| Popis: |
Compressed Sensing reconstructs the signal / image from a significantly less number of samples violating the Nyquist criteria. It exploits the sparsity present in the signal /image. Medical Imaging techniques like MRI (Magnetic Resonance Imaging), MRA (Magnetic Resonance Angiography), PET (Positron Emission Tomography) and MRSI (Magnetic Resonance Spectroscopic Imaging) are very popular and powerful medical tools and are used throughout the globe. The drawback associated with these important tools is that they have very slow data acquisition processes. On the other hand, all natural images are sparse in nature in some transform domain. Magnetic Resonance Angiograms are sparse in the image domain itself. More complex images like Magnetic Resonance Imaging of brain is sparse in some transform domain like Wavelet Transform etc. Compressed Sensing using this property of the medical images could significantly change the concept of scanning associated with the devices used in the sense that Compressed Sensing when applied could speed up the scanning process by a large margin. Using the inherent sparsity in the medical images, Compressed Sensing undersamples the k-space by acquiring very small amount of data from it and reconstructs the original image using non-linear optimization method. In this thesis, we have worked on the sampling schemes or patterns used to undersample the k-space or the Fourier space of different medical imaging techniques. Our sampling scheme when compared to the ones proposed by Dr. Lustig[1, 2] in his work, gives a better output. For a proper comparison, same amount of the data was acquired and the results were compared. |
