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Because a signal can often be easily corrupted during its transmission, registration, or storage, de-noising is an important field in the areas of communications systems and of signal and image processing, especially where defense and security applications are of concern. Techniques employing transform-based methods such as the Fourier transform, the cosine transform, and wavelets have already been applied successfully to this field when dealing with an image corrupted by noise having a Gaussian or uniform distribution. However, images where impulse or salt and pepper noise are introduced are typically treated using median or switched-median algorithms because the sudden discontinuities of impulse noise often present problems for conventional transform-based noise reduction approaches. Additionally, binary images cannot easily be de-noised by fast orthogonal transforms or wavelets.
A novel noise detection and reduction scheme using a fast logical (binary) transform-based Boolean minimization algorithm is presented. The presented approach is capable of de-noising both binary and multivalued images corrupted by impulse noise. A comparison with well-known methods is offered. Particularly, the algorithm reliably detects noise more effectively than existing switched-median methods, and de-noising results comparable to or better than those attainable with median filtering are possible. The technique performs especially well when operating on images of high complexity. The new technique does not require the use of a multiplication nor a sorting operation. In addition, we show that the presented de-noising procedure could be easily performed on an already compressed file or during the compression step. Furthermore, the simplicity of the transform makes a gate-level hardware realization practical for use with distributed sensors and inexpensive or high-speed imaging systems.
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