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The objective of the paper was to validate non-linear parametric models of computerised tomography point spread function (PSF), to investigate the role of model parameters and to verify the effect of different imaging conditions on estimated parameters. These models were then to be used experimentally to estimate the variation of PSF shape within the field of view of a scanner. Two parametric models of the PSF are presented. The Gaussian model is appropriate when PSF values are positive, and the damped cosine model can account for negative values. These models are non-linear and fully two-dimensional and do not assume radial symmetry. The models were fitted to images of a point source. The models accounted for over 99% of the variance in the PSF signal. Errors in modulation transfer function were limited to 5% when the appropriate model was selected. The difference in the blurring characteristics of three image reconstruction filters was well quantified by shape parameters, and position parameters located the PSF with subpixel accuracy. With a point source located 50mm directly above the centre of the field of view, the PSF was found to be anisotropic.

A new technique to identify linear time-varying systems from ensembles of input-output realisations is presented. First, a correlation-based least-squares method is derived. This method consists of solving, for each sampling time, a matrix equation involving estimates of the input autocorrelation and input-output cross-correlation functions computed from data across the ensemble. Then, the matrix inverse needed to solve this matrix equation is replaced with a pseudo-inverse. The model is thus constrained to describe only those components of the dynamics that can be reliably identified. Ignoring 'unidentifiable' components has virtually no adverse effect on the predicted outputs. Simulation results demonstrate that the pseudoinverse technique yields more reliable estimates of the dynamics than a previously proposed least-squares technique when the inputs are coloured and the output signal-to-noise ratio (SNR) is low. With the input spectrum flat up to approximately 10% of the sampling rate and an output SNR of 5dB, the mean variance accounted for (VAF) between the true instantaneous impulse response functions (IRFs) and the instantaneous IRFs estimated with the least-squares technique was 0.2%. In contrast, the mean VAF between the true instantaneous IRFs and the instantaneous IRFs estimated with the pseudoinverse technique was 89.0%.

The identification of non-parametric impulse response functions (IRFs) from noisy finite-length data records is analysed using the techniques of matrix perturbation theory. Based on these findings, a method for IRF estimation is developed that is more robust than existing techniques, particularly when the input is non-white. Furthermore, methods are developed for computing confidence bounds on the resulting IRF estimates. Monte Carlo simulations are used to assess the capabilities of this new method and to demonstrate its superiority over classical techniques. An application to the identification of dynamic ankle stiffness in humans is presented.

Knowledge of the point spread function (PSF) of an imaging system is important when studying the characteristics of the blur present in the images. Published experimental PSF identification techniques adapt classical one-dimensional linear system identification strategies using impulse, step function or periodic input signals. This study proposes and successfully applies a correlation method based on the Wiener-Hopf equation to identify the PSF of a CT scanner. The input consists of a series of pseudorandomly located holes. Results are found to be statistically equivalent to those obtained with the impulse method at a 90% two-sided confidence interval. Like the impulse method, it readily yields two-dimensional estimate, but the larger input circumvents the major objection to the use of a wire input. Furthermore, it is relatively immune to output noise, offering an advantage over edge methods. This resistance to noise may prove helpful for nuclear medicine imaging techniques, for which the signal-to-noise ratio is much lower than that X-ray for CT.

The preferred signals for non-parametric correlation-based point spread function identification are white noise or pseudo-random binary sequences (PRBSs). Given the difficulty of building a phantom based on either of these signals, a new input is devised that corresponds to pseudo-randomly located holes. The positions of the holes correspond to zeros in a 2-D PRBS. To optimise the design of the phantom and to ensure proper imaging procedure, a number of simulations are conducted. The effects of the following parameters on identification quality are investigated: the size of the holes and their minimum separation, the period of the PRBS, input-output translational and rotational mis-registration, pixel size and the presence of cupping. The factors affecting identification quality the most are rotational alignment, hole size and separation, as well as sequence length. During simulations, a point spread function offering characteristics similar to the Philips Tomoscan CX is identified. Optimal results are obtained when the signal consists of 0.6 mm holes, separated by 0.9 mm, whose position is based on a 32 x 32 PRBS generated with a ten-stage shift-register. When adequate rotational alignment is provided, it is shown that the pseudo-randomly located holes signal is a good substitute for a purely white signal when identifying the PSF of a CT scanner.

The problem of identifying optical system point spread functions (PSFs) arises frequently in the area of image processing and restoration. The paper presents a method for determining two-dimensional PSFs from input/output image signals. The PSF of the system is determined from a set of linear equations involving elements of the input autocorrelation function and the input/output cross-correlation function. The resulting PSF is the one that minimises the sum of squares difference between the actual output image and the predicted one.

A new technique is derived for estimating the conduction velocity of muscle fibre action potentials from surface EMG recordings in humans. The method is based on system identification and extends previous such methods by explicitly accounting for additive noise at the output as well as at the input. Experimental and simulation results demonstrate that at moderate noise levels the new method yields estimates comparable to those obtained with previous methods. However, simulation studies show that the new method should be particularly valuable at high noise levels, where it should provide much better estimates than previous techniques provided that an adequate representation of the noise is available.