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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