Sparse Geometrical Representations with Bandelets
Monday, February 3, 2003
Host: Davi Geiger, email@example.com, 212-998-3235
Finding sparse representations is at the core of signal processing for applications such as compression, estimation and inverse problems. For images, representations in wavelet bases are sub-optimal because they do not take advantage of existing geometrical regularities. Integrating geometry in harmonic analysis representations can potentially improve most image processing algorithms. After reviewing existing approaches, we introduce bandelet orthogonal bases whose vectors are adapted to follow the geometrical regularity of images. It is shown that the approximation error of piece-wise regular images in a bandelet basis has an optimal decay rate. This result is illustrated by applications to noise removal with thresholding estimators and to image compression.