Multi-dimensional wavelet tomography

Claim 1

A method for performing multi-dimensional wavelet tomography, said method comprising the steps of: a) iteratively projecting a multi-dimensional original image so as to produce a plurality of one-dimensional projections thereof; b) performing wavelet decomposition upon the one-dimensional projections to form a plurality of subimages thereof, the step of performing wavelet decomposition comprising: i) convolving the one-dimensional projections to form a scale filtered subimage and a wavelet filtered image; and ii) downsampling the scale filtered subimage and the wavelet filtered subimage; iii) wherein steps (i) and (ii) are iterated to obtain a desired resolution; c) reconstructing a desired portion of the original image from at least one of said subimages, the step of reconstructing a desired portion of the original image comprising back projection filtering the wavelet decomposed one-dimensional projections, back projection filtering comprising: i) upsampling a scale filtered subimage and a wavelet filtered image; ii) convolving the upsampled scale filtered image and wavelet filtered image; and iii) combining the convolved upsampled scale filtered image and wavelet filtered image.

Claim 2

A method for performing multi-dimensional wavelet tomography, said method comprising the steps of: a) iteratively projecting a multi-dimensional original image so as to produce a plurality of one-dimensional projections thereof; b) performing wavelet decomposition upon the one-dimensional projections to form a plurality of subimages thereof, the step of performing wavelet decomposition comprising: i) convolving the one-dimensional projections to form a scale filtered subimage and a wavelet filtered image; and ii) downsampling the scale filtered subimage and the wavelet filtered subimage; iii) wherein steps (i) and (ii) are iterated to obtain a desired resolution; c) reconstructing a desired portion of the original image from at least one of said subimages, the step of reconstructing a desired portion of the original image comprising back projection filtering the wavelet decomposed one-dimensional projections, back projection filtering comprising: i) upsampling a scale filtered subimage and a wavelet filtered image; ii) convolving the upsampled scale filtered image and wavelet filtered image; and iii) combining the convolved upsampled scale filtered image and wavelet filtered image.

Claim 3

A method for performing multi-dimensional wavelet tomography, said method comprising the steps of: a) iteratively projecting a multi-dimensional original image so as to produce a plurality of one-dimensional projections thereof; b) performing wavelet decomposition upon the one-dimensional projections to form a plurality of subimages thereof, the step of performing wavelet decomposition comprising: i) performing wavelet decomposition upon a two-dimensional array of one-dimensional projections in a first direction to form first scale and wavelet images; ii) transposing the first scale and wavelet images; and iii) performing wavelet decomposition upon the transposed first scale and wavelet images to form a horizontal scale vertical scale subimage, a horizontal scale vertical wavelet subimage, a horizontal wavelet vertical scale subimage, and a horizontal wavelet vertical wavelet subimage; c) wherein such wavelet decomposition facilitates segmentation and reconstruction of a selected portion of the original image.

Claim 4

A method for performing multi-dimensional wavelet tomography, said method comprising the steps of: a) iteratively projecting a multi-dimensional original image so as to produce a plurality of one-dimensional projections thereof; b) performing wavelet decomposition upon the one-dimensional projections to form a plurality of subimages thereof, the step of performing wavelet decomposition comprising: i) performing wavelet decomposition upon a two-dimensional array of one-dimensional projections in a first direction to form first scale and wavelet images; ii) transposing the first scale and wavelet images; and iii) performing wavelet decomposition upon the transposed first scale and wavelet images to form a horizontal scale vertical scale subimage, a horizontal scale vertical wavelet subimage, a horizontal wavelet vertical scale subimage, and a horizontal wavelet vertical wavelet subimage; c) wherein such wavelet decomposition facilitates segmentation and reconstruction of a selected portion of the original image.

Claim 5

A method for performing multi-dimensional wavelet tomography, said method comprising the steps of: a) iteratively projecting a multi-dimensional original image so as to produce a plurality of one-dimensional projections thereof; b) performing wavelet decomposition upon the one-dimensional projections to form a plurality of subimages thereof; c) reconstructing a desired portion of the original image from at least one of said subimages, the step of reconstructing a desired portion of the original image comprising; i) transposing a horizontal scale vertical scale subimage, horizontal scale vertical wavelet subimage, horizontal wavelet vertical scale subimage, and a horizontal wavelet vertical wavelet subimage; ii) performing one-dimensional recomposition upon the transposed horizontal scale vertical scale subimage and the transposed horizontal scale vertical scale subimage and the transposed horizontal scale vertical wavelet subimage to form a first recomposed image and performing one-dimensional recomposition upon the transposed horizontal wavelet vertical scale subimage and the transposed horizontal wavelet vertical wavelet subimage to form a second recomposed image; iii) transposing the first and second recomposed images, to form a horizontal scale image and a horizontal wavelet image, respectively; and iv) performing one-dimensional recomposition upon the horizontal scale image and the horizontal wavelet image to form a reconstructed image.

Claim 6

A method for performing multi-dimensional wavelet tomography, said method comprising the steps of: a) iteratively projecting a multi-dimensional original image so as to produce a plurality of one-dimensional projections thereof; b) performing wavelet decomposition upon the one-dimensional projections to form a plurality of subimages thereof; c) reconstructing a desired portion of the original image from at least one of said subimages, the step of reconstructing a desired portion of the original image comprising; i) transposing a horizontal scale vertical scale subimage, horizontal scale vertical wavelet subimage, horizontal wavelet vertical scale subimage, and a horizontal wavelet vertical wavelet subimage; ii) performing one-dimensional recomposition upon the transposed horizontal scale vertical scale subimage and the transposed horizontal scale vertical scale subimage and the transposed horizontal scale vertical wavelet subimage to form a first recomposed image and performing one-dimensional recomposition upon the transposed horizontal wavelet vertical scale subimage and the transposed horizontal wavelet vertical wavelet subimage to form a second recomposed image; iii) transposing the first and second recomposed images, to form a horizontal scale image and a horizontal wavelet image, respectively; and iv) performing one-dimensional recomposition upon the horizontal scale image and the horizontal wavelet image to form a reconstructed image.