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A system and method for determining from an arbitrary signal a characteristic signature or other characterizing feature and for distinguishing signals associated with one specific condition from those associated with one or more other conditions. The system uses dictionaries of plural sets of basis

A system and method for determining from an arbitrary signal a characteristic signature or other characterizing feature and for distinguishing signals associated with one specific condition from those associated with one or more other conditions. The system uses dictionaries of plural sets of basis signal elements, for example, combinations of orthogonal bases with different characteristics. It optimizes the fit of part of an arbitrary signal to one or more elements of one class of basis signals from a dictionary and iteratively fits the remainder of the arbitrary signal to elements of an optimal class of basis signals, either the original or a different class depending on the goodness of match between the residual part of the signal and the subsequent basis class.

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I claim: 1. Apparatus for ascertaining a signature characteristic of a collection of signals for discriminating between and among such signals and for classifying other signals using said signature, said apparatus comprising: a) a dictionary comprising a plurality of prototype signals; b) means fo

I claim: 1. Apparatus for ascertaining a signature characteristic of a collection of signals for discriminating between and among such signals and for classifying other signals using said signature, said apparatus comprising: a) a dictionary comprising a plurality of prototype signals; b) means for selecting a specific prototype signal such that for at least one signal of the collection an inner product with the selected prototype is non-zero; c) means for recording the selected prototype signal; d) means for subtracting from each signal in the collection a projection of that signal on the specific prototype signal and for redesignating the result of the subtraction as the signal in the collection for the next iteration; e) means for imposing a stop criterion; and f) means for directing the apparatus back to means (b) unless the stop criterion is met. 2. Apparatus for ascertaining a signature characteristic of a collection of signals for discriminating between and among such signals and for classifying other signals using said signature, comprising: a) a dictionary comprising a plurality of prototype signals; b) means for determining an inner product between each of the signals in the collection and at least one of the prototype signals in the dictionary; c) means for selecting a specific prototype signal such that for at least one signal of the collection the inner product of the specific prototype signal with the at least one signal of the collection is non-zero; d) means for recording the specific prototype signal and the inner product of each of the signals from the collection with the prototype signal; e) means for subtracting from each signal in the collection a projection of the signal on the specific prototype signal and for redesignating the result of the subtraction as the signal in the collection for the next iteration; f) means for imposing a stop criterion; and g) means for directing the apparatus back to means (b) unless the stop criterion is met. 3. Apparatus for ascertaining a signature characteristic of a collection of signals for discriminating between and among such signals and for classifying other signals using said signature, comprising: a) a dictionary comprising a plurality of prototype signals; b) a subdictionary which is a subset of the dictionary; c) means for determining an inner product p-norm for the signals in the collection for each of the prototype signals in the subdictionary; d) means for selecting a specific prototype signal in the subdictionary that substantially maximizes said inner product p-norm; e) means for recording the specific prototype signal and an inner product of each of the signals from the collection with the prototype signal; f) means for subtracting from each signal in the collection a projection of the signal on the specific prototype signal and for redesignating the result of the subtraction as the signal in the collection for the next iteration; g) means for imposing a stop criterion; and h) means for directing the apparatus back to means (c) unless the stop criterion is met. 4. Apparatus for ascertaining a signature characteristic of a collection of signals for discriminating between and among such signals and for classifying other signals using said signature, comprising: a) a dictionary comprising a plurality of prototype signals; b) a subdictionary which is a subset of the dictionary; c) means for determining an inner product p-norm for the signals in the collection for each of the prototype signals in the subdictionary; d) means for selecting a specific prototype signal in the subdictionary that substantially maximizes said inner product p-norm; e) means for determining, for each individual signal in the collection, a separate prototype signal that locally maximizes the magnitude of an inner product of the separate prototype signal with the individual signal from the collection; f) means for recording the separate prototype signal and the maximized inner product of each individual signal from the collection with each determined separate prototype signal; g) means for subtracting from each signal in the collection a projection of the signal on the specific prototype signal and for redesignating the result of the subtraction as the signal in the collection for the next iteration; h) means for imposing a stop criterion; and i) means for directing the apparatus back to means (c) unless the stop criterion is met. 5. A method for ascertaining and identifying similarities and differences among members of a collection of signals and for representing a collection of signals in an easily compared format, comprising the steps of: a) establishing a dictionary comprising a plurality of prototype signals; b) selecting a specific prototype signal from the dictionary such that an inner product of said prototype with at least one signal of the collection is non-zero; c) recording the selected prototype signal and recording its inner product with each of the signals from the collection; d) subtracting from each signal in the collection a projection of that signal on the selected prototype signal and redesignating the result of the subtraction as the signal in the collection for the next iteration; e) imposing a stop criterion; and f) repeating steps (b) through (e) until the stop criterion is met. 6. The method of claim 5, wherein the step of selecting a specific prototype signal from the dictionary comprises determining which prototype in the dictionary substantially maximizes an inner product p-norm for the signals in the collection. 