Introduction: Compressed Sensing (CS) has been recently proposed for accelerated MR image reconstruction from highly under-sampled data. A necessary condition for CS is the sparsity of the image itself in a transform domain. Theory: Sparse data helps to achieve incoherent artifacts, whichcan be removed easily using various iterative algorithms (for e.g. non-linear Conjugate Gradient) as part of CS. The image should be reconstructed by a non-linear algorithm that enforces both the sparsity of the image representation and consistency of the reconstruction with the acquired samples. Methods: This work presents the results obtained by applying CS on non-Cartesian k-space data acquired using highly under-sampled Radial and Spiral schemes. The CS reconstruction is performed using Individual Coil Method (ICM) and Collective Coil Method (CCM). The ICM approach considers the under-sampled data from each coil individually whereas CCM considers under-sampled data from the coils collectively for the reconstruction of the MR images. Results and Conclusion: Artifact Power (AP) and SNR are used as quantifying parameters to compare the quality of the reconstructed images. The results show that radial trajectory is a suitable choice for the CS in MRI. In terms of the method compatibility,ICM shows promising results.