In this paper,the study of projection properties of two-level factorials in view of geometry is reported.The concept of uniformity pattern is defined.Based on this new concept,criteria of uniformity resolution and min...In this paper,the study of projection properties of two-level factorials in view of geometry is reported.The concept of uniformity pattern is defined.Based on this new concept,criteria of uniformity resolution and minimum projection uniformity are proposed for comparing two-level factorials.Relationship between minimum projection uniformity and other criteria such as minimum aberration,generalized minimum aberration and orthogonality is made explict.This close relationship raises the hope of improving the connection between uniform design theory and factorial design theory.Our results provide a justification of orthogonality,minimum aberration,and generalized minimum aberration from a natural geometrical interpretation.展开更多
Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed sensing.This paper applies OMP to the sparse polynomial reconstruction problem.Distinguishing from classi...Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed sensing.This paper applies OMP to the sparse polynomial reconstruction problem.Distinguishing from classical research methods using mutual coherence or restricted isometry property of the measurement matrix,the recovery guarantee and the success probability of OMP are obtained directly by the greedy selection ratio and the probability theory.The results show that the failure probability of OMP given in this paper is exponential small with respect to the number of sampling points.In addition,the recovery guarantee of OMP obtained through classical methods is lager than that of ℓ_(1)-minimization whatever the sparsity of sparse polynomials is,while the recovery guarantee given in this paper is roughly the same as that of ℓ_(1)-minimization when the sparsity is less than 93.Finally,the numerical experiments verify the availability of the theoretical results.展开更多
基金partially supported by the Hong Kong RGC grant,RGC/HKBU 2044/02Pthe National Natural Science Foundation of China(Grant No.10071029)+1 种基金the Project-sponsored by SRF for ROCS(SEM)the NSF of Hubei Province for the second author.
文摘In this paper,the study of projection properties of two-level factorials in view of geometry is reported.The concept of uniformity pattern is defined.Based on this new concept,criteria of uniformity resolution and minimum projection uniformity are proposed for comparing two-level factorials.Relationship between minimum projection uniformity and other criteria such as minimum aberration,generalized minimum aberration and orthogonality is made explict.This close relationship raises the hope of improving the connection between uniform design theory and factorial design theory.Our results provide a justification of orthogonality,minimum aberration,and generalized minimum aberration from a natural geometrical interpretation.
基金supported by the National Natural Science Foundation of China(Grant No.12071019).
文摘Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed sensing.This paper applies OMP to the sparse polynomial reconstruction problem.Distinguishing from classical research methods using mutual coherence or restricted isometry property of the measurement matrix,the recovery guarantee and the success probability of OMP are obtained directly by the greedy selection ratio and the probability theory.The results show that the failure probability of OMP given in this paper is exponential small with respect to the number of sampling points.In addition,the recovery guarantee of OMP obtained through classical methods is lager than that of ℓ_(1)-minimization whatever the sparsity of sparse polynomials is,while the recovery guarantee given in this paper is roughly the same as that of ℓ_(1)-minimization when the sparsity is less than 93.Finally,the numerical experiments verify the availability of the theoretical results.
