Hemodynamics of the human brain may be studied with Dynamic Susceptibility Contrast MRI (DSC-MRI) imaging. The sequence of volumes obtained exhibits a strong spatiotemporal correlation, that can be exploited to predict which measurements will bring mostly the new information contained in the next frames. In general, the sampling speed is an important issue in many applications of the MRI, so that the focus of many current researches is to study methods to reduce the number of measurement samples needed for each frame without degrading the image quality. For the DSC-MRI, the frequency under-sampling of single frame can be exploited to make more frequent space or time acquisitions, thus increasing the time resolution and allowing the analysis of fast dynamics not yet observed. Generally (and also for MRI), the recovery of sparse signals has been achieved by Compressed Sensing (CS) techniques, which are based on statistical properties rather than deterministic ones.. By studying analytically the compound Fourier+Wavelet transform, involved in the processes of reconstruction and sparsification of MR images, we propose a deterministic technique for a rapid-MRI, exploiting the relations between the wavelet sparse representation of the recovered and the frequency samples. We give results on real images and on artificial phantoms with added noise, showing the superiority of the methods both with respect to classical Iterative Hard Thresholding (IHT) and to Location Constraint Approximate Message Passing (LCAMP) reconstruction algorithms.