Multispectral image denoising by well-posed anisotropic diffusion scheme with channel coupling

Abstract

A novel way to denoise multispectral images is proposed via an anisotropic diffusion based partial differential equation (PDE). A coupling term is added to the divergence term and it facilitates the modelling of interchannel relations in multidimensional image data. A total variation function is used to model the intrachannel smoothing and gives a piecewise smooth result with edge preservation. The coupling term uses weights computed from different bands of the input image and balances the interchannel information in the diffusion process. It aligns edges from different channels and stops the diffusion transfer using the weights. Well-posedness of the PDE is proved in the space of bounded variation functions. Comparison with the previous approaches is provided to demonstrate the advantages of the proposed scheme. The simulation results show that the proposed scheme effectively removes noise and preserves the main features of multispectral image data by taking channel coupling into consideration.

Weighted laplacian differences based multispectral anisotropic diffusion

“…(1)) corresponds to applying Perona-Malik type diffusion [1] and hence is essential in removing noise within channels. Wellposedness of the above PDE (1) can be proven using the theory of monotone operators [9] for functions of total variation type, g(s) = 1/s. We next describe a way to chose the weights ω i which are important in aligning edges between different channels and for reducing diffusion near them.…”

Gradient and Laplacian-Based Hyperspectral Anisotropic Diffusion

“…To effectively model the interband correlations in multispectral imagery, Prasath and Singh [33] added a Laplacian differences coupling term on the right-hand side (RHS) of (3) and presented a novel MAD process as follows:…”

“…To model the interband correlations in an efficient and explicit way, Prasath and Singh [33] presented a MAD method by introducing a coupling term to capture the interband correlations and preserve edge features among diffusion bands, along with a scalar anisotropic diffusion term. Moreover, they proved the well-posedness of the MAD PDE in the bounded variation space.…”

“…Moreover, they proved the well-posedness of the MAD PDE in the bounded variation space. Although the coupling term effectively combines salient edge features using gradient information from all the bands, the PDE in [33] with the dominant scalar diffusion term is essentially the marginal version of the Perona-Malik diffusion equation [7], which may result in the loss of subtle features due to the different local geometry in each band of multispectral images, especially in the case of a large number of spectral bands. In addition, the method is computationally expensive due to the considerable time cost of weighted total variation and the coupling term using the Laplacians of all bands.…”

Harmonic Active Contours

“…Generalizing the alignment term proposed by Kimmel and Bruckstein to multi-channel images is not trivial because, by considering images as vector fields in the image domain , the coupling of the different channels must be defined heuristically [16]- [19]. The natural way to treat multi-channel images is to interpret them as two-dimensional manifolds or surfaces embedded in R k+2 and make use of differential geometry to define equivalent alignment terms.…”