s This paper develops a Bayesian motion estimation algorithm for motioncompensated temporally recursive filtering of moving low-dose X-ray images (X-ray fluoroscopy). These images often exhibit a very low signalto-noise ratio. The described motion estimation algorithm is made robust against noise by spatial and temporal regularization. A priori expectations about the spatial and temporal smooth...

We propose a new algorithm for estimating NARMAX models with L1 regularization for models represented as a linear combination of basis functions. Due to the L1-norm penalty the Lasso estimation tends to produce some coefficients that are exactly zero and hence gives interpretable models. The novelty of the contribution is the inclusion of error regressors in the Lasso estimation (which yields a...

A wavelet multiscale iterative regularization method is proposed for the parameter estimation problems of partial differential equations. The wavelet analysis is introduced and a wavelet multiscale method is constructed based on the idea of hierarchical approximation. The inverse problem is decomposed into a sequence of inverse problems which rely on the scale variables and are solved approxima...

We present a family of linear regression estimators that provides a fine-grained tradeoff between statistical accuracy and computational efficiency. The estimators are based on hard thresholding of the sample covariance matrix entries together with `2-regularizion (ridge regression). We analyze the predictive risk of this family of estimators as a function of the threshold and regularization pa...

Active contours or snakes are widely used for segmentation and tracking. These techniques require the minimization of an energy function, which is generally a linear combination of a data fit term and a regularization term. This energy function can be adjusted to exploit the intrinsic object and image features. This can be done by changing the weighting parameters of the data fit and regulariza...

This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this tradeoff is determined by one crucial design parameter. The main contribution is a methodology to approximately calculate all solutions up to a certain tolerance to the model redu...

Image deconvolution is a challenging ill-posed problem when only partial information of the blur kernel is available. Certain regularization on sharp images has to be imposed to constrain the estimation of true images during the blind deconvolution process. Based on the observation that an image of sharp edges tends to minimize the ratio between the `1 norm and the `2 norm of its wavelet frame ...

In this paper, a methodology is investigated for signal recovery in the presence of nonGaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown parameters is analytically intractable, the estimation problem is derived in ...

A global robust M-estimation scheme for maximum a posteriori (MAP) image super-resolution which efficiently addresses the presence of outliers in the low-resolution images is proposed. In iterative MAP image super-resolution, the objective function to be minimized involves the highly resolved image, a parameter controlling the step size of the iterative algorithm, and a parameter weighing the d...