All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig1.eps}\end{figure}$ Figure 1: Original image, blurred version and blurred + noise version of the first image in the set (see text) and corresponding PSF. The images are $256 \times 256$ pixels, and the standard deviation of the noise is $10\%$ of the maximum value of the blurred image.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig2.eps}\end{figure}$ Figure 2: Deblurring of the image in Fig. 1 with the methods decribed in the text: (I) single-image Tikhonov (12) and ${\rm GCV^{(\vec{\varsigma})}_{\alpha}}$ (17); its version with the negative elements zeroed; (II) Tikhonov (5) and ${\rm GCV^{(\vec{g})}_{\alpha}}$ (26); (III) a classic iterative Projected Landweber Method (convergence after 61 iterations). Tikhonov has been used with $\vec{L}= \vec{I}$ and $\alpha = 1.4$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig3.eps}\end{figure}$ Figure 3: The same as Fig. 2 but obtained from an image contaminated with noise whose standard deviation is $1\%$ of the maximum value of the blurred image. For the Projected Landweber algorithm 2000 iterations have been carried out.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig4.eps}\end{figure}$ Figure 4: Original image, blurred version and blurred + noise version of the first image in the set (see text) and corresponding PSF. The images are $256 \times 256$ pixels, and the standard deviation of the noise is $10\%$ of the maximum value of the blurred image.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig5.eps}\end{figure}$ Figure 5: Deblurring of the image in Fig. 4 with the methods described in the text: (I) single-image Tikhonov (12) and ${\rm GCV^{(\vec{\varsigma})}_{\alpha}}$ (17); its version with the negative elements zeroed; (II) Tikhonov (5) and ${\rm GCV^{(\vec{g})}_{\alpha}}$ (26); (III) a classic iterative Projected Landweber Method (2000 iterations). Tikhonov has been used with $\vec{L}= \vec{I}$ and $\alpha = 1.4$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig6.eps}\end{figure}$ Figure 6: The same as Fig. 5 but obtained from an image contaminated with noise whose standard deviation is $1\%$ of the maximum value of the blurred image.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig7.eps}\end{figure}$ Figure 7: Original image, blurred version and blurred + noise version of the first image in the set (see text) and corresponding PSF. The original images was $600 \times 600$ pixels, but only the central $500 \times 500$ pixels are displayed (see text). The standard deviation of the noise is $10\%$ of the standard deviation of the blurred image.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig8.eps}\end{figure}$ Figure 8: Image $\varsigma (m,n)$ for the image shown in Fig. 4, single-image Tikhonov deblurring ( $\vec{L}=$ discrete Laplacian), its version with the negative elements zeroed, and the iterative Projected Landweber deblurring (convergence after 24 iterations).
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig9.eps}\end{figure}$ Figure 9: The same as Fig. 8 but obtained from an image contaminated with noise whose standard deviation is $1\%$ of the standard deviation of the blurred image. Tikhonov has been used with $\vec{L}= \vec{I}$ . For the Projected Landweber algorithm 2000 iterations have been carried out.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig10.eps}\end{figure}$ Figure 10: Histogram of the values of the estimated parameter $\lambda$ for the 100 experiments based in Fig. 6.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig11.eps}\end{figure}$ Figure 11: Convergence rates for the Projected Landweber algorithm in the numerical experiment corresponding to Fig. 3. Two starting guesses are used: the uniform image typical of the classic implementation of the algorithm, and the nonnegative single-image Tikhonov shown in Fig. 3.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig1.eps}\end{figure}$	Figure 1: Original image, blurred version and blurred + noise version of the first image in the set (see text) and corresponding PSF. The images are $256 \times 256$ pixels, and the standard deviation of the noise is $10\%$ of the maximum value of the blurred image.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig3.eps}\end{figure}$	Figure 3: The same as Fig. 2 but obtained from an image contaminated with noise whose standard deviation is $1\%$ of the maximum value of the blurred image. For the Projected Landweber algorithm 2000 iterations have been carried out.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig4.eps}\end{figure}$	Figure 4: Original image, blurred version and blurred + noise version of the first image in the set (see text) and corresponding PSF. The images are $256 \times 256$ pixels, and the standard deviation of the noise is $10\%$ of the maximum value of the blurred image.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0113fig6.eps}\end{figure}$	Figure 6: The same as Fig. 5 but obtained from an image contaminated with noise whose standard deviation is $1\%$ of the maximum value of the blurred image.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig7.eps}\end{figure}$	Figure 7: Original image, blurred version and blurred + noise version of the first image in the set (see text) and corresponding PSF. The original images was $600 \times 600$ pixels, but only the central $500 \times 500$ pixels are displayed (see text). The standard deviation of the noise is $10\%$ of the standard deviation of the blurred image.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig8.eps}\end{figure}$	Figure 8: Image $\varsigma (m,n)$ for the image shown in Fig. 4, single-image Tikhonov deblurring ( $\vec{L}=$ discrete Laplacian), its version with the negative elements zeroed, and the iterative Projected Landweber deblurring (convergence after 24 iterations).
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig9.eps}\end{figure}$	Figure 9: The same as Fig. 8 but obtained from an image contaminated with noise whose standard deviation is $1\%$ of the standard deviation of the blurred image. Tikhonov has been used with $\vec{L}= \vec{I}$ . For the Projected Landweber algorithm 2000 iterations have been carried out.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig10.eps}\end{figure}$	Figure 10: Histogram of the values of the estimated parameter $\lambda$ for the 100 experiments based in Fig. 6.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0113fig11.eps}\end{figure}$	Figure 11: Convergence rates for the Projected Landweber algorithm in the numerical experiment corresponding to Fig. 3. Two starting guesses are used: the uniform image typical of the classic implementation of the algorithm, and the nonnegative single-image Tikhonov shown in Fig. 3.
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