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Functional Magnetic Resonance Imaging (fMRI) requires ultra-fast imaging in order to capture the on-going spatio-temporal dynamics of the cognitive task. We make use of correlations in both k-space and time, and thereby reconstruct the time series by acquiring only a fraction of the data, using an improved form of the well-known dynamic imaging technique k-t BLAST (Broad-use Linear Acquisition Speed-up Technique). k-t BLAST (k-tB) works by unwrapping the aliased Fourier conjugate space of k-t ( y-f space). The unwrapping process makes use of an estimate of the true y-f space, obtained by acquiring a blurred unaliased version. In this paper, we propose two changes to the existing algorithm. Firstly, we improve the map estimate using generalized series reconstruction. The second change is to incorporate phase constraints from the training map. The proposed technique is compared with existing k-tB on visual stimulation fMRI data obtained on 5 volunteers. Results show that the proposed changes lead to gain in temporal resolution by as much as a factor of 6. Performance evaluation is carried out by comparing activation maps obtained using reconstructed images, against that obtained from the true images. We observe upto 10dB improvement in PSNR of activation maps. Besides, RMSE reduction on fMRI images, of about 10% averaged over the entire time series, with a peak improvement of 35% compared to the existing k-tB, averaged over 5 data sets, is also observed. [ABSTRACT FROM AUTHOR]