Abdullahu, K. (2021). Bayesian signal recovery with noisy side information in compressed sensing [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2022.59701
In this thesis we will explore how to combine compressed sensing recovery of several sets of variables, given several sets of measurements when the overall measurement matrix has certain structure. A problem with compressed sensing can be that the dimension of the signal to be recovered is very large and, hence, the measurement matrix is very large in some specific applications e.g. imaging problems. Matrices of large dimensions are hard to handle, so the idea is to investigate specific structures which reduce complexity and storage. One way is to introduce a structure where the measurement matrix is formed from sub-blocks (submatrices) in our case 5, 8 and 10 sub-blocks, where we implement the BAMP algorithm on these submatrices of the measurement matrix, and by exploiting the results of each BAMP, we will have more measurements (partially modified) for other BAMPs on other submatrices. In the end we will compare the results of this structure with the results of applying the BAMP on the full measurement matrix.
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In this thesis we will explore how to combine compressed sensing recovery of several sets of variables, given several sets of measurements when the overall measurement matrix has certain structure. A problem with compressed sensing can be that the dimension of the signal to be recovered is very large and, hence, the measurement matrix is very large in some specific applications e.g. imaging problems. Matrices of large dimensions are hard to handle, so the idea is to investigate specific structures which reduce complexity and storage. One way is to introduce a structure where the measurement matrix is formed from sub-blocks (submatrices) in our case 5, 8 and 10 sub-blocks, where we implement the BAMP algorithm on these submatrices of the measurement matrix, and by exploiting the results of each BAMP, we will have more measurements (partially modified) for other BAMPs on other submatrices. In the end we will compare the results of this structure with the results of applying the BAMP on the full measurement matrix.