313 research outputs found
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
We address the denoising of images contaminated with multiplicative noise,
e.g. speckle noise. Classical ways to solve such problems are filtering,
statistical (Bayesian) methods, variational methods, and methods that convert
the multiplicative noise into additive noise (using a logarithmic function),
shrinkage of the coefficients of the log-image data in a wavelet basis or in a
frame, and transform back the result using an exponential function. We propose
a method composed of several stages: we use the log-image data and apply a
reasonable under-optimal hard-thresholding on its curvelet transform; then we
apply a variational method where we minimize a specialized criterion composed
of an data-fitting to the thresholded coefficients and a Total
Variation regularization (TV) term in the image domain; the restored image is
an exponential of the obtained minimizer, weighted in a way that the mean of
the original image is preserved. Our restored images combine the advantages of
shrinkage and variational methods and avoid their main drawbacks. For the
minimization stage, we propose a properly adapted fast minimization scheme
based on Douglas-Rachford splitting. The existence of a minimizer of our
specialized criterion being proven, we demonstrate the convergence of the
minimization scheme. The obtained numerical results outperform the main
alternative methods
Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise
Recovering images corrupted by multiplicative noise is a well known
challenging task. Motivated by the success of multiscale hierarchical
decomposition methods (MHDM) in image processing, we adapt a variety of both
classical and new multiplicative noise removing models to the MHDM form. On the
basis of previous work, we further present a tight and a refined version of the
corresponding multiplicative MHDM. We discuss existence and uniqueness of
solutions for the proposed models, and additionally, provide convergence
properties. Moreover, we present a discrepancy principle stopping criterion
which prevents recovering excess noise in the multiscale reconstruction.
Through comprehensive numerical experiments and comparisons, we qualitatively
and quantitatively evaluate the validity of all proposed models for denoising
and deblurring images degraded by multiplicative noise. By construction, these
multiplicative multiscale hierarchical decomposition methods have the added
benefit of recovering many scales of an image, which can provide features of
interest beyond image denoising
Mathematical Model for Image Restoration Based on Fractional Order Total Variation
This paper addresses mathematical model for signal restoration based on fractional order total variation (FOTV) for multiplicative noise. In alternating minimization algorithm the Newton method is coupled with time-marching scheme for the solutions of the corresponding PDEs related to the minimization of the denoising model. Results obtained from experiments show that our model can not only reduce the staircase effect of the restored images but also better improve the PSNR as compare to other existed methods
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