Sparse Shape Reconstruction

作者：Aghasi Alireza^*; Romberg Justin

来源：SIAM Journal on Imaging Sciences, 2013, 6(4): 2075-2108.

DOI：10.1137/130911573

• sparse shapes
• parametric level set
• nonlinear compressed sensing

This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right elements and geometrically composing them through basic set operations to characterize desired regions in the image. This combinatorial problem can be relaxed and then solved using classical descent methods. The main component of this relaxation is forming certain compactly supported functions which we call "knolls" and reformulating the shape representation as a basis expansion in terms of such functions. To select suitable elements of the dictionary, our problem ultimately reduces to solving a nonlinear program with sparsity constraints. We provide a new sparse nonlinear reconstruction technique to approach this problem. The performance of the proposed technique is demonstrated with some standard imaging problems including image segmentation, X-ray tomography, and diffusive tomography.

• 出版日期2013