The first one is the Reflection Factor (RF) , which utilizes not only the singular values
but also right singular vector matrices to calculate the reflections, denoted as total weighted differences scaled by the singular values
dependent on the energy of the image.
is the SVD of [[PSI].sup.T][PHI], where U = [[u.sub.1],...,[u.sub.T]],V = [[v.sub.1],...,[v.sub.T]],[and] = diag([[sigma].sub.1],...,[[sigma].sub.T]), and T is the number of the nonzero singular value
(multiple singular value
calculated on multiplicity), [[sigma].sub.i] is the nonzero singular values
, and ui, vi are the corresponding left and right singular vectors.
The matrix pair's generalized singular values
(GSVs) (A, L) are ([A.sup.T][AL.sup.T]L)'s square roots, where L [member of] [R.sup.p X n] suffices m [greater than or equal to] n [greater than or equal to] p.
[greater than or equal to] [[delta].sub.n] in W = diag([[delta].sub.1], [[delta].sub.2], ..., [[delta].sub.n]) are the nonzero singular values
. To explore the relationship between the singular value
and image quality, we choose six images (Figures 3(a)-3(e)) with an increasing blur degree from the LIVE database , as shown in Figure 3.
Two representative ones are the Schatten-q quasi-norm [20, 23, 24] and the truncated nuclear norm [21, 25] which is also called the partial sum of singular values
[greater than or equal to] [S.sub.N] are the singular values
(SVs) of A.
decomposition (SVD), decomposes a matrix into left and right singular vectors and a diagonal matrix of singular values
Besides, on the other hand, envelope spectrums of these IMFs are obtained by Hilbert envelope spectrum analysis, which can be used to obtain the singular values
by singular decomposition on envelope spectrum matrix.
In , the singular values
of an original image are modified to embed watermark, without modifying the singular vectors.
For each example, we record the singular values
of J, as computed by the svd function of Matlab.
The I x L data matrix X has a singular value
decomposition X = P[DELTA][Q.sup.T] where P is the Left singular vectors, Q is the Right singular vectors and [DELTA] is the Diagonal matrix of singular values
The stability of the system controlled by the designed ILC controller is checked by the singular values
of stability matrix.