Over decades, many image-enhancement techniques have been proposed. Most of these techniques have been implemented, and their test results have been published. These techniques are surveyed, the underlying concepts briefly described, and their merits discussed. The goal is to help investigators in their selection of enhancement techniques suitable to their needs.

Digital image enhancement: A survey

We consider the image restoration problem with Gaussian-like point spread functions and reformulate it as an initial value problem for the backwards diffusion equation. This approach leads to rigorous bounds on the reliability of the restoration, as a function of the noise variance, without any assumptions on the spectral characteristics of either signal or noise.In the latter half of the paper, we then describe a powerful algorithm, based on the above reformulation, and successfully use it to restore a turbulence degraded image. Typically, a complete restoration and display requires 10 seconds of CDC 7600 computing time, for a $128 \times 128$ image. We also describe a restoration experiment where Gaussian blur was simulated, and multiplicative noise added according to Huang’s model. The algorithm performs competently even at low signal to noise ratios.

Digital Removal of Random Media Image Degradations by Solving the Diffusion Equation Backwards in Time

Optimal estimators are derived for a class of signal-dependent noise processes. Such processes are of interest in optics because phenomena, such as film grain noise, are often modeled in this manner. This paper demonstrates that when one ignores the presence of signal-dependent noise and instead assumes only signal-independent noise models, the resulting estimators may pay a severe penalty in performance. This “mismatch” problem is explored, with the results of Monte Carlo simulations of the performances of both optimum and mismatched estimators being presented. The Cramer-Rao lower bounds on the mean-square estimation errors for unbiased estimators are evaluated and compared with the lower bounds derived for the signal-independent noise case. Overall, the results indicate that improved performance will, in most cases, offset the increased complexity inherent in estimators designed for the signal-dependent noise model.

Optimal estimation in signal-dependent noise

Restoration of individual image points by the method of least squares is investigated. We show that restorations computed point by point appear the same as global restorations produced by Fourier techniques. Moreover, parameters that are related to noise, point-spread functions, or object texture can be varied easily from pixel to pixel, allowing a flexibility that is achieved only with computational difficulty in global restoration techniques. To restore individual pixels, only a few points in their neighborhood, need to be considered, and the matrices that must be inverted are small enough for practical computation. The sizes of these matrices can be reduced especially if the blurring point-spread function has symmetries.

Local image restoration by a least-squares method

Picture processing: 1976

A new technique for noise suppression has been designed and tested that allows detection of small and extremely low-contrast images. The procedure entails a double scan. A first scan is made with an aperture that provides about ten quantized levels (±2 sigma apart). Isolated spots are removed and the scene is rescanned with an aperture half the original diameter. Another quantization is performed, with the original quantization intervals, but only for points in the vicinity of object boundaries. The density values that can be assigned for these points are further restricted to those that occur in a surrounding region of that point, as determined by the primary scan.

Noise-cheating image enhancement*

An image enhancement technique called "Noise Cheating" allows the detection of low contrast objects in a noisy background. This technique has been applied to imagery degraded by blur and by noise. The technique is reviewed in this paper, and the results of its application are compared to the results using Wiener filtering. Comparisons are made on both computer simulated and laboratory-generated imagery. The results indicate that subjectively preferable restorations are achieved by Wiener filtering when blur, rather than image noise, is the dominant degrading factor, while noise cheating produces preferable results when noise is predominant.© (1976) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Patrick C. Hu

Papers

Noise-cheating image enhancement*

Experiments in Digital Restoration of Defocused Grainy Photographs by Noise Cheating and Fourier Techniques