Enhancement of Single and Composite Images Based on Contourlet Transform Approach

Image enhancement is an imperative step in almost every image processing algorithms. Numerous image enhancement algorithms have been developed for gray scale images despite their absence in many applications lately. This thesis proposes hew image enhancement techniques of 8-bit single and composite digital color images. Recently, it has become evident that wavelet transforms are not necessarily best suited for images. Therefore, the enhancement approaches are based on a new 'true' two-dimensional transform called contourlet transform. The proposed enhancement techniques discussed in this thesis are developed based on the understanding of the working mechanisms of the new multiresolution property of contourlet transform. This research also investigates the effects of using different color space representations for color image enhancement applications. Based on this investigation an optimal color space is selected for both single image and composite image enhancement approaches. The objective evaluation steps show that the new method of enhancement not only superior to the commonly used transformation method (e.g. wavelet transform) but also to various spatial models (e.g. histogram equalizations). The results found are encouraging and the enhancement algorithms have proved to be more robust and reliable

Locally adaptive image denoising by a statistical multiresolution criterion

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector in this framework. Numerical examples illustrate the usefulness of our approach. We also present an application in confocal microscopy

Multiresolution iterative reconstruction for region of interest imaging in X-ray cone-beam computed tomography

A method and apparatus is provided to generate a multiresolution image having at least two regions with different pixel pitches. The multiresolution image is reconstructed using projection data having various pixel pitches corresponding to the pixel pitches of the multiresolution image. By using a higher resolution inside regions of interest (ROIs) in both the image and projection domains and lower resolution outside the ROIs, fast image reconstruction can be performed while avoiding truncation artifacts, which result imaging is limited to an ROI excluding attenuation regions. Further, those regions of greater clinical relevance and greater structural variance within the reconstructed images can be selected to be within the ROIs to improve the clinical benefit of the multiresolution image. The multiresolution image can be reconstructed using an iterative reconstruction method in which the high- and low-resolution regions are uniquely evaluated

Wavelet representation of functions defined on tetrahedrical grids

In this paper, a method for representing scalar functions on volumes is presented. The method is based on wavelets and it can be used for representing volumetric data (geometric or scalar) defifined on non structured grids. The basic contribution is the extension of wavelets to represent scalar functions on volumetric domains of arbitrary topological type. This extension is made by constructing a wavelet basis defifined on any tetrahedrized volume. This basis construction is achieved using multiresolution analysis and the lifting schemeFacultad de Informátic

Randomized Multiresolution Scanning in Focal and Fast E/MEG Sensing of Brain Activity with a Variable Depth

We focus on electromagnetoencephalography imaging of the neural activity and, in particular, finding a robust estimate for the primary current distribution via the hierarchical Bayesian model (HBM). Our aim is to develop a reasonably fast maximum a posteriori (MAP) estimation technique which would be applicable for both superficial and deep areas without specific a priori knowledge of the number or location of the activity. To enable source distinguishability for any depth, we introduce a randomized multiresolution scanning (RAMUS) approach in which the MAP estimate of the brain activity is varied during the reconstruction process. RAMUS aims to provide a robust and accurate imaging outcome for the whole brain, while maintaining the computational cost on an appropriate level. The inverse gamma (IG) distribution is applied as the primary hyperprior in order to achieve an optimal performance for the deep part of the brain. In this proof-of-the-concept study, we consider the detection of simultaneous thalamic and somatosensory activity via numerically simulated data modeling the 14-20 ms post-stimulus somatosensory evoked potential and field response to electrical wrist stimulation. Both a spherical and realistic model are utilized to analyze the source reconstruction discrepancies. In the numerically examined case, RAMUS was observed to enhance the visibility of deep components and also marginalizing the random effects of the discretization and optimization without a remarkable computation cost. A robust and accurate MAP estimate for the primary current density was obtained in both superficial and deep parts of the brain.Comment: Brain Topogr (2020

Posterior sampling for inverse imaging problems on the sphere in seismology and cosmology

In this work, we describe a framework for solving spherical inverse imaging problems using posterior sampling for full uncertainty quantification. Inverse imaging problems defined on the sphere arise in many fields, including seismology and cosmology where images are defined on the globe and the cosmic sphere, and are generally high-dimensional and computationally expensive. As a result, sampling the posterior distribution of spherical imaging problems is a challenging task. Our framework leverages a proximal Markov chain Monte Carlo (MCMC) algorithm to efficiently sample the high-dimensional space of spherical images with a sparsity-promoting wavelet prior. We detail the modifications needed for the algorithm to be applied to spherical problems, and give special consideration to the crucial forward modelling step which contains computationally expensive spherical harmonic transforms. By sampling the posterior, our framework allows for full and flexible uncertainty quantification, something which is not possible with other methods based on, for example, convex optimisation. We demonstrate our framework in practice on full-sky cosmological mass-mapping and to the construction of phase velocity maps in global seismic tomography. We find that our approach is potentially useful at moderate resolutions, such as those of interest in seismology. However at high resolutions, such as those required for astrophysical applications, the poor scaling of the complexity of spherical harmonic transforms severely limits our method, which may be resolved with future GPU implementations. A new Python package, pxmcmc, containing the proximal MCMC sampler, measurement operators, wavelet transforms and sparse priors is made publicly available