7. The method of claim 5, wherein the step of selecting a specific prototype signal from the dictionary is followed by an additional step of searching for an improved prototype signal choice in the dictionary or in a second dictionary. 8. The method of claim 5, wherein the dictionary comprises a set of Gabor atoms. 9. A method for ascertaining and identifying similarities and differences among members of a collection of signals and for representing a collection of signals in an easily compared format, comprising the steps of: a) establishing a dictionary comprising a plurality of prototype signals; b) selecting a first specific prototype signal from the dictionary such that that an inner product of said prototype with at least one signal of the collection is non-zero; c) for each individual signal in the collection, selecting an improved prototype signal from the dictionary that is similar to the first specific prototype signal but has a larger inner product magnitude with said each individual signal; d) recording each improved prototype signal and recording its respective inner product with the corresponding signal from the collection; e) subtracting from each signal in the collection a projection of its respective improved prototype signal and redesignating the result of the subtraction as the signal in the collection for the next iteration; f) imposing a stop criterion; and g) repeating steps (b) through (f) until the stop criterion is met. 10. The method of claim 9, wherein the step of selecting a first specific prototype signal from the dictionary comprises determining which prototype in the dictionary substantially maximizes an inner product p-norm for the signals in the collection. 11. The method of claim 9, wherein the step of selecting an improved prototype for each individual signal in the collection is conducted by searching a dictionary that differs from the dictionary used to establish the first specific prototype. 12. The method of claim 9, wherein the dictionary comprises a set of Gabor atoms. 13. The method of claim 9, wherein a) the dictionary comprises a set of prototype signals that are parameterized in at least one variable; and b) the step of selecting an improved prototype for each individual signal in the collection is constrained in order to limit parameter variation between said improved prototypes. 14. A method of characterizing at least one group of signals and of expressing and visualizing its characteristics, comprising the steps of a) creating an aggregate collection of signals comprising all groups of interest; b) parameterizing a dictionary of prototype signals in at least one variable; c) applying the method of either claim 5 or claim 9 in order to represent each signal in said aggregate collection in terms of at least one prototype dictionary element; and d) calculating a parametric mean over at least one group of interest. 15. A method of ascertaining and characterizing similarities and differences in and between signals or groups of signals and of expressing and visualizing said characteristics, comprising the steps of: a) creating an aggregate collection of signals comprising all groups of interest; b) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said aggregate collection in terms of at least one prototype dictionary element; c) determining for each subgroup those component prototype elements selected in step (b) that satisfy a similarity threshold test; and d) determining for each pair of subgroups those component prototype elements selected in (b) that satisfy a difference threshold test. 16. The method of claim 15, wherein a) the dictionary comprises a set of prototype signals that are parameterized in at least one variable; and b) after applying either the method of claim 5 or the method of claim 9, a parametric mean is calculated for each signal group of interest. 17. The method of claim 15, wherein the similarity threshold test keeps only those components whose mean coefficients are larger in magnitude than some set value. 18. The method of claim 15, wherein the similarity threshold test keeps only those components whose coefficient and/or other parameter values are sufficiently close to the group mean. 19. The method of claim 15, wherein the similarity threshold test keeps only those components whose coefficients and/or other parameter values have sufficiently small group variance. 20. The method of claim 15, wherein the difference threshold test keeps only those components whose coefficients and/or other parameter values differ between groups by more than some threshold amount. 21. The method of claim 15, wherein the difference threshold test keeps only those components whose squared coefficients and/or other squared parameter values differ between groups by more than some threshold amount. 22. A method of reconstructing a representative average signature signal for a collection of signals and of visualizing said signature signal, comprising the steps of: a) parameterizing a dictionary of prototype signals in at least one variable; b) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; c) calculating a parametric mean over the signal group of interest; d) sub-selecting two or more prototype elements from the calculated parametric mean set by means of similarity or difference tests; and e) summing said sub-selected parametric mean prototype elements scaled by their respective parametric mean coefficient in order to recover a representative signal. 