### Table 2 Performance of various configurations for Fourier domain sub-module

1994

### TABLE II BASIC DISCRETE SIGNAL PROCESSING OPERATORS AND THEIR EFFECT IN THE FOURIER DOMAIN

### TABLE II BASIC DISCRETE SIGNAL PROCESSING OPERATORS AND THEIR EFFECT IN THE FOURIER DOMAIN

### Table 1: Change of Fourier coefficients after operations in the continuous spatial domain.

1999

Cited by 10

### Table 1: Change of Fourier coefficients after operations in the continuous spatial domain.

1999

Cited by 10

### Table 1. Filter types used for image degrada- tion. polar coordinate systems are given. We also use a root lter to enhance images. This nonlinear lter acts on image amplitudes in Fourier domain: ^ A = A ; lt; 1.

2000

Cited by 6

### Table 3: The average mean square errors between the projections derived from the Fourier Projection Theorem and those from spatial domain summing, for various viewing angles. The color values are normalized to the range between 0 and 255.

"... In PAGE 6: ... All the reported measurementsbelow are 2D mean square errors (MSE) from the head data set. Table3 shows the average mean square errors between the projection sums derived from the Fourier Projection Theorem and those from spatial domain summing, for subcubesof different sizes from different viewing angles. The pro- jection angles are specified in the second row in terms of multi- ples of #19.... ..."

### Table 1: Some properties of the Fourier transform

"... In PAGE 16: ...imension of u is 1=time, i.e., frequency). In the case of image processing, the signal is a function of space rather than time, and in that case the domain of the Fourier transform is called spatial frequency. Table1 summarizes some important properties of the one-dimensional Fourier transform. The symbol is used to denote convolution:... ..."

### Table 1: Calculated slope angles, m, for the words shown in Figures 12(a), 13(a), 13(c), 13(e), 13(g). The slope angles are speci ed relative to the x-axis.

"... In PAGE 4: ... Note that the histogram angles have been rotated by 90 . 3) Slope Correction Results: Table1 gives the results for the slope estimation methods. From these results, the Fourier Domain method was selected as the method... ..."

### Table 2: E ects of correcting the inverse ltering method on information content. discrete Fourier space is periodic, and this convolution can \wrap around quot; producing some undesirable border e ects. These can be seen in Figure 7(c). Zero-padding can be employed to ameliorate this. Figure 7(e) shows the result when this is done. The improvement to the deconvolution is shown at the borders of gure 7(f). Finally, this image ( gure 6) has been collected through a 128 128 rectangular window. This is equivalent to convolving the Fourier transform with a small sinc function ( gure 2). This has the e ect of \smearing out quot; the power spectrum of the image. To improve this, the original signal is multiplied by a Hamming window before it is deconvolved. The result of this windowing is the image in gure 7(g). The improvement is shown in gure 7(h). The di erence is most noticable at the high frequency sections of the image. The focus has enhanced because there is less leakage in the Fourier domain. Figure 7(g) could be considered the \correct quot; deconvolution.

"... In PAGE 14: ... Figure 7(g) could be considered the \correct quot; deconvolution. Table2 shows the information content of the deconvolutions shown in gure 7. These values are determined from the correlation coe cient of the image as desrcribed by Vollath ([29]).... ..."