Three dimensional (3D) nonuniform freehand scanning

A non-transitory computer-readable medium comprising a computer program for performing freehand scanning imaging, wherein the computer program is configured to cause at least one processor to execute:

• transforming a single spatial location with nonuniform input data using Nonuniform Discrete Fourier Transform (NDFT) for one spatial location to a singular spectral estimation, wherein the single spatial location is a component of a curved surface with nonuniform roll, pitch, and yaw or a point cloud with nonuniform roll, pitch, and yaw;
• translating the singular spectral estimation to zl, wherein zl is a common value of z for which to later recombine data for layer l, where l begins at zero;
• performing Inverse Spatial Fourier Transform on the translated spectrum to produce a translated data in a x- and y-spatial domain at z=zl;
• outputting three dimension (3D) translated data to an N-dimensional regularization from all measured locations, where all measured locations are regularized data resulting from a combined sum of all measured contributions;
• and
• outputting the regularized data to a synthetic aperture focusing technique (SAFT) algorithm to produce images layer-by-layer, whereby the process is repeated, by the at least one processor, for subsequent layers layer-by-layer, wherein boundaries for each layer are curved surfaces.

A system for performing freehand scanning imaging, comprising:

• memory comprising a set of instructions;
• and at least one processor, wherein the set of instructions is configured to cause at least one processor to execute:
• transforming a single spatial location with nonuniform input data using Nonuniform Discrete Fourier Transform (NDFT) for one spatial location to a singular spectral estimation, wherein the single spatial location is a component of a curved surface with nonuniform roll, pitch, and yaw or a point cloud with nonuniform roll, pitch, and yaw;
• translating the singular spectral estimation to zl, wherein zl is a common value of z for which to later recombine data for layer l, where l begins at zero;
• performing Inverse Spatial Fourier Transform on the translated spectrum to produce a translated data in a x- and y-spatial domain at z=zl;
• outputting three dimension (3D) translated data to an N-dimensional regularization from all measured locations, where all measured locations are regularized data resulting from a combined sum of all measured contributions;
• and
• outputting the regularized data to a synthetic aperture focusing technique (SAFT) algorithm to produce images layer-by-layer, whereby the process is repeated, by the at least one processor, for subsequent layers layer-by-layer, wherein boundaries for each layer are curved surfaces.