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.

Most of the algorithms for tomographic reconstruction face the same problem: high computational complexity. In order to tackle this problem, this paper proposes a general multi-resolution approach that enables a flexible choice of reconstruction focus and thus saves computational power in reconstructions. The approach is demonstrated in this paper based on a reconstruction algorithm using a (improper) Markov random field prior with sparsifying NUV terms (nor-mal with unknown variance), where the unknown variances are learned by approximate EM (expectation maximization). The experimental and practical results show that both for simulated and real-world objects the proposed framework yields satisfying results with much lower computational cost.

The paper considers the problem of joint system identification and input signal estimation of an unknown linear system from noisy observations of the output signal. The input signal is assumed to be sparse, and each individual input pulse may affect the system in its own (and unknown) way. Based on ideas from sparse Bayesian learning, we derive an efficient expectation maximization (EM) algorithm for jointly estimating all unknown quantities. Unlike related prior work, the proposed algorithm does not alternate between estimating the input signal and estimating the system parameters; instead, all unknown quantities are jointly updated in each EM step. We give closed-form expressions for these EM updates, which can be efficiently computed by Gaussian message passing.

Cell depolarization runs essentially in a uniform motion along the muscular tissue, which creates transient electrical potential differences measurable by nearby electrodes. Inferring the depolarization speed and direction from measurements is of great interest for physicians. In cardiology, this is part of the inverse ECG problem which often requires a large number of electrodes and intense computational power even if the simple common model of the single equivalent moving dipole (SEMD) is applied. In this paper, we model a depolarization process as a straight-line movement of a SEMD. We provide an efficient algorithm based on linear state space models that infers the SEMD movement using only 3 measurement channels from a tetrahedral electrode and with the presence of interferences. Our algorithm is tested both on simulated and experimental data.

Detecting and inferring the trajectory of a moving magnet from magnetic field measurements is a challenge due to a wide range of time scales and amplitudes of the recorded signals and limited computational power of devices embedding a magnetometer. In this paper, we model the magnetic field measurements using a bank of autonomous linear state space models and provide an efficient algorithm based on local likelihood filtering for reliably detecting and inferring the gesture causing the magnetic field variations.

Surprisingly many signal processing problems can be approached by locally fitting autonomous deterministic linear state space models to the data. In this paper, we introduce local statistical models for such cases and discuss the computation both of the corresponding estimates and of local likelihoods for different models.