23. A method of reconstructing a signature signal representative of the similarity or difference between signals or groups of signals within a collection and of visualizing said signature signal, comprising the steps of: a) parameterizing a dictionary of prototype signals in at least one variable; applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; c) calculating a parametric mean for each signal or subgroup of signals; d) sub-selecting at least one prototype element relevant to the comparison between subgroups from the calculated parametric mean sets; and e) summing said sub-selected parametric mean elements scaled by their proportional coefficients in order to recover a representative signal. 24. A method of ascertaining and characterizing similarities and differences between a collection of at least one signal and a group of uncorrelated baseline signals, comprising the steps of: a) parameterizing a dictionary of prototype signals in at least one variable, including at least the variable of position; b) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; c) calculating a list of parametric mean prototype elements for the collection as a function of position by averaging all parameters except position; d) calculating the RMS amplitude over all possible positions of each of the parametric mean prototype elements within the baseline signal group; and e) rescaling the coefficients derived in step (b) by the RMS baseline amplitude values. 25. The method of claim 24, additionally comprising the step of making comparisons between at least one signal with the baseline data by considering the proportionate change in said signal relative to the baseline for specific selected prototype elements scaled by their RMS amplitude. 26. A method of comparing a collection of signals to itself in order to automatically discover components of interest, comprising the steps of: a) parameterizing a dictionary of prototype signals in at least one variable, including at least the variable of position; b) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; c) calculating a list of parametric mean prototype elements for the collection as a function of position by averaging all parameters except position; d) calculating the RMS amplitude over all possible positions of each of the parametric mean prototype elements within the collection of signals; and e) rescaling the coefficients derived in (b) by the RMS baseline amplitude values. 27. A method of data compression and retrieval for a collection of signals and of noise reduction for a collection of signals, comprising the steps of: a) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; b) applying at least one threshold to sub-select a list of at least one prototype element from those derived in step (a); c) storing information sufficient to describe said sub-selected prototype elements, along with respective coefficients for each signal; and d) reconstructing each signal from the sum of stored prototype elements multiplied by their respective coefficients. 28. A method of data compression and retrieval for a collection of signals and of noise reduction for a collection of signals, comprising the steps of a) parameterizing a dictionary of prototype signals in at least one variable, including at least the variable of position; b) designating a group of baseline signals; c) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; d) calculating a list of parametric mean prototype elements for the collection as a function of position by averaging all parameters except position; e) calculating the RMS amplitude over all possible positions of each of the parametric mean prototype elements within the baseline signal group; f) rescaling the coefficients derived in step (c) by the RMS baseline amplitude values; g) applying at least one threshold to sub-select a list of at least one prototype element from those derived in step (c); h) storing information sufficient to describe said sub-selected prototype elements, along with respective coefficients for each signal; and i) reconstructing each signal from the sum of stored prototype elements multiplied by their respective coefficients. 29. The method of claim 28, wherein the designated baseline signal group includes at least one signal from the target collection of signals to be processed. 30. A method of data compression and retrieval for a collection of signals and of noise reduction for a collection of signals, comprising the steps of a) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element, with stopping criteria selected such that the algorithm will end with signal residuals smaller in magnitude than a desired resolution; b) storing information sufficient to describe the selected prototype dictionary elements, along with respective coefficients for each signal; and c) reconstructing each signal from the sum of stored prototype elements multiplied by their respective coefficients. 31. A method of data compression and retrieval for a collection of signals and of noise reduction for a collection of signals, comprising the steps of a) parameterizing a dictionary of prototype signals in at least one variable, including at least the variable of position; b) designating a group of baseline signals; c) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element, with stopping criteria selected such that the algorithm will end with signal residuals smaller in magnitude than a desired resolution; d) calculating a list of parametric mean prototype elements for the collection as a function of position by averaging all parameters except position; e) calculating the RMS amplitude over all possible positions of each of the parametric mean prototype elements within the baseline signal group; f) rescaling the coefficients derived in step (c) by the RMS baseline amplitude values; g) storing information sufficient to describe said sub-selected prototype elements, along with respective coefficients for each signal; and h) reconstructing each signal from the sum of stored prototype elements multiplied by their respective coefficients. 32. The method of claim 31, wherein the designated baseline signal group includes at least one signal from the target collection of signals to be processed. 