Recent advances allow for the construction of filters with precisely defined frequency response for use in Raman chemical spectroscopy. In this paper we give a probabilistic interpretation of the output of such filters and use this to give an algorithm to design optimal filters to minimize the mean squared error in the estimated photon emission rates for multiple spectra. Experiments using these filters demonstrate that detecting as few as ~10 Raman scattered photons in as little time as ~30μs can be sufficient to positively distinguish chemical species. This speed should allow "chemical imaging" of samples.
Functional (time-dependent) Magnetic Resonance Imaging can be used to
determine which parts of the brain are active during various limited
activities; these parts of the brain are called activation regions.
In this preliminary study we describe some experiments that are suggested from the following questions: Does one get improved results by analyzing the complex image data rather than just the real magnitude image data? Does wavelet shrinkage smoothing improve
images? Should one smooth in time as well as within and between slices? If so, how should one model the relationship between time smoothness (or correlations) and spatial smoothness (or correlations). The measured data is really the Fourier coefficients of the complex image---should we remove noise in the Fourier domain before computing the complex images? In this preliminary study we describe some experiments related to these questions.