Sparse Shape Reconstruction
This addresses image reconstruction challenges in fields like medical imaging, but it appears incremental as it builds on existing variational and sparse methods.
The paper tackles the problem of shape-based image reconstruction by introducing a technique that uses a shape dictionary and sparsity constraints to select and compose shapes through set operations, demonstrating performance on standard imaging problems like segmentation and tomography.
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 proposed technique is demonstrated with some standard imaging problems including image segmentation, X-ray tomography and diffusive tomography.