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The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l1 greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l1 greedy algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in the successful recovery of randomly generated Gaussian sparse signals from data generated by Gaussian random matrices. In particular, the generalized l1 greedy algorithm performs extraordinarily well in recovering random sparse signals with nonzero small entries. The stability of the generalized l1 greedy algorithm with respect to its parameters and the impact of noise on the recovery of Gaussian sparse signals are also studied.
Teaching and Education (T&E) constitute the most
important activity in knowledge transfer from generation to generation. This
can explain why government organizations consider the training of highly
qualified personnel as one of the most important criteria in the selection of
research and development (R&D) grant applications. A university professor
should thus not only play the role of researcher, but also that of teacher.
T&E and R&D combine to form an inseparable relationship for university
professors. By shooting for excellence in T&E, we could get a new
perception of a familiar field or initiate a brand new field altogether, which
would in turn enhance our research. The quest for excellence in R&D leads
to deeper and better understanding of materials taught, and progress in R&D
enriches our T&E endeavors. Here, the author shares a beneficial experience
from T&E to R&D.