Linear prediction theory of a homogeneous random field with discrete parameters (XIII)
XU Ye-ji · 2004
Generally, linear prediction problems of a homogeneous random field {x(m, n)} with discrete parameters are as fallows:Let T and T′ are two sets of (m, n), {x(m, n)} have been observed if (m, n)∈T. But {x(m′, n′)} are unknown quantities if (m′, n′)∈T′. One wants to predict {x(m′, n′), (m′, n′)∈T′} by the linear combination of the {x(m, n), (m, n)∈T} and its limit in terms of square mean, such that its error of squar mean is minimum.In this paper, two types of linear prediction are discussed:1. T={(m,n),-∞m∞,n≤0}\{(m_k,0),k=1,2,…,N}T_ 6(N); T′= T —_ 6(N)T′_ 6(N)2. T={(m, n), -∞m∞,n=n_i0, i=1, 2, …, N}∪{(m, n), -∞m∞, n=l_j0, j=1, 2, …, M}∪{(m, 0), -∞m∞}\{(m_k, 0), k=1, 2, …, K}T_ 11(N, M, K), T′= T —_ 11(N, M, K)T′_ 11(N, M, K).