Open Access

Table A.1.

Symbols in algorithm descriptions.

Symbol Description
% The integer modulo operator
The assignment operator
∥⋯∥ The Euclidean norm operator
FFT(⋯) The Fourier transform operator implemented with FFT algorithm
IFFT(⋯) The inverse Fourier transform operator
The element-wise complex conjugation operator
ϵ A small number specified as an input parameter
i and j Array indices
N and M Numbers of rows and columns of the original kernel matrix
k Cluster index
K The number of clusters
J The expected number of principal components
d Array of N elements represents the observed data
H N × M array representing the original kernel matrix
X N × M array representing the shifted kernel matrix so that row vectors are aligned
X0 Array of N elements storing the arithmetic average of the M column vectors of X
T N × J array representing the principal component scores of the N row vectors of X, i.e., T[i] is the principal
component score of X[i]
R N × M array storing residuals in PCA Subroutine 2
λ and λp Estimates of the eigenvalue of the covariance in Subroutine 2
S Array of K lists, while the kth list S[k] contains all the row numbers of vectors classified into the kth cluster
at the current step
L Array of K elements representing the numbers of vectors
in the K clusters, e.g. L[k] is the number of vectors in the kth cluster
C (and Cp) K × J array, the kth row of which stores the central vector of the kth cluster calculated at the current step
(and the previous step), represented by principal component scores
Y An K × M array storing the central vectors of each cluster in pixel-wise representation
D An K × N array representing the Euclidean distance between the N shifted vectors and central vectors of the K
clusters, e.g. D[k][i] represents the Euclidean distance between the ith shifted vector X[i] and the kth
central vector C[k]
P An K × N × M array representing the K circulant kernel matrices in Eq. (3)
A An K × N × N array representing the K diagonal coefficient matrices in Eq. (3)
a An K × N array representing the vectors of diagonal elements of the K matrices
w An array of M elements representing the normalization factor in Eq. (19)
f (and fp) Array of M elements representing the object image estimated at the current step (and the previous step)
r An array of N elements
q An array of M elements

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