# US 9,619,902 B2 · Filter for tomographic reconstructions > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 9,619,902 B2 - Document ID: US9619902B2 - Status: Granted - Kind: B2 - Application number: 14/233,585 - Filed: 2012-07-17 - Published: 2014-08-07 - Granted: 2017-04-11 - Earliest claimed: 2011-07-19 - Assignees: Universiteit Antwerpen; Cwi - Applicants: Kees Joost Batenburg; Jan Sijbers; Linda Plantagie - Inventors: Kees Joost Batenburg; Jan Sijbers; Linda Plantagie - Web page: https://patentgrep.com/patent/US9619902B2 ## CPC - G06T 12/00: Tomographic reconstruction from projections - G01N 23/046: using tomography, e.g. computed tomography [CT] - G06T 12/20: Inverse problem, i.e. transformations from projection space into object space - G06T 2211/421: Filtered back projection [FBP] - G06T 2211/424: Iterative - G06T 2211/436: Limited angle - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL - G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q) ## Abstract A method for applying a filter component for an analytical tomographic reconstruction technique, e.g. filtered backprojection, used in tomographic comprises providing an algebraic reconstruction algorithm for reconstructing a spatial representation of a volume of interest from a projection data set. It thereby takes into account a geometry of the tomographic imaging. The method also comprises applying the algebraic reconstruction algorithm to a plurality of virtual projection data sets—corresponding with a basis vector of a basis for the projection space—to produce a plurality of reconstructed spatial representations and determining the filter component using the plurality of reconstructed spatial representations, and applying the filter. Applying the analytical reconstruction technique with the determined filter component may inherit beneficial properties from the algebraic reconstruction algorithm, e.g. versatility and robustness to noise, without incurring the associated computational cost. ## Claims ### Claim 1 A method for applying in a tomographic imaging system a filter component for an analytical tomographic reconstruction technique used in tomographic imaging in the tomographic imaging system, the method comprising: obtaining an algebraic reconstruction algorithm for reconstructing a spatial representation of a volume of interest from a projection data set, the algebraic reconstruction algorithm taking into account a geometry of the tomographic imaging, applying the algebraic reconstruction algorithm to a plurality of virtual projection data sets to produce a plurality of reconstructed spatial representations, and determining the filter component using the plurality of reconstructed spatial representations, implementing the filter component in the tomographic imaging system, wherein each virtual projection data set correspond with a basis vector of a basis for the projection space. ### Claim 2 (depends on 1) A method according to claim 1, wherein determining of the filter component comprises combining values from the plurality of reconstructed spatial representations corresponding to at least one reference location in the space of the spatial representation of the volume of interest. ### Claim 3 (depends on 1) A method according to claim 1, wherein the plurality of virtual projection data sets comprises at least two non-zero elements corresponding to different projection angles according to said geometry of the tomographic imaging, so that determining comprises determining a filter component having dedicated components for each of the different projection angles. ### Claim 4 (depends on 1) A method according to claim 1, wherein the at least one reference location comprises the geometrical center of the volume of interest. ### Claim 5 (depends on 1) A method according to claim 1, wherein said taking into account a geometry of the tomographic imaging comprises characterizing the geometry with a projection matrix. ### Claim 6 (depends on 1) A method according to claim 1, wherein said taking into account a geometry of the tomographic imaging comprises providing an algorithm for computing at least one element of a projection matrix, in which the projection matrix characterizes the geometry. ### Claim 7 (depends on 1) A method according to claim 1, wherein the determined filter component, when used in said analytical tomographic reconstruction technique to reconstruct a first spatial representation of a volume of interest from a projection data set obtained by performing said tomographic imaging, produces a first value in the first spatial representation at said at least one reference location that is substantially equal to a second value in a second spatial representation at said at least one reference location, in which the second spatial representation is obtained by applying said algebraic reconstruction algorithm to the projection data set. ### Claim 8 (depends on 1) A method according to claim 1, wherein the algebraic reconstruction algorithm comprises ART or SIRT. ### Claim 9 (depends on 1) A method according to claim 1, wherein the analytic tomographic reconstruction technique comprises filtered backprojection. ### Claim 10 (depends on 1) An analytic tomographic reconstruction for reconstructing a spatial representation of a volume of interest, comprising the steps of applying a filter component calculated using a method according to claim 1, determining projection data by scanning the volume of interest with a tomographic imaging device, the projection data comprising a plurality of projection views obtained from a plurality of projection angles, each projection view comprising a plurality of observation values obtained at a plurality of detection locations, and reconstructing the spatial representation of the volume of interest using the projection data, the filter component and a backprojection operation. ### Claim 11 (depends on 10) A method according to claim 10, wherein at least one sectional planar representation of the volume of interest is reconstructed. ### Claim 12 (depends on 10) A method according to claim 10, wherein at least one volumetric representation of the volume of interest is reconstructed. ### Claim 13 (depends on 10) A method according to claim 10, wherein the projection data are determined using conical beam geometry. ### Claim 14 (depends on 10) A method according to claim 10, wherein the projection data are determined using fan beam geometry. ### Claim 15 (depends on 10) A method according to claim 10, wherein said reconstructing comprises applying the filter component resulting in a least square approximation resulting in an effective averaging of noise on the projection data. ### Claim 16 (depends on 1) A filter component for an analytical tomographic reconstruction technique used in tomographic imaging, obtained by a method according to claim 1. ### Claim 17 A non-transitory computer-readable medium having instructions stored therein, which, when implemented on one or more processing units, cause the one or more processing units to perform a method for applying in a tomographic imaging system a filter component for an analytical tomographic reconstruction technique used in tomographic imaging in the tomographic imaging system, the method comprising: obtaining an algebraic reconstruction algorithm for reconstructing a spatial representation of a volume of interest from a projection data set, the algebraic reconstruction algorithm taking into account a geometry of the tomographic imaging, applying the algebraic reconstruction algorithm to a plurality of virtual projection data sets to produce a plurality of reconstructed spatial representations, and determining the filter component using the plurality of reconstructed spatial representations, implementing the filter component in the tomographic imaging system, wherein each virtual projection data set correspond with a basis vector of a basis for the projection space. ### Claim 18 (depends on 16) A data storage device for storing a filter component according to claim 16. ### Claim 19 (depends on 10) An image or volumetric image obtained by an analytic tomographic reconstruction method for reconstructing a spatial representation of a volume of interest according to claim 10.