Apparatus and methods for image and signal processing
First Claim
1. A method of processing a set of input data X(v) representing a desired signal component plus an undesired contamination component, the method comprising the following steps:
- obtaining an ensemble-averaged power spectrum of the signal component, <
|KS(v)|2>
;
obtaining an ensemble-averaged power spectrum of the contamination component, <
|KN(v)|2>
;
forming a term B2=<
|KN(v)|2>
/<
|KS(v)|2>
;
forming a filter function W(v), where |W(v)|=[1+b2B(v)2]−
1, and b is greater than zero;
forming a term U(v), where |U(v)|=[W(v)(1−
W(v))]½
; and
processing X(v) to form a result U(v) X(v).
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Abstract
An apparatus and methods for efficiently processing signal and image data are described. The invention provides a representation of signal and image data that can be used as a figure of merit to compare and characterize different signal processing techniques. The representation can be used as an intermediate result that is may be subjected to further processing, and/or may be used as a control element for processing operations. As a provider of an intermediate result, the invention can be used as a step in processes for the transduction, storage, enhancement, refinement, feature extraction, compression, coding, transmission, or display of image, audio and other data. The invention improves manipulation of data from intrinsically unpredictable, or partially random sources. The result is a concise coding of the data in a form permitting robust and efficient data processing, a reduction in storage demands, and restoration of original data with minimal error and degradation. The invention provides a system of coding source data derived from the external environment, whether noise-free or contaminated by random components, and regardless of whether the data are represented in its natural state, such as photons, or have been pre-processed.
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Citations
32 Claims
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1. A method of processing a set of input data X(v) representing a desired signal component plus an undesired contamination component, the method comprising the following steps:
-
obtaining an ensemble-averaged power spectrum of the signal component, <
|KS(v)|2>
;
obtaining an ensemble-averaged power spectrum of the contamination component, <
|KN(v)|2>
;
forming a term B2=<
|KN(v)|2>
/<
|KS(v)|2>
;
forming a filter function W(v), where |W(v)|=[1+b2B(v)2]−
1, and b is greater than zero;
forming a term U(v), where |U(v)|=[W(v)(1−
W(v))]½
; and
processing X(v) to form a result U(v) X(v). - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method of processing data representative of visual images, the method comprising the following steps:
-
forming a filter function W(v), where |W(v)|=[1+b2B(v)2]−
1, b2 is a constant selected to satisfy |W(v)|<
1 for all v, and B(v) is proportional to v;
forming a term U(v), where |U(v)|=[W(v)(1−
W(v))]½
; and
processing X(v) to form result U(v) X(v). - View Dependent Claims (9, 10, 11, 13, 14, 16, 17, 19, 20)
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12. A method of characterizing a data processing operation which processes input data X to form a result Y, comprising the following steps:
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forming a function W, where |W| is proportional to |Y|/|X|;
forming a function U, where |U| is equal to [|W|(1−
|W|)]½
;and applying the function U to the input data X to obtain the result U(v) X(v).
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15. A method of characterizing a data processing operation that processes input data X to form a result Y, comprising the following steps:
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forming a function W, where |W| is proportional to |Y|/|X|;
forming a function Z, where |Z| is equal to [(1−
|W|)/|W|]½
;and applying the function Z to the output data Y to obtain the result Z(v) Y(v).
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18. A signal processing system, comprising:
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a data input node for inputting a signal X to be processed;
a digital computing apparatus including at least a central processor unit and memory programmed to operate on an input signal to implement operations of;
forming a first processing function W, wherein the amplitude spectrum W(v) is given by W(v)=(1+b2B(v)2)−
1;
where b is a constant and B(v) is a positive, real valued function of frequency;
forming a second processing function U having an amplitude spectrum given by [|W|(1−
|W|)]½
;applying the second processing function U to the input data;
performing a desired signal processing operation on the result of applying the second processing function U to the input data; and
a display device for displaying a result of operations implemented by said digital computing apparatus.
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21. A method of processing a signal, comprising the following steps:
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providing a signal generated by a stochastic process, the signal including a stochastic source component and a random process component;
inputting the signal to a filter having an amplitude spectrum W1(v), where v is a frequency component of the signal, the filter output representing a weighting of the frequency component a greater amount if it is more likely attributable to the stochastic source than to the random process; and
weighting the output of the filter by a function having an amplitude spectrum W2(v), where W2(v) is given by [(1−
W1(v))/W1(v)]½
. - View Dependent Claims (22, 23, 24, 25, 27, 28, 29)
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26. A signal processor, comprising:
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means for inputting data X(v) representing a desired signal component plus an undesired contamination component;
filter means for filtering the data so input, the filter means having an amplitude spectrum W(v), where |W(v)|[1+b2B(v)2]−
1, B(v) is a positive, real valued function, and b is a positive number;
means for weighting an output of the filter means by U(v), where |U(v)|=[W(v)(1−
W(v))]½
;
means for providing a weighted output of the filter means as a control signal to vary amplitude spectrum of the filter means; and
means for processing X(v) to form the result U(v) X(v).
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30. A method of enhancing regions of an image in which contrast discontinuities are present, the image formed from a plurality of signals generated by a stochastic process, wherein each signal includes a stochastic source component and a random process component, the method comprising the following steps:
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weighting the signals by a filter function having an amplitude spectrum W1(v), where v is a frequency component of the signal, the amplitude spectrum acting to selectively weight the frequency component greater if it is more likely attributable to the stochastic source than to the random process;
weighting the output of the filter function by a function having an amplitude spectrum W2(v), where W2(v) is given by [(1−
W1(v))/W1(v)]½
;and adding a result of weighting output of the filter function by W2 (v) to output of the filter function to form components of an enhanced image. - View Dependent Claims (31, 32)
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Specification