A New Integer-to-Integer Transform

This chapter presents a detailed analysis of an integer-to-integer transform that is closely related to the discrete Fourier transform, but that offers insights into signal structure that the DFT does not. The transform is analyzed for its underlying properties using concepts from number theory. Theorems are given along with proofs to help establish the salient features of the transform. Two kinds of redundancy exist in the transform. It is shown how redundancy implicit in the transform can be eliminated to obtain a simple form. Closed-form formulas for the forward and inverse transforms are presented

Image statistical frameworks for digital image forensics

The advances of digital cameras, scanners, printers, image editing tools, smartphones, tablet personal computers as well as high-speed networks have made a digital image a conventional medium for visual information. Creation, duplication, distribution, or tampering of such a medium can be easily done, which calls for the necessity to be able to trace back the authenticity or history of the medium. Digital image forensics is an emerging research area that aims to resolve the imposed problem and has grown in popularity over the past decade. On the other hand, anti-forensics has emerged over the past few years as a relatively new branch of research, aiming at revealing the weakness of the forensic technology. These two sides of research move digital image forensic technologies to the next higher level. Three major contributions are presented in this dissertation as follows. First, an effective multi-resolution image statistical framework for digital image forensics of passive-blind nature is presented in the frequency domain. The image statistical framework is generated by applying Markovian rake transform to image luminance component. Markovian rake transform is the applications of Markov process to difference arrays which are derived from the quantized block discrete cosine transform 2-D arrays with multiple block sizes. The efficacy and universality of the framework is then evaluated in two major applications of digital image forensics: 1) digital image tampering detection; 2) classification of computer graphics and photographic images. Second, a simple yet effective anti-forensic scheme is proposed, capable of obfuscating double JPEG compression artifacts, which may vital information for image forensics, for instance, digital image tampering detection. Shrink-and-zoom (SAZ) attack, the proposed scheme, is simply based on image resizing and bilinear interpolation. The effectiveness of SAZ has been evaluated over two promising double JPEG compression schemes and the outcome reveals that the proposed scheme is effective, especially in the cases that the first quality factor is lower than the second quality factor. Third, an advanced textural image statistical framework in the spatial domain is proposed, utilizing local binary pattern (LBP) schemes to model local image statistics on various kinds of residual images including higher-order ones. The proposed framework can be implemented either in single- or multi-resolution setting depending on the nature of application of interest. The efficacy of the proposed framework is evaluated on two forensic applications: 1) steganalysis with emphasis on HUGO (Highly Undetectable Steganography), an advanced steganographic scheme embedding hidden data in a content-adaptive manner locally into some image regions which are difficult for modeling image statics; 2) image recapture detection (IRD). The outcomes of the evaluations suggest that the proposed framework is effective, not only for detecting local changes which is in line with the nature of HUGO, but also for detecting global difference (the nature of IRD)

A matrix model for simple Hurwitz numbers, and topological recursion

We introduce a new matrix model representation for the generating function of simple Hurwitz numbers. We calculate the spectral curve of the model and the associated symplectic invariants developed in [Eynard-Orantin]. As an application, we prove the conjecture proposed by Bouchard and Marino, relating Hurwitz numbers to the spectral invariants of the Lambert curve exp(x)=y exp(-y).Comment: 24 pages, 3 figure

Respiratory organ motion in interventional MRI : tracking, guiding and modeling

Respiratory organ motion is one of the major challenges in interventional MRI, particularly in interventions with therapeutic ultrasound in the abdominal region. High-intensity focused ultrasound found an application in interventional MRI for noninvasive treatments of different abnormalities. In order to guide surgical and treatment interventions, organ motion imaging and modeling is commonly required before a treatment start. Accurate tracking of organ motion during various interventional MRI procedures is prerequisite for a successful outcome and safe therapy. In this thesis, an attempt has been made to develop approaches using focused ultrasound which could be used in future clinically for the treatment of abdominal organs, such as the liver and the kidney. Two distinct methods have been presented with its ex vivo and in vivo treatment results. In the first method, an MR-based pencil-beam navigator has been used to track organ motion and provide the motion information for acoustic focal point steering, while in the second approach a hybrid imaging using both ultrasound and magnetic resonance imaging was combined for advanced guiding capabilities. Organ motion modeling and four-dimensional imaging of organ motion is increasingly required before the surgical interventions. However, due to the current safety limitations and hardware restrictions, the MR acquisition of a time-resolved sequence of volumetric images is not possible with high temporal and spatial resolution. A novel multislice acquisition scheme that is based on a two-dimensional navigator, instead of a commonly used pencil-beam navigator, was devised to acquire the data slices and the corresponding navigator simultaneously using a CAIPIRINHA parallel imaging method. The acquisition duration for four-dimensional dataset sampling is reduced compared to the existing approaches, while the image contrast and quality are improved as well. Tracking respiratory organ motion is required in interventional procedures and during MR imaging of moving organs. An MR-based navigator is commonly used, however, it is usually associated with image artifacts, such as signal voids. Spectrally selective navigators can come in handy in cases where the imaging organ is surrounding with an adipose tissue, because it can provide an indirect measure of organ motion. A novel spectrally selective navigator based on a crossed-pair navigator has been developed. Experiments show the advantages of the application of this novel navigator for the volumetric imaging of the liver in vivo, where this navigator was used to gate the gradient-recalled echo sequence

