Hamid Nawab

Diagnosis Using the Formal Theory of a Signal-Processing System

Many signal-processing systems can be viewed as transforming their input signals into a representation of the real-world scenario from which the signals originated. Such systems usually have parameters whose settings are selected on the basis of the class of expected input scenarios. Finding the appropriate parameter settings for a class of input scenarios usually involves testing the system against typical and/or important input scenarios from that class. Whenever the system output does not match the input scenario, the parameter settings responsible for the fault are identified. The system user can then adjust the system parameters to ensure correct system behavior for such scenarios. The diagnostic process of identifying the parameters responsible for system faults is generally difficult because the signal-processing system carries out a complicated mathematical transformation involving a multistage algorithm that generates an enormous amount of intermediate data. A new approach to the diagnosis of such systems is developed. The approach is based on the availability of an abstract and possibly qualitative description of the input scenario and the use of an alternative system model derived from the underlying mathematical theory that explicitly represents the phenomena responsible for any incorrect processing. This approach to diagnosis models a system as a combination of processes that transform the user-specified abstract description of the input scenario into the system output. Whenever the correct answer is obtained at the system output, each process reduces to an identity transformation at the level of abstraction of the system output.

Principal components analysis of the short-time Fourier transform

The authors introduce a novel time-frequency representation, the principal short-time Fourier transform (PSTFT), as a reduced-data characterization of the nonstationary spectral content of a sequence. To form the PSTFT, the authors apply principal components analysis to STFT frequency slices and retain only the first principal component information. This information alone allows for exact reconstruction of the original sequence from its PSTFT representation. The PSTFT retains explicit information about the nonstationary spectral content of a sequence, as well as implicit information necessary for reconstruction of the sequence. The results obtained are extended to other time-frequency distributions, which include the Wigner-Ville distribution, the complex energy density, and the radar ambiguity function.<<ETX>>

Model variety analysis: determining the need for knowledge-based signal processing

The integration of mathematically formulated signal processing algorithms into signal understanding systems is addressed. If control parameter adjustment is found to be necessary, a signal processing algorithm is said to have a model variety problem with respect to the class of input signals in the application domain. The necessity for such parameter adjustments implies that knowledge-based techniques must be used to adjust the signal processing parameters. A systematic framework is presented for analytically determining whether a given signal processing algorithm has a model variety problem with respect to a particular application domain. The framework is illustrated for the short-time Fourier transform algorithm as applied to the problem of non-speech sound analysis.<<ETX>>

A representation for the orientation-dependent appearance of 3-D objects

A technique is presented for matching 3-D object models to a segmented region of an image taken from an unknown viewer direction. An appearance graph is defined to capture the appearance variations with viewpoint. The appearance graphs are created at multiple levels of abstraction, allowing for orientation determination from noisy images. The method for searching the appearance graphs for the most appropriate viewpoint consists of reducing feature differences between a given aspect and the segmented region at a given level of abstraction. Both the representation techniques and the search method are described, as well as a system implementing these methods.<<ETX>>

Conceptual diagnosis of signal processing systems

Signal processing systems usually have parameters whose settings are selected on the basis of the class of expected input signals. Finding the appropriate parameter settings for a class of inputs usually involves testing the system against typical and/or important inputs from that class. Whenever the system produces an incorrect output, the parameter settings responsible for the fault are identified. The system user can then adjust the system parameters in order to ensure correct system behavior. The diagnostic process of identifying the parameters responsible for system faults is generally difficult because the signal processing system carries out a complicated mathematical transformation involving a multi-stage algorithm that generates an enormous amount of intermediate data. We develop a new approach to the diagnosis of such systems. The approach is based on the availability of an abstract and possibly qualitative description of the input scenario and the use of an alternative system model derived from the underlying mathematical theory that explicitly represents the phenomena responsible for any incorrect processing.