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L1-norm minimization for octonion signals

An algorithm for recovering the octonion signals in both noiseless and noise contaminated scenarios by solving an L1-norm minimization problem is presented. The L1-norm minimization problem over the octonion field is solved by converting it to an equivalent second-order cone programming problem over the real number field, which can be readily solved by convex optimization solvers like CVX. An application example of the proposed algorithm is also given for practical guidelines of perfect recovery of octonion signals. The proposed algorithm may find its potential application when CS theory meets the octonion signal processing.