We present a computationally efficient approach for estimating the functional connectivity analysis in resting state Functional Magnetic Resonance Imaging (rs-fMRI) using ICA. The proposed approach sparsifies the data using voxels with high BOLD values (signal intensity) and nullifies the ones accounting for pseudo activations. In other words, the spatial complexity of rs-fMRI data is efficiently reduced by projecting data such that it has highest covariance and variance. This operation is followed by low-rank projection of sparsified data to reduce the temporal resolution leading to faster ICA algorithmic run times. Experimental results confirm that the proposed approach is about 4 χ faster, and can consistently find noise-free and more number of significantly active functional networks, compared to existing methods. The robustness of this approach is validated by bootstrapping based reliability tests using ICASSO toolbox.