### Table 2.2: Properties of the two-dimensional Fourier transform.

### Table 2. Pseudo-code used to calculate the radial Fourier transform (RFT) of a two dimensional Fourier amplitude spectrum (G[.]).

### Table 2: Timing results in seconds on the CM-5 for di erent implementations of the Pasciak algorithm. The three major steps in the algorithm are shown, were the ltering step is combined with that of the two-dimensional inverse Fourier transform. The last column shows the total time needed for reconstruc- tion.

"... In PAGE 7: ... The parameter N has the same meaning. The results are shown in Table2 for di erent values of N. In the interpolation step there is some communica- tion between processors when at a certain point the actual interpolation is computed.... In PAGE 8: ... The last column shows the total time needed for reconstruc- tion. When the timing results in Table2 are compared to the timings for ltered backprojection (Table 1), it can be concluded that the Pasciak method is indeed faster than ltered backprojection. 5 Conclusions Of the reconstruction algorithms considered, the l- tered backprojection algorithm turns out to be the most di cult to parallelise.... ..."

### Table 4.2: Timing results in seconds on the CM-5 for di erent implementations of the Pasciak algorithm. The three major steps in the algorithm are shown, were the ltering step is combined with that of the two- dimensional inverse Fourier transform. The last column shows the total time needed for reconstructing.

### Table 1: Symmetry properties of the QFT. r stands for the real part, i for the i{imaginary and so on. f which is even with respect to x and y, foe denotes the part which is odd with respect to x and even with respect to y and so on. Because the two{dimensional Fourier transform has only two components | one real component and one imaginary component | it is not able to separate these four components of di erent symmetry. However, the QFT has symmetry{splitting properties that are analogous to the properties of the one{dimensional Fourier transform: The transform of the fee{part of a real two{dimensionalsignal is real, the foe{part is transformed into an i{imaginary part, feo into the j{imaginary and foo into the k{imaginary part. The symmetry of the signal is preserved by the QFT. We can easily see this by looking at the QFT as two sequentially performed one{dimensional Fourier transforms: First we perform a one{dimensional Fourier transform on f(x) with respect to x keeping y xed and call the result ~ f:

1997

Cited by 6

### Table 3: Construction cost for the two-dimensional optimal cosine transform preconditioner.

"... In PAGE 19: ... 5.3 Cosine Transform for TV denoising and deblurring Since the matrix A is a general dense matrix, from Table3 we deduce that the cost of constructing the preconditioner c2(A) would be n4, which can easily be... ..."

### Table 8: A comparison of the performance of nine two-dimensional inversion routines as a function of M for the transform in (52) with inverse function in (53). The execution time is in seconds on an 0:2 GHz cpu.

2006

Cited by 3

### TABLE 2.1. Some examples of two-dimensional di erential invariants under orthogonal transformations, expressed in (i) Cartesian coordinates, (ii) tensor notation, and (iii) gauge coordinates, respectively.

### Table 5.1: Timing results in seconds for a full two-dimensional wavelet transform of an M M array, i.e. 2 log M levels.

### Table 1: Results for the two-dimensional landscapes.

"... In PAGE 1: ... Each method uses an optimized mutation rate for that method. The results of testing the algorithm on the two-dimensional landscapes are given in Table1 . The Tukey-Kramer test was... ..."