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Object detection by two-dimensional linear prediction

Published in:
MIT Lincoln Laboratory Report TR-632

Summary

An important component of any automated image analysis system is the detection and classification of objects. In this report, we consider the first of these problems where the specific goal is to detect anomalous areas (e.g., man-made objects) in textured backgrounds such as trees, grass, and fields of aerial photographs. Our detection algorithm relies on a significance test which adapts itself to the changing background in such a way that a constant false alarm rate is maintained. Furthermore, this test has a potentially practical implementation since it can be expressed in terms of the residuals of an adaptive two-dimensional linear predictor. The algorithm is demonstrated with both synthetic and realworld images.
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Summary

An important component of any automated image analysis system is the detection and classification of objects. In this report, we consider the first of these problems where the specific goal is to detect anomalous areas (e.g., man-made objects) in textured backgrounds such as trees, grass, and fields of aerial photographs...

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Implementation of 2-D digital filters by iterative methods

Published in:
IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP-30, No. 3, June 1982, pp. 473-87.

Summary

A two-dimensional (2-D) rational filter can be implemented by an iterative computation involving only finite-extent impulse response (FIR) filtering operations, provided a certain convergence criterion is met. In this paper, we generalize this procedure so that the convergence criterion is satisfied for any stable 2-D rational transfer function. One formulation which guarantees convergence invokes a relaxed form of the iterative computation along with prefiltering the numerator and denominator polynomials of the rational transfer function. This implementation may be applied with a frequency-varying relaxation parameter for increasing the rate of convergence. An alternative generalization uses several previously computed iterates, unlike our first modification which utilizes only the most recently computed iterate. This formulation can potentially guarantee convergence and also increase the convergence rate without the requirement of prefiltering. Another extension of the iterative computation incorporates constraints (e.g., positivity or finite extent) on the output of each iteration. Proof of convergence of such constrained iterations relies on the concept of a nonexpansive operator. In particular, the error introduced within the converging solution resulting from a finite-extent constraint is shown to satisfy a homogeneous partial difference equation. Finally, this error computation leads to an important link between our iterative implementation with constraints and an iterative solution to partial difference equations (e.g., Laplace's equation) with known boundary conditions.
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Summary

A two-dimensional (2-D) rational filter can be implemented by an iterative computation involving only finite-extent impulse response (FIR) filtering operations, provided a certain convergence criterion is met. In this paper, we generalize this procedure so that the convergence criterion is satisfied for any stable 2-D rational transfer function. One formulation...

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Signal reconstruction from the short-time Fourier transform magnitude

Published in:
IEEE-ASSP Int. Conf., 2 May 1982.

Summary

In this paper, a signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT. Furthermore, various algorithms are developed which reconstruct signal from appropriate samples of the STFT magnitude. Several of the algorithms can also be used to obtain signal estimates from the processed STFT magnitude, which generally does not have a valid short-time structure. These algorithms are successfully applied to the time-scale modification and noise reduction problems in speech processing. Finally, the results presented here have similar potential for other applications areas, including those with multidimensional signals.
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Summary

In this paper, a signal is shown to be uniquely represented by the magnitude of its short-time Fourier transform (STFT) under mild restrictions on the signal and the analysis window of the STFT. Furthermore, various algorithms are developed which reconstruct signal from appropriate samples of the STFT magnitude. Several of...

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Iterative techniques for minimum phase signal reconstruction from phase or magnitude

Published in:
IEEE Trans. on Acoustics, Speech & Signal Processing, Vol. ASSP-29, No.6, Dec. 1981, pp.1187-1193.

Summary

In this paper, we develop iterative algorithms for reconstructing a minimum phase sequence from pthhea se or magnitude of its Fourier transform. These iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain. This approach is the basis of a new means of computing the Hilbert transform of the log-magnitude or phase of the Fourier transform of a minimum phase sequence which does not require phase unwrapping. Finally, we discuss the potential use of this iterative computation in determining samples of the unwrapped phase of a mixed phase sequence.
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Summary

In this paper, we develop iterative algorithms for reconstructing a minimum phase sequence from pthhea se or magnitude of its Fourier transform. These iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain. This approach is...

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Recursive two-dimensional signal reconstruction from linear system input and output magnitudes

Published in:
Proc. IEEE, Vol. 69, No. 5, May 1981, pp. 667-668.

Summary

A recursive algorithm is presented for reconstructing a two-dimensional complex signal from its magnitude and the magnitude of the output of a known linear shift-invariant system whose input is the desired signal. The recursion has a simple geometric interpretation, and is easily extended to causal, shift-varying systems.
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Summary

A recursive algorithm is presented for reconstructing a two-dimensional complex signal from its magnitude and the magnitude of the output of a known linear shift-invariant system whose input is the desired signal. The recursion has a simple geometric interpretation, and is easily extended to causal, shift-varying systems.

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Convergence of iterative nonexpansive signal reconstruction algorithms

Published in:
IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP-29, No. 5, October 1981, pp. 1052-1059.

Summary

Iterative algorithms for signal reconstruction from partial time- and frequency-domain knowledge have proven useful in a number of application areas. In this paper, a general convergence proof, applicable to a general class of such iterative reconstruction algorithms, is presented. The proof relies on the concept of a nonexpansive mapping in both the time and frequency domains. Two examples studied in detail are time-limited extrapolation (equivalently, band-limited extrapolation) and phase-only signal reconstruction. The proof of convergence for the phase-only iteration is a new result obtained by this method of proof. The generality of the approach allows the incorporation of nonlinear constraints such as time- (or space-) domain positivity or minimum and maximum value constraints. Finally, the underrelaxed form of these iterations is also shown to converge even when the solution is not guaranteed to be unique.
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Summary

Iterative algorithms for signal reconstruction from partial time- and frequency-domain knowledge have proven useful in a number of application areas. In this paper, a general convergence proof, applicable to a general class of such iterative reconstruction algorithms, is presented. The proof relies on the concept of a nonexpansive mapping in...

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