Smoothed-NUV Priors for Imaging.

Variations of L1 -regularization including, in particular, total variation regularization, have hugely improved computational imaging. However, sharper edges and fewer staircase artifacts can be achieved with convex-concave regularizers. We present a new class of such regularizers using normal priors with unknown variance (NUV), which include smoothed versions of the logarithm function and smoothed versions of Lp norms with p ≤ 1 . All NUV priors allow variational representations that lead to efficient algorithms for image reconstruction by iterative reweighted descent. A preferred such algorithm is iterative reweighted coordinate descent, which has no parameters (in particular, no step size to control) and is empirically robust and efficient. The proposed priors and algorithms are demonstrated with applications to tomography. We also note that the proposed priors come with built-in edge detection, which is demonstrated by an application to image segmentation.

Estimation of the Cardiac Field in the Esophagus Using a Multipolar Esophageal Catheter.

The rapid progress of invasive therapeutic options for cardiac arrhythmias increases the need for accurate diagnostics. The surface electrocardiogram (ECG) is still the standard of noninvasive diagnostics but lacks atrial signal resolution. By contrast, esophageal electrocardiography (EECG) yields atrial signals of high amplitude and with a high signal-to-noise ratio. Esophageal electrocardiography has become fast and safe, but the mechanical constraints of esophageal measuring catheters and the "random" motion of the catheter inside the subject's esophagus limit the spatial resolution of EECG signals. In this paper, we propose a method to estimate the electrical field projected onto the esophagus with an increased spatial resolution, using commonly available esophageal catheters. In a first step, we estimate the time-varying catheter position, and in a second step, we estimate the projected electrical field with enhanced spatial resolution. The proposed algorithm comprises several consecutive optimization steps, where each intermediate step produces not just a single point estimate, but a cost function over multiple solutions, which reduces the information loss at each processing step. We conclude with examples from a clinical trial, where the fields of cardiac arrhythmias are presented as two-dimensional contour plots.