Geert Uytterhoeven

Image de‐noising by integer wavelet transforms and generalized cross validation

De-noising algorithms based on wavelet thresholding replace small wavelet coefficients by zero and keep or shrink the coefficients with absolute value above the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. To estimate this optimal threshold, we use Generalized Cross Validation. This procedure has linear complexity and is fully automatic, i.e., it does not require an estimate for the noise energy. This paper uses the method for wavelet transforms that map integer gray-scale pixel values to integer wavelet coefficients. An image with artificial noise is used to illustrate the optimality properties of the estimator. Not all theoretical requirements for a successful application of the method are strictly fulfilled in the integer transform case. However, this has little influence on practical results.

WAILI: a software library for image processing using integer wavelet transforms

WAILI is a wavelet transform library, written in C++. It includes some basic image processing operations based on the use of wavelets and forms the backbone of more complex image processing operations. We use the Cohen-Daubechies- Feauveau biorthogonal wavelets. The wavelet transforms are integer transforms, calculated using the integer version of the Lifting Scheme. WAILI is available in source form for research purposes.

A Wavelet Toolbox for Large Scale Image Processing

The wavelet transform has proven to be a valuable tool for image processing applications, like image compression and noise reduction. In this paper we present a scheme to process very large images that do not fit in the memory of a single computer, based on the software library WAILI (Wavelets with Integer Lifting). Such images are divided into blocks that are processed quasi independently, allowing efficient parallel programming. The blocking is almost completely transparent to the user.