Imaging and Computing Seminar

Gabriel Peyre

Sparse Processing of Images

In this talk, I will review recent work on the sparse representations of natural images. I will focus on the application of these emerging models for the resolution of various imaging problems, which include compression, denoising and super-resolution of images, as well as compressive sensing and compressive wave computations.

Natural images exhibit a wide range of geometric regularities, such as curvilinear edges and oscillating textures. Adaptive image representations select bases from a dictionary of orthogonal or redundant frames that are parameterized by the geometry of the image. If the geometry is well estimated, the image is sparsely represented by only a few atoms in this dictionary. The resolution of ill-posed inverse problems in image processing is then regularized using sparsity constraints in these adapted representations.