33. A method of data compression for a sequential collection of signals, comprising the steps of a) storing information sufficient to reconstruct a first signal; b) creating a sub-collection of signals comprising at least one previously stored signal and at least one additional signal; c) applying either the method of claim 5 or the method of claim 9 in order to represent each signals in said sub-collection in terms of at least one prototype dictionary element; d) sub-selecting those prototype elements that represent differences between each additional signal and the previous signal or group of signals within the sub-collection; and e) storing information sufficient to describe said sub-selected prototype elements, along with respective coefficients for each additional signal in the sub-collection. 34. A method of data compression for a sequential collection of signals, comprising the steps of: a) parameterizing a dictionary of prototype signals in at least one variable, including at least the variable of position; b) storing information sufficient to reconstruct a first signal; c) creating a sub-collection of signals comprising at least one previously stored signal and at least one additional signal; d) designating a group of baseline signals; e) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; f) calculating a list of parametric mean prototype elements for the collection as a function of position by averaging all parameters except position; g) calculating the RMS amplitude over all possible positions of each of the parametric mean prototype elements within the baseline signal group; h) rescaling the coefficients derived in step (e) by the RMS baseline amplitude values; f) sub-selecting those prototype elements that represent differences between each additional signal and the previous signal or group of signals within the sub-collection; and i) storing information sufficient to describe said sub-selected prototype elements, along with respective coefficients for each additional signal in the sub-collection. 35. The method of claim 34, wherein the designated baseline signal group includes at least one signal from the target collection of signals to be processed. 36. A method of automatically re-aligning signals with unknown jitter variations in at least one parameter in order to compensated for said jitter, comprising the steps of: a) creating an aggregate collection of the signals of interest; b) parameterizing a dictionary of prototype signals in at least one variable, including at least those variables to be re-aligned; c) applying either the method of claim 5 or the method of claim 9 to represent each signal in said aggregate collection in terms of at least one prototype dictionary element; d) calculating a parametric mean over the signal group of interest; e) for each signal in the collection, correcting each jittered parameter by an amount proportionate to its mean variation from the respective group parametric mean. 37. A method of automatically generating an application-specific dictionary from a general-purpose dictionary, based upon on a collection of at least one signal, comprising the steps of a) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; b) applying at least one threshold to extract a subset of the resulting prototype elements derived in (a); and c) creating a new dictionary based on said subset of extracted prototype elements and/or combinations thereof. 38. A method of automatically generating an application-specific dictionary from a general-purpose dictionary, based upon on a collection of at least one signal, comprising the steps of: a) parameterizing a dictionary of prototype signals in at least one variable, including at least the variable of position; b) designating a group of baseline signals; c) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; d) calculating a list of parametric mean prototype elements for the collection as a function of position by averaging all parameters except position; e) calculating the RMS amplitude over all possible positions of each of the parametric mean prototype elements within the baseline signal group; f) rescaling the coefficients derived in step (c) by the RMS baseline amplitude values; g) applying at least one threshold to extract a subset of the resulting prototype elements derived in (c); and h) creating a new dictionary based on said subset of extracted prototype elements and/or combinations thereof. 39. The method of claim 38, wherein the designated baseline signal group includes at least one signal from the target collection of signals to be processed. 40. A method of automatically sorting novel data based upon a collection of at least one previous group of related data, comprising the steps of a) applying either the method of claim 5 or the method of claim 9 in order to represent each data signal in said collection in terms of at least one prototype dictionary element; b) applying at least one threshold to extract a subset of the prototype elements derived in (a); and c) determining an inner product between each novel data signal and the sub-selected prototype elements derived in (b). 41. A method of automatically sorting novel data based upon a collection of at least one previous group of related data, comprising the steps of: a) parameterizing a dictionary of prototype signals in at least one variable, including at least the variable of position; b) designating a group of baseline signals; c) applying either the method of claim 5 or the method of claim 9 in order to represent each signal in said collection in terms of at least one prototype dictionary element; d) calculating a list of parametric mean prototype elements for the collection as a function of position by averaging all parameters except position; e) calculating the RMS amplitude over all possible positions of each of the parametric mean prototype elements within the baseline signal group; f) rescaling the coefficients derived in step (c) by the RMS baseline amplitude values; g) applying at least one threshold to extract a subset of the prototype elements derived in (c); and h) determining an inner product between each novel data signal and the sub-selected prototype elements derived in step (g). 42. The method of claim 41, wherein the designated baseline signal group includes at least one signal from the collection of previous groups of related data.