In this paper, blind image separation is performed, exploiting the property of sparseness to represent images. A new sparse representation called forward difference method is proposed. It is known that most of the independent component analysis (ICA) basis functions, extracted from images are sparse and gives unreliable sparseness measure. In the proposed method, the image mixture is first transformed to sparse images. These images are divided into blocks and for each block the sparseness measure 0 norm is applied. The block having the most sparseness is considered to determine the separation matrix. The efficiency of the proposed method is compared with other sparse representation functions.
Blind image separation is a method of recovering the original images from a set of image mixtures, with no information about the source images or about the mixing process. Blind source separation problem has been used to extract sources from one-dimensional mixture signals such as speech, whereas, application of source separation for images (two-dimensional signals) has been examined to a limited extent. The independent component analysis (ICA) method assumes statistical independence of the source signals and at least one of the source could be non-gaussian. These assumptions do not hold for image mixing conditions. An alternative approach is to use Kalman filter that operates on the noisy input data recursively to produce statistically optimal estimate of the underlying sources. In this paper, a robust filter on H-infinity norm is proposed and compared with for image separation of Kalman filter. The extension of the algorithms to a simple and block based approach wherein the image mixture is converted to a sparse representation is proposed. The image mixture is subdivided into blocks of known sizes and the sparseness of each block is measured using l_0 norm and the block with maximum sparseness is used for extraction of original sources. This reduces the computational complexity that exists with the large dimensions of images. The algorithms are validated for natural image data sets and also for window reflection images taken under different lighting conditions. The analysis results suggest that the proposed methods provide significantly good quality of separation as measured by the performance metrics.
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