Principal-component characterization of noise for infrared images

Abstract

Principal-component decomposition is applied to the analysis of noise for infrared images. It provides a set of eigenimages, the principal components, that represents spatial patterns associated with different types of noise. We provide a method to classify the principal components into processes that explain a given amount of the variance of the images under analysis. Each process can reconstruct the set of data, thus allowing a calculation of the weight of the given process in the total noise. The method is successfully applied to an actual set of infrared images. The extension of the method to images in the visible spectrum is possible and would provide similar results.

Automatic classification for noise of infrared images into processes by means of the principal component analysis

“…Then, it is possible to retrieve the original frames with only a subset of principal components what is called "principal components rectification", or, what is the same, to filter the complete whole of data to extract features or interest directly related with some specific components 6,7 (see Figure 1). Besides the eigenimages , the method gives two other parameters, eigenvalues and eigenvectors.…”

“…Accordingly, the directions in the scatter plot given by α E represents the direction along which the variance α λ is encountered. 5,7 Then, principal components can be seen as a translation to the mean and a rigid rotation of the scatter plot reference system to obtain a new set of frames exhibiting a negligible covariance among them.…”

“…This is done assuming that, when taking into account the uncertainty due to sampling of M pixels, two eigenvalues could be considered equal, their principal components belongs to the same process. 7 If this is the case, the eigenvectors associated to this two eigenvalues define a plane. If we make a rotation by a certain angle in a direction perpendicular to this plane we obtain a new couple of eigenvectors and principal components.…”

“…Then it has no sense to consider the frames reconstructed by each one, but the ones reconstructed by both of them due to the non-negligible degree of covariance among them when taking another set of data. 7 The same reasoning that worked for two eigenvalues can be extended to the set of eigenvalues that could be considered consecutively equal. Then, it is possible to make a definition of process as follows: A process is defined as a filtered set of frames generated by a subset of principal components (eigenimages) being their eigenvalues consecutive undistinguishable respect to a statistical criterium.…”

“…These outputs are grouped into processes. 7 After that, the eigenvectors associated with processes containing a single Principal Component are fitted to a harmonic function. Due to the finite interval of sampling and the orthonormalization of the eigenvectors, not all frequencies can appear in the fitting of the evolution of the eigenvectors.…”