Compressed Sensing

Compressed Sensing

Compressed Sensing (CS) is a way to reconstruct an image using fewer acquisition points. Often times in MRI, acquired signals are repeated. In theory a few selected points in MRI can be sampled and the rest can be estimated to cut the scan time while preserving the image quality. The ability to acquire the image faster is a great benefit in MR. Not only it will cut down on the imaging time but also increase the efficiency at which images are constructed. A successful application of CS requires 3 important aspects: Transform Sparsity: The desired image must have a sparse representation in a known transform domain. Incoherence of Undersampling Artifacts: The aliasing artifacts in a linear reconstruction caused by k-space undersampling must be incoherent (noise-like) in the sparsifying transform domain. 7 Nonlinear Reconstruction: The image must be reconstructed by a non-linear method which enforces both sparsity of the image representation and consistency of the reconstruction with the acquired samples. (Lustig,2007) The goal for applying CS in MRI is to be able to decrease the scan time by sampling less of the k-space, this decrease in scan time will be beneficial in certain scans which require faster acquisition. For example in cardiac imaging the acquisition of the image is timed with respiration and the heart rate (Otazo,2010).