Statistical image modelling using interscale phase relationships of complex wavelet coefficients

A novel method for modelling the statistics of 2D photographic images useful in image restoration is defined. The new method is based on the Dual Tree Complex Wavelet Transform (DT-CWT) but a phase rotation is applied to the coefficients to create complex coefficients whose phase is shift-invariant at multiscale edge and ridge features. This is in addition to the magnitude shift invariance achieved by the DT-CWT. The increased correlation between coefficients adjacent in space and scale provides an improved mechanism for signal estimation. © 2006 IEEE.

Modelling within-host spatiotemporal dynamics of invasive bacterial disease

Mechanistic determinants of bacterial growth, death, and spread within mammalian hosts cannot be fully resolved studying a single bacterial population. They are also currently poorly understood. Here, we report on the application of sophisticated experimental approaches to map spatiotemporal population dynamics of bacteria during an infection. We analyzed heterogeneous traits of simultaneous infections with tagged Salmonella enterica populations (wild-type isogenic tagged strains [WITS]) in wild-type and gene-targeted mice. WITS are phenotypically identical but can be distinguished and enumerated by quantitative PCR, making it possible, using probabilistic models, to estimate bacterial death rate based on the disappearance of strains through time. This multidisciplinary approach allowed us to establish the timing, relative occurrence, and immune control of key infection parameters in a true host-pathogen combination. Our analyses support a model in which shortly after infection, concomitant death and rapid bacterial replication lead to the establishment of independent bacterial subpopulations in different organs, a process controlled by host antimicrobial mechanisms. Later, decreased microbial mortality leads to an exponential increase in the number of bacteria that spread locally, with subsequent mixing of bacteria between organs via bacteraemia and further stochastic selection. This approach provides us with an unprecedented outlook on the pathogenesis of S. enterica infections, illustrating the complex spatial and stochastic effects that drive an infectious disease. The application of the novel method that we present in appropriate and diverse host-pathogen combinations, together with modelling of the data that result, will facilitate a comprehensive view of the spatial and stochastic nature of within-host dynamics. © 2008 Grant et al.