Although statistical image reconstruction methods for X-ray CT can provide improved image quality at reduced patient
doses, computation times for 3D axial and helical CT are a challenge. Rapidly converging algorithms are needed for
practical use. Augmented Lagrangian methods based on variable splitting recently have been found to be effective for
image denoising and deblurring applications.5 These methods are particularly effective for non-smooth regularizers such
as total variation or those involving the 1 norm. However, when standard "split Bregman" methods6 are applied directly
to 3D X-ray CT problems, numerous auxiliary variables are needed, leading to undesirably high memory requirements.7
For minimizing regularized, weighted least-squares (WLS) cost functions, we propose a new splitting approach for CT,
based on the alternating direction method of multipliers (ADMM)1,5 that has multiple benefits over previous methods: (i)
reduced memory requirements, (ii) effective preconditioning using modified ramp/cone filters, (iii) accommodating very
general regularizers including edge-preserving roughness penalties, total variation methods, and sparsifying transforms
like wavelets. Numerical results show that the proposed algorithm converges rapidly, and that the cone filter is particularly
effective for accelerating convergence.
Image acquisition systems invariably introduce blur, which necessitates the use of deblurring algorithms
for image restoration. Restoration techniques involving regularization require appropriate
selection of the regularization parameter that controls the quality of the restored result. We focus
on the problem of automatic adjustment of this parameter for nonlinear image restoration using
analysis-type regularizers such as total variation (TV). For this purpose, we use two variants of
Stein's unbiased risk estimate (SURE), Predicted-SURE and Projected-SURE, that are applicable
for parameter selection in inverse problems involving Gaussian noise. These estimates require
the Jacobian matrix of the restoration algorithm evaluated with respect to the data. We derive
analytical expressions to recursively update the desired Jacobian matrix for a fast variant of the
iterative reweighted least-squares restoration algorithm that can accommodate a variety of regularization
criteria. Our method can also be used to compute a nonlinear version of the generalized
cross-validation (NGCV) measure for parameter tuning. We demonstrate using simulations that
Predicted-SURE, Projected-SURE, and NGCV-based adjustment of the regularization parameter
yields near-MSE-optimal results for image restoration using TV, an analysis-type 1-regularization,
and a smooth convex edge-preserving regularizer.
Passive localisation and bearing estimation of underwater acoustic sources is a problem of great interest in the area of ocean acoustics. Bearing estimation techniques often perform poorly due to the low signal-to-noise ratio (SNR) at the sensor array. This paper proposes signal enhancement by wavelet denoising to improve the performance of the bearing estimation techniques. Methods have been
developed in the recent past to effectively perform wavelet denoising in the multisensor scenario (wavelet array denoising). Following one such approach, the acoustic signal received at the array is spatially decorrelated and then denoised. The denoised and recorrelated signal is then used for bearing estimation employing known bearing estimation techniques (MUSIC and Subspace Intersection). It is shown that wavelet array denoising improves the performance of the bearing estimators significantly. Also the case of perturbed arrays is considered as a special case for application of wavelet array denoising. Simulation results show that the denoising estimator has lower mean square error and higher resolution.
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