Deblurring is the inverse problem of restoring an image that has been blurred and possibly corrupted with noise. Deconvolution refers to the case where the blur to be removed is linear and shift-invariant so it may be expressed as a convolution of the image with a point spread function. Convolution corresponds in the Fourier domain to multiplication, and deconvolution is essentially Fourier div...

This article introduces a regularized logistic discrimination method that is especially suited for discretized stochastic processes (such as periodograms, spectrograms, EEG curves, etc.). The proposed method penalizes the total variation of the discriminant directions, giving smaller misclassification errors than alternative methods, and smoother and more easily interpretable discriminant direc...

This paper is devoted to the total variation (TV) based approach to image denoising and restoration. The restored image minimizes total variation in the class of images which satisfy the contraints given by the image acquisition model. We compute some explicit solutions of the denoising model which explain some of the features observed in numerical experiments. We also comment on some alternati...

We develop a new formulation of Stein’s method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a coupling between the original distribution and the “discrete equilibrium” distribution from renewal theory. We illustrate the approach in four nontrivial exam...

This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization, and our results may be the first of this kind. In particular, we show that from O(s log(N)) nonadaptive linear measurements, an image can be reconstructed to within the best s-term approximation of its gradient, up to a logarithmic factor...

Compressed Imaging is the theory that studies the problem of image recovery from an under-determined system of linear measurements. One of the most popular methods in this field is Total Variation (TV) Minimization, known for accuracy and computational efficiency. This paper applies a recently developed Separable Sensing Operator approach to TV Minimization, using the Split Bregman framework as...

1 Reducing variation in total knee replacements A new study in the journal Health Affairs of total knee replacement (TKR) confirms that wide variations in care exist among hospitals based on factors such as geographic location. The High Value Healthcare Collaborative found significant variations in TKR among the 5 participating health care systems. Among these were length of stay (LOS), where p...

We propose a new way of deinterlacing using a total variation scheme. Starting by the Bayesian inference formulation of total variation we do MAP by rewriting the problem into PDEs that can be solved by simple numerical schemes. Normally deinterlacing schemes are developed ad hoc with online hardware implementation directly at eye, sometimes with some frequency analysis as only theoretical base...

We consider 3-point numerical schemes for scalar Conservation Laws, that are oscillatory either to their dispersive or anti-diffusive nature. Oscillations are responsible for the increase of the Total Variation (TV); a bound on which is crucial for the stability of the numerical scheme. It has been noticed ([AKM01], [AMT04], [AMS08]) that the use of non-uniform adaptively redefined meshes, that...

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this end, we give a general upper bound “à la Pinsker” enabling us to study our problem firstly via usual functional inequalities (Poincaré inequality, weak Poincar...