Some filtering techniques for digital image processing

This thesis is primarily concerned with the theory and implementation of several digital filtering methods as applied to restoration and edge detection of noise contaminated images that are further degraded due to either linear motion of the object or defocusing of the camera. It is known that restoring a severely blurred but noise-free image is relatively easy, but restoring a blurred picture that has been corrupted by noise is not. This is especially the case when the noise is wide-band, since conventional linear filtering techniques using lowpass, highpass, bandpass, or their combinations will in general not work. This thesis proposes a class of linear, recursive regularization filters (R-filters). These R-filters extend the one-dimensional recursive R-filters proposed by M. Unser and his co-workers in 1991 for noise removal to the two-dimensional case. The R-filters derived are image independent, therefore they can be designed off-line and stored in the computer. Furthermore, the conventional single-parameter regularization methods are extended to a multiple-parameter setting, rendering a better balance of fidelity and smoothness of restored images. In addition, other image processing tasks such as edge detection and enhancement can also be performed within this R-filter framework.;Filtering techniques other than R-filters may also be useful in various image processing tasks. In particular, a modified Weiner filter for the restoration of blurred images is presented, showing how low-order one-dimensional and two-dimensional linear finite impulse response filters can be used for detecting edges in noisy images.;Conventional smoothing filters always tend to blur the images, so for noise removal tasks, the filter should have the ability to preserve features in an image while reducing the noise. Two approaches are taken here. In the first, the Lee filter is extended to two nonlinear filters utilizing local statistics of the degraded image. The nonlinear filters so designed have the advantage that they reduce noise without blurring the details of the image. The second approach proposed for noise removal is a two-step regularization algorithm. In the first step of the algorithm, a smoothing filter is applied to reduce the noise level of the image. In the second step of the algorithm, an R-filter is applied to restore the image treating the smoothing filter in the first step as a degradation operator.;Finally, a blur identification approach is proposed, that makes use of the distribution of relative minima of the power spectra of subimages that are obtained from the given degraded image. This algorithm is efficient for the identification of the linear motion blur, difocused blur, and exponential blur. As the second method for blur identification, a two-phase blind restoration algorithm is proposed. In the first phase of the algorithm, the blur function is identified by the preceding blur identification approach. The power spectra of the subimages are then estimated. In the second phase, Wiener filtering is employed to obtain a restored image using the estimated power spectra obtained in phase one. (Abstract shortened by UMI.).