Sparse Representation of Images based on RBF Neural Network

In this paper, we present a model and corresponding algorithm for sparse representing of image data. We use a RBF neural network with a small number of ellipse Gaussian functions to approximate the input images. The sparisty of the image data is achieved by solving a nonlinear optimization problem with $L_{1}$-regularization in our model. Experimental results illustrate that our method can represent the input images with good accuracy by much less number of ellipse Gaussian functions. The method is applicable for representing general surfaces and shapes.

[1]  Minxin Chen,et al.  Sparse Representation of Gaussian Molecular Surface , 2019, ArXiv.

[2]  Ling Xia,et al.  Image reconstruction in Compressed Sensing based on single-level DWT , 2014, 2014 IEEE Workshop on Electronics, Computer and Applications.

[3]  Stéphane Mallat,et al.  Sparse geometric image representations with bandelets , 2005, IEEE Transactions on Image Processing.

[4]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[5]  Joel A. Tropp,et al.  Just relax: convex programming methods for identifying sparse signals in noise , 2006, IEEE Transactions on Information Theory.

[6]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[7]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[8]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[9]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[10]  S. O. Aase,et al.  A simple design of sparse signal representations using overlapping frames , 2001, ISPA 2001. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis. In conjunction with 23rd International Conference on Information Technology Interfaces (IEEE Cat..

[11]  Kjersti Engan,et al.  Design of signal expansions for sparse representation , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[12]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[13]  D. Donoho.  For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution , 2006 .

[14]  Michael P. Friedlander,et al.  Probing the Pareto Frontier for Basis Pursuit Solutions , 2008, SIAM J. Sci. Comput..