<title>Wavelet transforms for infrared applications</title>

Abstract

The wavelet transform has gained much in popularity recently. Although the concepts underlying the wavelet transform have been used for some time, it is only in the last seven years that it began to have an impact, especially on signal and image processing. Wavelets have applications in differential equations, signal processing, image and video compression, and many other domains. We provide a brief introduction to wavelets and wavelet analysis, and compare the wavelet and Fourier transforms. The wavelet transform allows us to analyze nonstationary signals, which the Fourier transform cannot. This is a very important property of wavelets. A wavelet decomposition makes it possible to analyze a signal both in time (or space) and frequency domains and is appropriate for multiresolution analysis. One interesting application of wavelets is image fusion. For this application we take the wavelet transform of images coming from different sensors (e.g., visible and infrared). This provides us with a multiresolution description of visible and infrared images. The two images are then merged at each level of resolution. Applying the inverse wavelet transform on the resulting image generates a new image which is a composite of the two original ones. This concept can be applied to more than two images whether they are in the same spectral band or not. Some results are presented and compared with the classical pyramidal algorithms of Burt and Toet.