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2784results about "Reconstruction from projection" patented technology

Method and apparatus for compressed sensing

The invention provides a method and apparatus for making reduced numbers of measurements compared to current practice and still give acceptable quality reconstructions of the object of interest. In one embodiment, a digital signal or image is approximated using significantly fewer measurements than with traditional measurement schemes. A component x of the signal or image can be represented as a vector with m entries; traditional approaches would make m measurements to determine the m entries. The disclosed technique makes measurements y comprising a vector with only n entries, where n is less than m. From these n measurements, the disclosed invention delivers an approximate reconstruction of the m-vector x. In another embodiment, special measurement matrices called CS-matrices are designed for use in connection with the embodiment described above. Such measurement matrices are designed for use in settings where sensors can allow measurements y which can be represented as y=Ax+z, with y the measured m-vector, x the desired n-vector and z an m-vector representing noise. Here, A is an n by m matrix, i.e. an array with fewer rows than columns. A technique is disclosed to design matrices A which support delivery of an approximate reconstruction of the m-vector x, described above. Another embodiment of the invention discloses approximate reconstruction of the vector x from the reduced-dimensionality measurement y within the context of the embodiment described above. Given the measurements y, and the CS matrix A, the invention delivers an approximate reconstruction x# of the desired signal x. This embodiment is driven by the goal of promoting the approximate sparsity of x#.

Methods and apparatus for back-projection and forward-projection

The invention provides improvements in reconstructive imaging of the type in which a volume is reconstructed from a series of measured projection images (or other two-dimensional representations) generated by projection of a point x-ray source (or other radiation source), positioned at a distinct focus, through the volume to a plane at which the respective projection image is acquired (“detector plane”). In one aspect, the improvements are with respect to back-projecting a two-dimensional representation lying in the detector plane (representing, for example, a difference between an originally-acquired measured projection image and a subsequently-generated estimate thereof) to generate three-dimensional representation (which can be used, for example, to update an estimate of the volume). According to this aspect, for each of one or more slices of the 3D representation parallel to the projection plane and for each distinct focus at which a projection is generated, the following steps are performed in connection with the back-projection: (i) warping the first 2D representation to generate a second 2D representation by applying to the first 2D representation a selected linear mapping, where that selected linear mapping would map, in order to match dimensions of the respective slice within the 3D representation, a region defined by projection, at the respective focus, of comers of that slice onto the detector plane, and (ii) incrementing values of each of one or more voxels of the respective slice by an amount that is a function of a value of a correspondingly indexed pixel of the second 2D representation. A related aspect provides improvements with respect to forward-projecting, as well as in iterative (and non-iterative) methodologies that incorporate both back-projection and forward-projection.
Owner:PME IP
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