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Coded Aperture Projection
(2008)

In computer vision, optical defocus is often described as convolution with a filter kernel that corresponds to an image of the aperture being used by the imaging device. The degree of defocus correlates to the scale of the kernel. Convolving an image with the inverse aperture kernel will digitally sharpen the image and consequently compensate optical defocus. This is referred to as deconvolution or inverse filtering. In frequency domain, the reciprocal of the filter kernel is its inverse, and deconvolution reduces to a division. Low magnitudes in the Fourier transform of the aperture image, however, lead to intensity values in spatial domain that exceed the displayable range. Therefore, the corresponding frequencies are not considered, which then results in visible ringing artifacts in the final projection. This is the main limitation of previous approaches, since in frequency domain the Gaussian PSF of spherical apertures does contain a large fraction of low Fourier magnitudes. Applying only small kernel scales will reduce the number of low Fourier magnitudes (and consequently the ringing artifacts) -- but will also lead only to minor focus improvements. To overcome this problem, we apply a coded aperture whose Fourier transform has less low magnitudes initially. Consequently, more frequencies are retained and more image details are reconstructed.