964 research outputs found
Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization
Multiplicative noise (also known as speckle noise) models are central to the
study of coherent imaging systems, such as synthetic aperture radar and sonar,
and ultrasound and laser imaging. These models introduce two additional layers
of difficulties with respect to the standard Gaussian additive noise scenario:
(1) the noise is multiplied by (rather than added to) the original image; (2)
the noise is not Gaussian, with Rayleigh and Gamma being commonly used
densities. These two features of multiplicative noise models preclude the
direct application of most state-of-the-art algorithms, which are designed for
solving unconstrained optimization problems where the objective has two terms:
a quadratic data term (log-likelihood), reflecting the additive and Gaussian
nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a
total variation or wavelet-based regularizer/prior). In this paper, we address
these difficulties by: (1) converting the multiplicative model into an additive
one by taking logarithms, as proposed by some other authors; (2) using variable
splitting to obtain an equivalent constrained problem; and (3) dealing with
this optimization problem using the augmented Lagrangian framework. A set of
experiments shows that the proposed method, which we name MIDAL (multiplicative
image denoising by augmented Lagrangian), yields state-of-the-art results both
in terms of speed and denoising performance.Comment: 11 pages, 7 figures, 2 tables. To appear in the IEEE Transactions on
Image Processing
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
Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery
In this work we address the problem of recovering sparse solutions to non
linear inverse problems. We look at two variants of the basic problem, the
synthesis prior problem when the solution is sparse and the analysis prior
problem where the solution is cosparse in some linear basis. For the first
problem, we propose non linear variants of the Orthogonal Matching Pursuit
(OMP) and CoSamp algorithms; for the second problem we propose a non linear
variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the
success rates of our algorithms on exponential and logarithmic functions. We
model speckle denoising as a non linear sparse recovery problem and apply our
technique to solve it. Results show that our method outperforms state of the
art methods in ultrasound speckle denoising
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Ultrasound Image Filtering and Reconstruction Using DCT/IDCT Filter Structure
In this paper, a new recursive structure based on the convolution model of discrete cosine transform (DCT) for designing of a finite impulse response (FIR) digital filter is proposed. In our derivation, we start with the convolution model of DCT-II to use its Z-transform for the proposed filter structure perspective. Moreover, using the same algorithm, a filter base implementation of the inverse DCT (IDCT) for image reconstruction is developed. The computational time experiments of the proposed DCT/IDCT filter(s) demonstrate that the proposed filters achieve faster elapsed CPU time compared to the direct recursive structures and recursive algorithms for the DCT/IDCT with Arbitrary Length. Experimental results on clinical ultrasound images and comparisons with classical Wiener filter, non-local mean (NLM) filter and total variation (TV) algorithms are used to validate the improvements of the proposed approaches in both noise reduction and reconstruction performance for ultrasound images
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