Triet M. Le

A Variational Approach to Reconstructing Images Corrupted by Poisson Noise

We propose a new variational model to denoise an image corrupted by Poisson noise. Like the ROF model described in [1] and [2], the new model uses total-variation regularization, which preserves edges. Unlike the ROF model, our model uses a data-fidelity term that is suitable for Poisson noise. The result is that the strength of the regularization is signal dependent, precisely like Poisson noise. Noise of varying scales will be removed by our model, while preserving low-contrast features in regions of low intensity.

Fast Cartoon + Texture Image Filters

Can images be decomposed into the sum of a geometric part and a textural part? In a theoretical breakthrough, [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. Providence, RI: American Mathematical Society, 2001] proposed variational models that force the geometric part into the space of functions with bounded variation, and the textural part into a space of oscillatory distributions. Meyers models are simple minimization problems extending the famous total variation model. However, their numerical solution has proved challenging. It is the object of a literature rich in variants and numerical attempts. This paper starts with the linear model, which reduces to a low-pass/high-pass filter pair. A simple conversion of the linear filter pair into a nonlinear filter pair involving the total variation is introduced. This new-proposed nonlinear filter pair retains both the essential features of Meyers models and the simplicity and rapidity of the linear model. It depends upon only one transparent parameter: the texture scale, measured in pixel mesh. Comparative experiments show a better and faster separation of cartoon from texture. One application is illustrated: edge detection.

Image and Video Colorization Using Vector-Valued Reproducing Kernel Hilbert Spaces

Motivated by the setting of reproducing kernel Hilbert space (RKHS) and its extensions considered in machine learning, we propose an RKHS framework for image and video colorization. We review and study RKHS especially in vectorial cases and provide various extensions for colorization problems. Theory as well as a practical algorithm is proposed with a number of numerical experiments.

A VARIATIONAL MODEL FOR INFINITE PERIMETER SEGMENTATIONS BASED ON LIPSCHITZ LEVEL SET FUNCTIONS: DENOISING WHILE KEEPING FINELY OSCILLATORY BOUNDARIES

We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the Chan–Vese model [T. F. Chan and L. A. Vese, IEEE Trans. Image Process., 10 (2000), pp. 266–277], where the length penalization of the boundaries is replaced by the area of their neighborhood of thickness

Cartoon+Texture Image Decomposition

\varepsilon

Local scales on curves and surfaces

. Our aim is to keep fine details and irregularities of the boundaries while denoising additive Gaussian noise. For the numerical computation we revisit the classical

(Φ,Φ * ) Image Decomposition Models and Minimization Algorithms

BV

Computational methods for image restoration, image segmentation, and texture modeling

level set formulation [S. Osher and J. A. Sethian, J. Comput. Phys., 79 (1988), pp. 12–49] considering suitable Lipschitz level set functions instead of

Image Decomposition Using Total Variation and div(BMO)

BV

Image decompositions using bounded variation and generalized homogeneous Besov spaces

ones.