Regularization Tools and Models for Image and Signal Reconstruction

* ABSTRACT The present paper proposes a synthetic overview of regularization techniques for the reconstruction of piecewise regular signals and images. The stress is put on Tikhonov penalized approach and on subsequent non-quadratic and halfquadratic generalizations. On one hand, a link is made between the detection-estimation formulation and the non-convex penalization approach. On the other hand, it is highlighted that convex penalizing functions provide a good edge-preserving compromise between quadratic regularization and the numerically burdensome detection-estimation approach.