# US 2014/0195200 A1 · Smart Data Sampling and Data Reconstruction > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2014/0195200 A1 - Document ID: US20140195200A1 - Status: Published application - Kind: A1 - Application number: 14/239,303 - Filed: 2012-08-20 - Published: 2014-07-10 - Earliest claimed: 2011-08-18 - Assignees: University of Antwerp - Inventors: Annie Cuyt; Wen-Shin Lee - Web page: https://patentgrep.com/patent/US20140195200A1 ## CPC - G06F 17/10: Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} - H03M 7/3062: {Compressive sampling or sensing} - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C) ## Abstract A computer-based method for characterizing data dependent on at least one variable is described. The method comprises sampling the data in a smart manner by sampling the data in a finite sequence of sampling points, the finite sequence of sampling points being controlled by a magnifying factor for controlling a spacing between elements of the finite sequence of sampling points and being determined such that function values of functions of a family of functions in said finite sequence of sampling points satisfy a recurrence relation. A corresponding device also is described as well as software-related products. ## Claims ### Claim at position 1 1-31. (canceled) ### Claim 32 A computer-based method for characterizing data dependent on at least one variable, the method comprising: obtaining a family of functions having a domain corresponding to said at least one variable and a codomain corresponding to said data, said family of functions sharing a common construction parameterized by at least one parameter, obtaining a magnifying factor for controlling a spacing between elements in a finite sequence of sampling points wherein the data will be sampled, obtaining a finite sequence of measurements of said data by sampling said data in said finite sequence of sampling points, said finite sequence of sampling points being controlled by said obtained magnifying factor and determined such that the values of the functions of said family of functions in said finite sequence of sampling points satisfy a recurrence relation, and outputting a property of the data taking into account said finite sequence of measurements. ### Claim 33 (depends on 32) The method according to claim 32, wherein the method further comprises determining a subset of said family of functions said determining making use of said recurrence relation satisfied in said finite sequence of sampling points. ### Claim 34 (depends on 33) The method according to claim 33, wherein said outputting a property of the data comprises outputting a representation of the data based on the subset of said family of functions. ### Claim 35 (depends on 32) The method according to claim 32, wherein function parameters defining functions of the determined subset of said family of functions are at least not all integer. ### Claim 36 (depends on 32) The method according to claim 32, wherein said magnifying factor is an integer or a rational number. ### Claim 37 (depends on 36) The method according to claim 36, wherein said magnifying factor is different from one. ### Claim 38 (depends on 33) The method according to claim 33, wherein said subset of said family of functions is a sparse subset. ### Claim 39 (depends on 34) The method according to claim 34, further comprising determining a set of weight factors for representing said data as a linear combination of said subset of said family of functions. ### Claim 40 (depends on 32) The method according to claim 32, wherein selecting the magnifying factor comprises selecting the magnifying factor for controlling a numerical conditioning of said characterizing of said data. ### Claim 41 (depends on 32) The method according to claim 32, wherein selecting the magnifying factor comprises selecting the magnifying factor for reducing the number of sampling points below less than dictated by the Nyquist rate. ### Claim 42 (depends on 33) The method according to claim 33, wherein a cardinality of said finite sequence of sampling points is imposed as a predetermined cardinality, and/or wherein a cardinality of said finite sequence of sampling points is probed for, and/or wherein the cardinality is determined iteratively. ### Claim 43 (depends on 32) The method according to claim 32, wherein the method comprises performing a sparsity check by determining a numerical rank of a matrix or matrices constructed from said recurrence relation using the finite sequence of measurements. ### Claim 44 (depends on 33) The method according to claim 33, in which said determining of said subset comprises applying an inverse application of a technique based on the Chinese remainder theorem. ### Claim 45 (depends on 33) The method according to claim 33, in which said obtaining measurements comprises further sampling said data in a further finite sequence of sampling points in order to take into account a periodicity of said family of functions in determining a subset of said family of functions. ### Claim 46 (depends on 45) The method according to claim 45, wherein further sampling comprises further sampling said data in a further finite sequence of sampling points such that a location of said further finite sequence of sampling points is at least also determined by a value of an identification shift for uniquely determining said subset of said family of functions. ### Claim 47 (depends on 32) The method according to claim 32, wherein the method comprises performing a divide and conquer step. ### Claim 48 (depends on 32) A computer-program product for, when executed on a computing means, performing a method according to claim 32. ### Claim 49 A device for characterizing data dependent on at least one variable, the device comprising: a numerical processing unit adapted for obtaining, for the data to be characterized, a finite sequence of measurements of said data by sampling said data in said finite sequence of sampling points, said finite sequence of sampling points being controlled by a magnifying factor for controlling a spacing between elements in the finite sequence of sampling points and being determined such that the values of the functions of a family of functions in said finite sequence of sampling points satisfy a recurrence relation, said family of functions having a domain corresponding to said at least one variable and a codomain corresponding to said data and said family of functions sharing a common construction parameterized by at least one parameter, the numerical processing unit furthermore being adapted for determining a property of the data, and an output means for outputting a property of the data, taking into account the finite sequence of measurements. ### Claim 50 (depends on 49) A device according to claim 49, the device furthermore comprising an input means for obtaining one or more of the data to be characterized, the family of functions or the magnifying factor. ### Claim 51 (depends on 32) A signal representing data, to be characterised, modelled or reconstructed, whereby the signal is obtained using a method according to claim 32.