Edge-preserving Regularization Method Research Articles

Comparison Study of Regularizations in Spectral Computed Tomography Reconstruction.

The energy-resolving photon-counting detectors in spectral computed tomography (CT) can acquire projections of an object in different energy channels. In other words, they are able to reliably distinguish the received photon energies. These detectors lead to the emerging spectral CT, which is also called multi-energy CT, energy-selective CT, color CT, etc. Spectral CT can provide additional information in comparison with the conventional CT in which energy integrating detectors are used to acquire polychromatic projections of an object being investigated. The measurements obtained by X-ray CT detectors are noisy in reality, especially in spectral CT where the photon number is low in each energy channel. Therefore, some regularization should be applied to obtain a better image quality for this ill-posed problem in spectral CT image reconstruction. Quadratic-based regularizations are not often satisfactory as they blur the edges in the reconstructed images. As a result, different edge-preserving regularization methods have been adopted for reconstructing high quality images in the last decade. In this work, we numerically evaluate the performance of different regularizers in spectral CT, including total variation, non-local means and anisotropic diffusion. The goal is to provide some practical guidance to accurately reconstruct the attenuation distribution in each energy channel of the spectral CT data.

The ANN based detector to remove random-valued impulse noise in images

This paper presents an artificial neural network (ANN) based method to detect random-valued impulse noise (RVIN) in images. The proposed method employs the ANN to decide whether a pixel is corrupted or not with RVIN. The inputs of the ANN are the rank ordered absolute differences (ROAD) and the rank-ordered logarithmic difference (ROLD) values. After the detection process is completed, the corrupted pixels are restored by the edge-preserving regularization (EPR) method which allows edges and noise-free pixels to be preserved. The performance of the proposed method is evaluated on different test images and compared with ten different comparison filters from the literature. Simulation results indicate that the proposed method provides significant improvement over comparison filters especially for high noise densities.

A new nonlinear filter constructed from the Newton method and EPR in image restoration

The edge-preserving regularization method (EPR) is effective to remove Gaussian noise and impulse noise in image restorations, but till now, we could not say that the problem has been solved very efficiently by state of the art optimization method. In our paper, we will construct a new nonlinear filter from the edge-preserving model and the Newton method, the parameter estimation model in the nonlinear filter will be established, and the solution existence of the model will be proved at the same time. Numerical results demonstrate that the nonlinear filter removes the Gaussian noise from an image as effectively as the edge-preserving regularization method does, and the time for the nonlinear filter to restore an image is less than half time for the edge-preserving regularization method.

A random-valued impulse noise removal algorithm with local deviation index and edge-preserving regularization

In this paper, we present a two-phase random-valued impulse noise removal algorithm based on local deviation index (LDI) and edge-preserving regularization. In the first phase, we define an image statistic LDI. Then with image pixels’ LDI values, the outlier candidates are identified. In the second phase, the image is denoised by an edge-preserving regularization method. Extensive experimental results indicate that our method performances better than many existing filters do for its robust image restoration and accurate noise detection.

Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography

In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method presented here, a potential function with edge-preserving properties is introduced as a regularized term in an objective function. With the minimization of this proposed objective function, an iterative method to solve this optimization problem is presented in which half-quadratic regularization is introduced to simplify the minimization task. Both numerical and experimental data are employed to justify the proposed technique. The reconstruction results indicate that edge-preserving regularization provides a superior performance over Tikhonov regularization.

A hybrid convex variational model for image restoration

We propose a new hybrid model for variational image restoration using an alternative diffusion switching non-quadratic function with a parameter. The parameter is chosen adaptively so as to minimize the smoothing near the edges and allow the diffusion to smooth away from the edges. This model belongs to a class of edge-preserving regularization methods proposed in the past, the ϕ -function formulation. This involves a minimizer to the associated energy functional. We study the existence and uniqueness of the energy functional of the model. Using real and synthetic images we show that the model is effective in image restoration.

Effect of regularization parameters on geophysical reconstruction

In this paper we discuss the edge-preserving regularization method in the reconstruction of physical parameters from geophysical data such as seismic and ground-penetrating radar data. In the regularization method a potential function of model parameters and its corresponding functions are introduced. This method is stable and able to preserve boundaries, and protect resolution. The effect of regularization depends to a great extent on the suitable choice of regularization parameters. The influence of the edge-preserving parameters on the reconstruction results is investigated and the relationship between the regularization parameters and the error of data is described.

Three-dimensional quantitative microwave imaging from measured data with multiplicative smoothing and value picking regularization

This paper presents reconstructions of four targets from the 3D Fresnel database. The electromagnetic inverse scattering problem is treated as a nonlinear optimization problem for the complex permittivity in an investigation domain. The goal of this paper is to explore the achievable reconstruction quality when such a quantitative inverse scattering approach is employed on real world measurements, using only single-frequency data. Two regularization techniques to reduce the ill-possedness of the inverse scattering problem are compared. The first one is a multiplicative smoothing regularization, applied directly to the cost function, which yields smoothed reconstructions of the homogeneous Fresnel targets without much experimentation to determine the regularization parameter. The second technique is the recently proposed value picking (VP) regularization which is particularly suited for the class of piecewise (quasi-)homogeneous targets, such as those of the Fresnel database. In contrast to edge-preserving regularization methods, VP regularization does not operate on the spatial distribution of permittivity values, but it clusters them around some reference values, the VP values, in the complex plane. These VP values are included in the cost function as auxiliary optimization variables and their number can be gradually increased using a stepwise relaxed VP regularization scheme. Both regularization strategies are incorporated in a Gauss–Newton minimization framework with line search. It is shown that the reconstruction quality using single-frequency Fresnel data is good when using multiplicative smoothing and even better when using the VP regularization. In particular, the completely blind reconstruction of the mystery target in the database provides us with a detailed quantitative image of a plausible object.

A new method for parameter estimation of edge-preserving regularization in image restoration

In image restoration, the so-called edge-preserving regularization method is used to solve an optimization problem whose objective function has a data fidelity term and a regularization term, the two terms are balanced by a parameter λ . In some aspect, the value of λ determines the quality of images. In this paper, we establish a new model to estimate the parameter and propose an algorithm to solve the problem. In order to improve the quality of images, in our algorithm, an image is divided into some blocks. On each block, a corresponding value of λ has to be determined. Numerical experiments are reported which show efficiency of our method.

MIT image reconstruction based on edge-preserving regularization

Tikhonov regularization has been widely used in electrical tomography to deal with the ill-posedness of the inverse problem. However, due to the fact that discontinuities are strongly penalized, this approach tends to produce blurred images. Recently, a lot of interest has been devoted to methods with edge-preserving properties, such as those related to total variation, wavelets and half-quadratic regularization. In the present work, the performance of an edge-preserving regularization method, called ARTUR, is evaluated in the context of magnetic induction tomography (MIT). ARTUR is a deterministic method based on half-quadratic regularization, where complementary a priori information may be introduced in the reconstruction algorithm by the use of a nonnegativity constraint. The method is first tested using an MIT analytical model that generates projection data given the position, the radius and the magnetic permeability of a single nonconductive cylindrical object. It is shown that even in the presence of strong Gaussian additive noise, it is still able to recover the main features of the object. Secondly, reconstructions based on real data for different configurations of conductive nonmagnetic cylindrical objects are presented and some of their parameters estimated.

Modeling anisotropic undersampling of magnetic resonance angiographies and reconstruction of a high-resolution isotropic volume using half-quadratic regularization techniques

In this paper we address the problem of reconstructing a high resolution volumic image from several low resolution data sets. A solution to this problem is proposed in the particular framework of magnetic resonance angiography (MRA), where the resolution is limited by a trade-off between the spatial resolution and the acquisition time, both being proportional to the number of samples acquired in k-space. For this purpose only the meaningful spatial frequencies of the 3D k-space of the vessel are acquired, which is achieved using successive acquisitions with decreased spatial resolution, leading to highly anisotropic data sets in one or two specific directions. The reconstruction of the MRA volume from these data sets relies on an edge-preserving regularization method and leads to two different implementations: the first one is based on a conjugate gradient algorithm, and the second one on half-quadratic developments. The hyper parameters of the method were experimentally determined using a set of simulated data, and promising results were obtained on aorta and carotid artery acquisitions, where on the one hand a good fidelity to the acquired data is maintained, and on the other hand homogeneous areas are smooth and edges are well preserved. Half-quadratic regularization proved to be particularly well adapted to the MRA problem and leads to a fast iterative algorithm requiring only scalar and FFT computations.

Globally convergent iterative numerical schemes for nonlinear variational image smoothing and segmentation on a multiprocessor machine

We investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel. A general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown. We characterize various edge-preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework. As a by-product, global convergence can be proven under conditions slightly weaker than these stated in the literature. Efficient Krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine. The performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed-up factors are reported.

Determination of the relaxation time spectrum from dynamic moduli using an edge preserving regularization method

For the numerical determination of a continuous relaxation time spectrum from rheological data so-called regularization methods are necessary. The regularization method based on Tikhonov regularization and commonly used in rheology assumes the relaxation time spectrum to be smooth. Accordingly, this method is not able to properly resolve spectra containing edges or at least large curvatures as proposed in the literature. In order to reconstruct such spectra a novel edge preserving regularization (EPR) method was developed which extends the properties of the commonly used method. In order to demonstrate the efficiency of EPR it is compared with the commonly used regularization method by means of simulated and experimental data. This reveals that EPR is able to prove whether or not the theoretically predicted edge containing spectra for high-molecular-weight, monodisperse polymers are compatible with experimental data.

Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction

Gradient-based iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shift-invariant, i.e., for those with approximately block-Toeplitz or block-circulant Hessians. However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging, the Hessian of the weighted least-squares objective function is quite shift-variant, and circulant preconditioners perform poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shift-variant imaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. We also propose a new efficient method for the line-search step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.