On pp-adic LL-functions for Hilbert modular forms

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does not require any small slope or non-criticality assumptions on the $p$-refinement. The main new ingredients are an adelic definition of a canonical map from overconvergent cohomology to a space of locally analytic distributions on the relevant Galois group and a smoothness theorem for certain eigenvarieties at critically refined points.Comment: 88 page

The role of metabotropic glutamate receptors in the thalamocortical circuit during spontaneous epileptic activity

Spontaneous epileptic activity resembling spike wave discharges (SWD) characteristic of Generalized Absence (GA) epilepsy was induced in rat thalamocortical (TC) slices by incubating the slices in low-Mg2- artificial cerebrospinal fluid (ACSF) Extracellular field potentials were recorded in the cortex and thalamus to determine the effects of the broad spectrum metabotropic glutamate receptor (mGluR) agonist, trans- (1S, 3R)-1-Amino-1, 3-cyclopentanedicarboxylic acid (ACPD), ACPD elicited concentration dependent effects on the duration of SWD. At 1 μM ACPD (n=3) there were no significant changes in duration of activity. At 20 μM, 11 of 13 slices displayed a decrease in duration of activity (mean = 40.47 ± 5.07). In all cases, 200 μM ACPD (n=6) transformed SWD into single spike activity. Furthermore, the broad spectrum mGluR antagonist, (S)-α-Methyl-4-carboxyphenlglycine ((S)-MCPG), when pre-applied to TC slices at 500. μM followed by co-application with 200 μM ACPD (n=3), prevented SWD from switching into single spike activity. To determine the site of action of the mGluR agonist. experiments involving regional perfusion of 200 μM ACPD to the cortex (n=3) and thalamus (n=4) were conducted. mGluR activation in the cortex was unable to block SWD, while perfusion of the mGluR agonist to the thalamus transformed SWD into single spikes on all occasions. mGluRs may provide an alternative therapeutic target for the pharmacological treatment of GA epilepsy

Magnetic resonance imaging and navigation of ferromagnetic thermoseeds to deliver thermal ablation therapy

Minimally invasive therapies aim to deliver effective treatment whilst reducing off-target burden, limiting side effects, and shortening patient recovery times. Remote navigation of untethered devices is one method that can be used to deliver targeted treatment to deep and otherwise inaccessible locations within the body. Minimally invasive image-guided ablation (MINIMA) is a novel thermal ablation therapy for the treatment of solid tumours, whereby an untethered ferromagnetic thermoseed is navigated through tissue to a target site within the body, using the magnetic field gradients generated by a magnetic resonance imaging (MRI) system. Once at the tumour, the thermoseed is heated remotely using an alternating magnetic field, to induce cell death in the surrounding cancer tissue. The thermoseed is then navigated through the tumour, heating at pre-defined locations until the entire volume has been ablated. The aim of this PhD project is to develop MINIMA through a series of proof-of-concept studies and to assess the efficacy of the three key project components: imaging, navigation, and heating. First, an MR imaging sequence was implemented to track the thermoseeds during navigation and subsequently assessed for precision and accuracy. Secondly, movement of the thermoseeds through a viscous fluid was characterised, by measuring the effect of different navigation parameters. This was followed by navigation experiments performed in ex vivo tissue. To assess thermoseed heating, a series of in vitro experiments were conducted in air, water, and ex vivo liver tissue, before moving onto in vivo experiments in the rat brain and a murine subcutaneous tumour model. These final experiments allowed the extent of cell death induced by thermoseed heating to be determined, in both healthy and diseased tissue respectively