Data processing: measuring – calibrating – or testing – Measurement system – Measured signal processing
Reexamination Certificate
1998-11-09
2001-03-27
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Measured signal processing
C702S189000, C702S066000
Reexamination Certificate
active
06208951
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to a method and an apparatus for the identification and/or separation of complex composite signals into its deterministic and noisy components. More particularly, this invention relates to a method for separating complex composite signals made available in the form of digitized data and an apparatus which appropriately converts the monitored signals obtained, from medical diagnostic equipment, molecular spectroscopy, seismographic analysis, tomography, image cleaning, chemical reactors/reaction data etc. into its deterministic (true signal) and noisy components.
BACKGROUND OF THE INVENTION
Detecting and/or separation of the underlying deterministic dynamics from noisy data obtained from complex systems is of considerable importance. Estimating the deterministic content of a monitored digital sequence (usually sequential or time-series) continues to evade satisfactory solution, despite considerable efforts over the years. This problem is central to most measured data and is especially important in applications when data is collected from medical diagnostic and scanning equipment, seismographic instruments, tomography, image analyzers, molecular spectroscopy, chemical reactors/reactions etc. The central problem is, therefore, to identify and/or separate from the composite signal, its deterministic and noise components.
PRIOR ART REFERENCES
One of the methods for the detection and/or separation of the deterministic components of the signal is by band-pass filtering using Fast Fourier Transform (FFT) (Cohen, L.,
Time
-
frequency analysis
, Prentice Hall, Englewood Cliffs, 1995) where assumptions about the frequency distribution of the noise can be made and thereby suppress those frequency components before inversion to the time domain. Thus for example, low pass filters cut off the high frequency components in the signal. This is disadvantageous when all-frequency noise is present in the signal or when the signal component itself is broadband. Fourier filtering is especially unsatisfactory when the signal dynamics originate from systems exhibiting deterministic chaos.
Another method uses kernel estimators or spline estimators but a major disadvantage of these standard smoothing techniques is the fact that they do not resolve local structures well enough (Hardle, W.,
Applied nonparametric regression
, Econometric Society Monographs, Cambridge University Press, 1990).
Another method used for the detection and separation of the composite signals is singular value analysis to reconstruct the dynamics (Broomhead, D. and King, G. P.,
Physica D
, 20 217, 1986, Cawley, R and Hsu,G.-H,
Phys. Rev. A
. 46 3057, 1992). Here the original time-series is projected onto a subspace spanned by the corresponding singular vectors, namely those spanning the largest fraction of the total variance of the data. The remaining orthogonal directions then contain most of the noise. However, these methods are nontrivial and difficult to implement because of the abstract notions involved.
Yet another method which is very commonly employed in the recent times for the detection and separation of the deterministic components of signal is based on the theory of wavelet transforms (WT) (Vettererli, M. & Kovacevic,
Wavelets and subband coding
, Prentice Hall, PTR, Englewood Cliffs, 1995).
Wavelet transform methods are increasingly used as tools for studying multiscale, nonstationary processes in various fields. General methodologies for multiresolution signal processing, sub-band coding and also mutigrid techniques have led to applications in image and speech processing, data compression, communication, quantum mechanics, medicine, spectroscopy, etc. Wavelet transforms often complement Fourier transforms (FT) techniques because the spectrum of frequencies present in the signal may be analyzed at various scales with the added advantage of time localization. Methods based on the WT have proved to be efficient and easy to implement.
Wavelets are derived from rapidly oscillating functions with mean zero and obtained by suitable scaling of analyzing function to match the desired frequencies with simultaneous translations in time. A wide variety of analyzing functions amenable for discrete or continuous time analysis are known. (Strang, G and Nguyen, T
Wavelets and Filter Banks
, Wellesley-Cambridge Press, Wellesley, Mass., 1996). Typical wavelet examples are: the discrete Haar (following a box function), the continuous Morlet (a sine function modulated by a Gaussian envelope), Mexican hat (second derivative of a Gaussian), Daubechies spanning a wide range of discrete and continuous properties (including compact support) depending on the number of wavelet filter coefficients, Lemarie, biorthogonal spline, Malvar, Coiflet, Meyer, Symlet, etc. Concisely stated, WT is a generalization of the FT and is obtained by taking the inner product of a set of basis wavelets (dependent on the resolution, translation and choice of the wavelet) with the available data X. Systematic applications for varying oscillating scales a of the wavelet and also their localization b yields scale-frequency information in a scalogram of wavelet coefficients W, rather than the frequency periodogram in a FT analysis.
The hitherto used wavelet methods for the detection and separation of the composite signals are mainly based on the concept of thresholding the wavelet coefficients obtained from a single transformation. Hard thresholding cuts off coefficients below a certain threshold A while soft-thresholding reduces all coefficients at various scales by the threshold value (Donoho, D. L., Johnstone, I. M., Kerkyacharian, Picard, D.,
J Royal Stat. Soc., Series B
57, 301). The threshold value is determined by statistical calculations and is dependent on the standard deviation of the noise (Nason, G. P.,
Wavelet regression by cross
-
validation
, Dept. of Mathematics, Univ. of Bristol, 1994) and the length of the signal. The specified threshold value may also be used to evaluate special cost functions or entropy functionals for generating appropriate basis. However, considerable improvements are still needed for applications in precision applications like medical diagnostics, seismographic analysis, image analysis etc., thereby resulting in incorrect inferences. This is because it is known that noise can be present at all frequencies and eliminating components based on statistical thresholding may not be adequate enough.
The application of WT to reducing speckle noise has been described in U.S. Pat. No. 5,497,777 (General Electric Company, 1996). In another continuing patent with the same topic (U.S. Pat. No. 5,619,998, General Electric Company, 1997), a procedure whereby a coherent in imaging system signal is reduced of speckle noise by nonlinear adaptive thresholding of wavelet coefficients by WT has been described. The resulting image has an improved signal-to-noise ratio. The method followed thresholds the wavelet coefficients from the finest scale to the coarsest scale after dividing the imaging system signal into a number of subinterval signals of equal length. Coefficients in the various scales of the wavelet transform that relate to noise are identified in each subinterval and these are eliminated before an inverse discrete wavelet transformation. It may be noted that the procedure followed was based on analyzing the scalogram of wavelet coefficients obtained by a single WT of data contained in a subinterval. It will be advantageous and beneficial to have a process by means of which noise at all scales will be identified in a systematic and rational manner without thresholding based on properties of the signal.
SUMMARY OF THE INVENTION
Accordingly, the applicants have devised an advantageous and beneficial process wherein noise at all scales will be identified in a systematic and rational manner without thresholding based on properties of the signal. Particularly, the present invention discloses an improved and systematic method for the identification and/or separation of composite signals into
Dixit Narendra Madhukar
Kulkarni Bhaskar Dattatraya
Kumar Viruthiamparambath Ravi
Vaish Nitin
Barbee Manuel L.
Council of Scientific & Industrial Research
Hoff Marc S.
Pennie & Edmonds LLP
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