Date of Award
Master of Science
Electrical and Computer Engineering
Accurate signal recovery from under-determined system of equations is a topic of considerable interest. Compressive sensing (CS) gives an approach to find a solution to this system when the unknown signal is sparse. Regularized modied CS (noisy) propose an approach to find the solution to the under-determined system of equations when we are provided with 1- Partial part of signal support denoted by T and 2- A prior estimate of signal value on this support denoted by mu_T . In many applications, e.g sequential MRI reconstruction, the sparse signal support and its nonzero signal values change slowly over time. Inspired by this fact, we propose an algorithm utilizing reg-mod-CSN for sequential signal reconstruction such that the prior estimate of T and mu_T is generated from the previous time instant.
Our major focus in this work is to study the "stability" of the proposed algorithm for recursive reconstruction of sparse signal sequences from noisy measurements. By "stability" we mean that the number of misses from the current support estimate; the number of extras in it; and the l_2 norm of the reconstruction error remain bounded by a time-invariant value at all times. For achieving this goal, we need a signal model that can represent the sequential signals in real applications. It should satisfy three constraint; 1- The distribution of the signal entries should follow the same distribution as real sequential signals; 2- It follows the same evolutionary pattern as the real sequential signals over time and 3-The signal support changes dynamically over time. In the two proposed signal model, we tried to satisfy these three constraints. Using these signal models, we analyzed the performance of the proposed algorithm and found the condition such that the system remain stable. These conditions are weaker in compare with older methods like CS and mod-CS. At the end, we show empirically that reg-mod-CS achieves a lower reconstruction error in compare with mod-CS and CS.
Raisali, Fardad, "Stability (over time) of regularized modified CS (noisy) for recursive causal sparse reconstruction" (2012). Graduate Theses and Dissertations. 12973.