Reconstruction from projections, RP (1), has been revaluated for MRI applications, especially for real time and functional MRI (fMRI). In fact, RP methods reduce the effects due to motion because the centre of k-space is over-sampled and it is sampled at the start of the reading time, thus eliminating movement occurring in the last period of the reading interval. Moreover RP methods improve the signal to noise ratio (SNR) in the reconstructed image as a result of over-sampling of the central region of the k-space. It has been demonstrated elsewhere (2) that it may be possible to reduce the number of collected projections, below the minimum required to obtain an image of a given dimension without artefacts, if information about sample internal symmetries and shape can be collected during acquisition. In fact, the method presented in (2) is able to collect a near optimal set of projections without any a-priori information about the sample, by calculating the information content of the projections through an entropy function, during the progress of the acquisition process (for this reason, we refer to it as the blind adaptive method). This method, suffers from two limitations: some important projections are excluded from the acquired set, especially in the proximity of entropy function minima or maxima; it is necessary to use efficient software (dedicated hardware is also to be recommended) to calculate the information content of the collected projections during the sequence repetition time, without wasting time. Aims of this work is to overcome these limitations by presenting a method which collects a-priori information about the sample through the preliminary measurement of two circular paths at different distances from the k-space centre. The directions of the most informative projections can then be set using information acquired from the power spectra of these paths of coefficients.
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