Abstract: A system and method for improving the detail of a digital signal comprising at least three dimensions can be implemented by extracting a plurality of data cubes containing two x-planes, two y-planes, two z-planes, and amplitude information at eight locations in this x, y, and z space. A primary and secondary direction and a data plane for each data cube can then be selected based on difference calculations of eight locations in the x, y, and z directions, resulting in a 2×2 data square. This data square can then be used to compute a network neighborhood, which can subsequently be used to calculate first and second order gradient information. The first and second order gradient information can be used to construct an output signal that has greater detail than the input signal.

Abstract: A system and method for improving the detail of an input digital signal, such as a signal comprising a two dimensional image, can be implemented by computing first and second order gradients of the input signal. These gradients can be represented as quaternions. The logarithm of the quaternions can be used to determine the magnitude and orientation of gradient vectors in the input signal. This gradient magnitude and gradient orientation information can be used to construct an output digital signal that has greater detail than the input digital signal.

Abstract: A system and method for improving the detail of an input digital signal, such as a signal comprising a two dimensional image, can be implemented by computing first and second order gradients of the input signal. These gradients can be represented as quaternions. The logarithm of the quaternions can be used to determine the magnitude and orientation of gradient vectors in the input signal. This gradient magnitude and gradient orientation information can be used to construct an output digital signal that has greater detail than the input digital signal.