual-tree complex wavelet transform (DT-CWT) produces high quality denoised images

Multiscale analysis of high frequency exchange rate time series

Imperial Users onl

Distortion-constraint compression of three-dimensional CLSM images using image pyramid and vector quantization

The confocal microscopy imaging techniques, which allow optical sectioning, have been successfully exploited in biomedical studies. Biomedical scientists can benefit from more realistic visualization and much more accurate diagnosis by processing and analysing on a three-dimensional image data. The lack of efficient image compression standards makes such large volumetric image data slow to transfer over limited bandwidth networks. It also imposes large storage space requirements and high cost in archiving and maintenance. Conventional two-dimensional image coders do not take into account inter-frame correlations in three-dimensional image data. The standard multi-frame coders, like video coders, although they have good performance in capturing motion information, are not efficiently designed for coding multiple frames representing a stack of optical planes of a real object. Therefore a real three-dimensional image compression approach should be investigated. Moreover the reconstructed image quality is a very important concern in compressing medical images, because it could be directly related to the diagnosis accuracy. Most of the state-of-the-arts methods are based on transform coding, for instance JPEG is based on discrete-cosine-transform CDCT) and JPEG2000 is based on discrete- wavelet-transform (DWT). However in DCT and DWT methods, the control of the reconstructed image quality is inconvenient, involving considerable costs in computation, since they are fundamentally rate-parameterized methods rather than distortion-parameterized methods. Therefore it is very desirable to develop a transform-based distortion-parameterized compression method, which is expected to have high coding performance and also able to conveniently and accurately control the final distortion according to the user specified quality requirement. This thesis describes our work in developing a distortion-constraint three-dimensional image compression approach, using vector quantization techniques combined with image pyramid structures. We are expecting our method to have: 1. High coding performance in compressing three-dimensional microscopic image data, compared to the state-of-the-art three-dimensional image coders and other standardized two-dimensional image coders and video coders. 2. Distortion-control capability, which is a very desirable feature in medical 2. Distortion-control capability, which is a very desirable feature in medical image compression applications, is superior to the rate-parameterized methods in achieving a user specified quality requirement. The result is a three-dimensional image compression method, which has outstanding compression performance, measured objectively, for volumetric microscopic images. The distortion-constraint feature, by which users can expect to achieve a target image quality rather than the compressed file size, offers more flexible control of the reconstructed image quality than its rate-constraint counterparts in medical image applications. Additionally, it effectively reduces the artifacts presented in other approaches at low bit rates and also attenuates noise in the pre-compressed images. Furthermore, its advantages in progressive transmission and fast decoding make it suitable for bandwidth limited tele-communications and web-based image browsing applications