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The modulated image is gyrator transformed and then phase- and amplitude truncated to get second encrypted image and second decryption key.

Second, Jacobian scaled ("modulated") images were calculated and subsequently transformed to Montreal Neurological Institute space using affine transformation.

The resulting modulated images were smoothed with a 16-mm full-width at half-maximum kernel to accommodate anatomical variation among subjects and enable Gaussian random field theory for statistical inferences.

The segmented, normalized, and modulated images were smoothed using a Gaussian kernel of 10-mm full-width at half-maximum (FWHM) and entered into a regression model with AQ.

Modulated images are corrected for the final volume of the surrounding area as measured by the degree of local compression in the normalisation process (i.e., the Jacobian determinates of the deformation).

The frequency of the modulated fringe image is 1/18 cycles/pixel and the carrier frequencies fc1 and fc2 are 1/14 and 1/6 cycles/pixel respectively.

Previously, modulated imaging was performed with scanning spectral filters or computed tomography [ 29], which required long exposure times or slow image reconstruction, respectively.

Subsequently, each channel of the secret image is normalized, phase encoded, multiplied by modulated user image, and then gyrator transformed to obtain the gyrator spectrum of secret image.

Once the modulated component is extracted, a 2D Fourier Transform of the image is performed and a few spatial frequencies are selected.

Finally, each modulated, warped GM image was transformed to MNI space and smoothed with an 8 mm FWHM (full-width at half-maximum) Gaussian kernel filter.

The resulting 'modulated' images were affine-transformed to MNI space and smoothed with a 12 mm full width at half maximum isotropic Gaussian kernel.