The Mathematical Foundations of 3D Compton Scatter Emission Imaging

The mathematical principles of tomographic imaging using detected (unscattered) X- or gamma-rays are based on the two-dimensional Radon transform and many of its variants. In this paper, we show that two new generalizations, called conical Radon transforms, are related to three-dimensional imaging processes based on detected Compton scattered radiation. The first class of conical Radon transform has been introduced recently to support imaging principles of collimated detector systems. The second class is new and is closely related to the Compton camera imaging principles and invertible under special conditions. As they are poised to play a major role in future designs of biomedical imaging systems, we present an account of their most important properties which may be relevant for active researchers in the field

A parallel VLSI architecture for a digital filter of arbitrary length using Fermat number transforms

A parallel architecture for computation of the linear convolution of two sequences of arbitrary lengths using the Fermat number transform (FNT) is described. In particular a pipeline structure is designed to compute a 128-point FNT. In this FNT, only additions and bit rotations are required. A standard barrel shifter circuit is modified so that it performs the required bit rotation operation. The overlap-save method is generalized for the FNT to compute a linear convolution of arbitrary length. A parallel architecture is developed to realize this type of overlap-save method using one FNT and several inverse FNTs of 128 points. The generalized overlap save method alleviates the usual dynamic range limitation in FNTs of long transform lengths. Its architecture is regular, simple, and expandable, and therefore naturally suitable for VLSI implementation

Scattered Radiation Emission Imaging: Principles and Applications

Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested in the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to overcome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically, it consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image formation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on circular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular invertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical simulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential applications in various fields

On the V-Line Radon Transform and Its Imaging Applications

Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results

A VLSI pipeline design of a fast prime factor DFT on a finite field

A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). A pipeline structure is used to implement this prime factor DFT over GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented

A role for jasmonates in the release of dormancy by cold stratification in wheat

Hydration at low temperatures, commonly referred to as cold stratification, is widely used for releasing dormancy and triggering germination in a wide range of species including wheat. However, the molecular mechanism that underlies its effect on germination has largely remained unknown. Our previous studies showed that methyl-jasmonate, a derivative of jasmonic acid (JA), promotes dormancy release in wheat. In this study, we found that cold-stimulated germination of dormant grains correlated with a transient increase in JA content and expression of JA biosynthesis genes in the dormant embryos after transfer to 20 (o)C. The induction of JA production was dependent on the extent of cold imbibition and precedes germination. Blocking JA biosynthesis with acetylsalicylic acid (ASA) inhibited the cold-stimulated germination in a dose-dependent manner. In addition, we have explored the relationship between JA and abscisic acid (ABA), a well-known dormancy promoter, in cold regulation of dormancy. We found an inverse relationship between JA and ABA content in dormant wheat embryos following stratification. ABA content decreased rapidly in response to stratification, and the decrease was reversed by addition of ASA. Our results indicate that the action of JA on cold-stratified grains is mediated by suppression of two key ABA biosynthesis genes, TaNCED1 and TaNCED2.This project was funded by a CSIRO Office of the Chief Executive PDF scheme

A single chip VLSI Reed-Solomon decoder

A new VLSI design of a pipeline Reed-Solomon decoder is presented. The transform decoding technique used in a previous design is replaced by a time domain algorithm. A new architecture that implements such an algorithm permits efficient pipeline processing with minimum circuitry. A systolic array is also developed to perform erasure corrections in the new design. A modified form of Euclid's algorithm is implemented by a new architecture that maintains the throughput rate with less circuitry. Such improvements result in both enhanced capability and a significant reduction in silicon area, therefore making it possible to build a pipeline (31,15)RS decoder on a single VLSI chip

Direct observation of dynamic surface acoustic wave controlled carrier injection into single quantum posts using phase-resolved optical spectroscopy

A versatile stroboscopic technique based on active phase-locking of a surface acoustic wave to picosecond laser pulses is used to monitor dynamic acoustoelectric effects. Time-integrated multi-channel detection is applied to probe the modulation of the emission of a quantum well for different frequencies of the surface acoustic wave. For quantum posts we resolve dynamically controlled generation of neutral and charged excitons and preferential injection of holes into localized states within the nanostructure.Comment: 10 pages, 4 figure

Testing Australian standard consumers' understanding of the language used to describe wine

With reference to 64 common descriptors of the sensory properties of wine (e.g., tannic, full-bodied, etc.), we investigated the extent to which these terms are understood by Australian standard consumers in relation to an opposite property (i.e., as happens in the case of experts). The study also determined how consistently these dimensions were among the group of participants. The results confirmed that the sensorial dimensions relating to wine can be modeled in terms of opposites for standard wine consumers in more than 80% of cases. However, there was a great deal of variability between the properties in terms of the opposites which were elicited indicating that some terms are less open to ambiguity while others are associated with many different opposites. A comparison of the results with those from similar studies with Italian and Vietnamese participants is addressed in the final section. Practical Applications The aim of the study was to replicate previous research conducted with Italian participants, but in this case involving Australian participants, with a view to compare participants from a traditional wine-producing country with those from a relatively newly established wine-producing country. A similar study had already been carried out with Vietnamese participants, that is, with consumers from a country with less familiarity with grape wines. The importance of this study rests on the fact that English is one of the most commonly spoken languages in the world and, as such, the study represents a relevant evolution of the original research. Opposites seem to be a useful point of reference for standard consumers in all of these countries in terms of their understanding of the terms used to describe wine. This and the fact that there seems to be a certain degree of uncertainty regarding people's understanding of many of these terms indicate that it may be necessary to reconceptualize the sensory dimensions relating to wine. From a practical point of view, this is certainly of interest to wine producers since it can help in the marketing of their products

VLSI architectures for computing multiplications and inverses in GF(2-m)

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation