From many fewer acquired measurements than suggested by the Nyquist sampling
theory, compressive sensing (CS) theory demonstrates that, a signal can be
reconstructed with high probability when it exhibits sparsity in some domain.
Most of the conventional CS recovery approaches, however, exploited a set of
fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a
signal, which are irrespective of the non-stationarity of natural signals and
cannot achieve high enough degree of sparsity, thus resulting in poor CS
recovery performance. In this paper, we propose a new framework for image
compressive sensing recovery using adaptively learned sparsifying basis via L0
minimization. The intrinsic sparsity of natural images is enforced
substantially by sparsely representing overlapped image patches using the
adaptively learned sparsifying basis in the form of L0 norm, greatly reducing
blocking artifacts and confining the CS solution space. To make our proposed
scheme tractable and robust, a split Bregman iteration based technique is
developed to solve the non-convex L0 minimization problem efficiently.
Experimental results on a wide range of natural images for CS recovery have
shown that our proposed algorithm achieves significant performance improvements
over many current state-of-the-art schemes and exhibits good convergence
property.

本文提出了一种使用自适应学习的稀疏化基础通过 L0 最小化方法进行图像压缩感知恢复的新框架，通过稀疏表示重叠的图像块，极大地减少了阻塞伪影和限制了 CS 解决方案空间。实验结果表明，我们的算法在 CS 恢复上取得了显着的性能提升。