Marcelo Victor Wüst Zibetti

Determining the regularization parameters for super-resolution problems

We derive a novel method to determine the parameters for regularized super-resolution problems, addressing both the traditional regularized super-resolution problem with single- and multiple-parameters and the simultaneous super-resolution problem with two parameters. The proposal relies on the joint maximum a posteriori (JMAP) estimation technique. The classical JMAP technique provides solutions at low computational cost, but it may be unstable and presents multiple local minima. We propose to stabilize the JMAP estimation, while achieving a cost function with a unique global solution, by assuming a gamma prior distribution for the hyperparameters. The resulting fidelity is similar to the quality provided by classical methods such as GCV, L-curve and Evidence, which are computationally expensive. Experimental results illustrate the low complexity and stability of the proposed method.

Simultaneous super-resolution for video sequences

In this work, we propose a new super-resolution algorithm to simultaneously estimate all frames of a video sequence. The new algorithm is based on the Bayesian maximum a posteriori estimation. In contrast to other multi-frame super-resolution algorithms, the proposed algorithm does not include the motion in the observation model. Instead, transformations caused by the motion are used as a prior information in order to achieve smoothness in the motion trajectory. The proposed algorithm provides lower computational complexity than the traditional super-resolution algorithms when several frames need to be restored. The new algorithm is also robust to motion errors and outliers. We provide results to illustrate the superiority of the new method.

A Sparse Reconstruction Algorithm for Ultrasonic Images in Nondestructive Testing

Ultrasound imaging systems (UIS) are essential tools in nondestructive testing (NDT). In general, the quality of images depends on two factors: system hardware features and image reconstruction algorithms. This paper presents a new image reconstruction algorithm for ultrasonic NDT. The algorithm reconstructs images from A-scan signals acquired by an ultrasonic imaging system with a monostatic transducer in pulse-echo configuration. It is based on regularized least squares using a l1 regularization norm. The method is tested to reconstruct an image of a point-like reflector, using both simulated and real data. The resolution of reconstructed image is compared with four traditional ultrasonic imaging reconstruction algorithms: B-scan, SAFT, ω-k SAFT and regularized least squares (RLS). The method demonstrates significant resolution improvement when compared with B-scan—about 91% using real data. The proposed scheme also outperforms traditional algorithms in terms of signal-to-noise ratio (SNR).

Estimation of the parameters in regularized simultaneous super-resolution

We describe a method for automatic determination of the regularization parameters for the class of simultaneous super-resolution (SR) algorithms. This method, proposed in (Zibetti et al., 2008c), is based on the joint maximum a posteriori (JMAP) estimation technique, which is a fast alternative to estimate the parameters. However, the classical JMAP technique can be unstable and may generate multiple local minima. In order to stabilize the JMAP estimation, while achieving a cost function with a unique global solution, we derive an improved solution by modeling the JMAP hyperparameters with a gamma prior distribution. In this work, experimental results are provided to illustrate the effectiveness of the proposed method for automatic determination of the regularization parameters for the simultaneous SR. Moreover, we contrast the proposed method to a reference method with known fixed parameters as well as to other parameter selection methods based on the L-curve. These results validate the proposed method as a very attractive alternative for estimating the regularization parameters.

Separate magnitude and phase regularization in MRI with incomplete data: Preliminary results

In Magnetic Resonance Imaging (MRI) studies, for clinical applications and for research as well, reduction of scanning time is an essential issue. This time reduction could be obtained by using fast acquisition sequences, such as EPI and spiral k-space trajectories, and by acquiring less data, this being possible based on the new sampling theories that gave rise to the so called Compressed Sampling (CS for short). However the main assumption for the application of CS to Fourier data is that magnitude and phase are both sparse in some given domain. This assumption is not always true for fast acquisition sequences because of the non-homogeneities of the main magnetic field. In this article we propose a new model for MRI with different regularization penalties for magnitude and phase. Magnitude regularization exploits the sparsity assumption on the signal and the suggested penalty for phase takes into account its smoothness. We show results of numerical experiments with simulated data.

Outlier Robust and Edge-Preserving Simultaneous Super-Resolution

In this work, we propose a new robust and edge-preserving super-resolution algorithm to simultaneously estimate all frames of a sequence. The new algorithm is based on the regularized super-resolution approach. In contrast to other multi-frame super-resolution algorithms, the proposed algorithm does not include the motion in the observation model. Instead, transformations caused by the motion are used in the prior model to produce a sequence with improved quality and smoothness in the motion trajectory. We use a Huber norm in the prior term to achieve an algorithm robust to outliers in the motion model while avoiding blurring of edges. The proposed method is significantly more robust than other simultaneous super-resolution methods. We provide results to illustrate the performance of the algorithm.

Improving compressive sensing in MRI with separate magnitude and phase priors

Compressive sampling/compressed sensing (CS) has shown that it is possible to perfectly reconstruct non-bandlimited signals sampled well below the Nyquist rate. Magnetic Resonance Imaging (MRI) is one of the applications that has benefited from this theory. Sparsifying operators that are effective for real-valued images, such as finite difference and wavelet transform, also work well for complex-valued MRI when phase variations are small. As phase variations increase, even if the phase is smooth, the sparsifying ability of these operators for complex-valued images is reduced. If the phase is known, it is possible to remove it from the complex-valued image before applying the sparsifying operator. Another alternative is to use the sparsifying operator on the magnitude of the image, and use a different operator for the phase, i.e., one related to a smoothness enforcing prior. The proposed method separates the priors for the magnitude and for the phase, in order to improve the applicability of CS to MRI. An improved version of previous approaches, by ourselves and other authors, is proposed to reduce computational cost and enhance the quality of the reconstructed complex-valued MR images with smooth phase. The proposed method utilizes

Superiorization of incremental optimization algorithms for statistical tomographic image reconstruction

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