Abstract:
Compressed sensing theory is based on the novel idea that, a specific class of signals i.esparse signals can be recovered by sampling below the traditional sampling rate, as used incommunication systems theory.
Thus the important challenge in compressed sensing is to reconstruct an undersampled
sparse signal. The amount of undersampling possible for a signal having a particular sparsityneeds to be known. Phase transition of a particular algorithm represents the sparsity vsundersampling ratios in the form of a phase diagram. Therefore, the limit for undersamplingis revealed in the phase transition.Phase transition improvement is required in order to be able to recover original sparsesignal by even less number of samples. Currently, new recovery algorithms that providehigher phase transition curves are being developed.
In this thesis, we use the approach of utilizing deterministic sensing matrices in place
of random sensing matrices for reconstruction. Random sensing matrices have already beenemployed to discover the limit on undersampling. The deterministic sensing matrices used inthis thesis belong to a class of sensing matrices that have lower coherence. The deterministicsensing matrices utilized in this thesis were obtained using best antipodal spherical codes.
Experiments have been performed on few recovery algorithms in order to check the impactof this particular type of deterministic matrices. The impact of noise is also visualized onthe phase transition of these algorithms.
From the results of the experiments it is concluded that BP and AMP algorithms have
almost same phase transitions for both random and deterministic sensing matrices. However,OMP shows a marked improvement by employing deterministic sensing matrix. Thussuitable sensing matrix may optimize phase transition of existing algorithms.
