In sparse representation problem, there is always interest to reduce the solution space by introducing additional constraints. This can lead to efficient application-specific algorithms. Despite known advantages of sparsity and non-negativity for image data representation, limited studies have addressed these characteristics simultaneously, due to the challenges involved. In this paper, we propose a novel inexpensive sparse non-negative reconstruction method. We utilise a non-negativity penalty term within a convex function while imposing sparsity at the same time. Our method, termed as SnSA (smooth non-negative sparse approximation) applies a novel thresholding strategy on the sparse coefficients during the minimisation of the proposed convex function. The main advantage of SnSA algorithm is that hard zeroing the negative samples which leads to unstable and non-optimal sparse solution is avoided. Instead, a differentiable smoothing function is proposed that allows gradual suppression of negative samples leading to a sparse non-negative solution. This way, the algorithm is driven towards a solution with a balance in maximising the sparsity and minimising the reconstruction error. Our numerical and experimental results on both synthetic signals and well-established face and handwritten image databases, indicate higher classification performance of the proposed method compared to the state-of-the-art techniques.

在稀疏表示问题中，总是有兴趣通过引入额外的约束来减少解决方案空间。这可以导致高效的特定于应用程序的算法。尽管已知图像数据表示的稀疏性和非负性优势，但由于所涉及的挑战，有限的研究同时解决了这些特征。在本文中，我们提出了一种新颖的廉价稀疏非负重建方法。我们在凸函数中使用非负惩罚项，同时施加稀疏性。我们的方法，称为 SnSA（平滑非负稀疏近似），在最小化提议的凸函数期间对稀疏系数应用一种新的阈值策略。SnSA 算法的主要优点是避免了对负样本进行硬归零导致不稳定和非最佳稀疏解的情况。相反，提出了一种可微的平滑函数，它允许逐步抑制负样本，导致稀疏的非负解。通过这种方式，算法朝着在最大化稀疏性和最小化重建误差方面取得平衡的解决方案发展。我们在合成信号和完善的人脸和手写图像数据库上的数值和实验结果表明，与最先进的技术相比，所提出的方法具有更高的分类性能。提出了一种可微的平滑函数，它允许逐步抑制负样本，从而产生稀疏的非负解。通过这种方式，算法朝着在最大化稀疏性和最小化重建误差方面取得平衡的解决方案发展。我们在合成信号和完善的人脸和手写图像数据库上的数值和实验结果表明，与最先进的技术相比，所提出的方法具有更高的分类性能。提出了一种可微的平滑函数，它允许逐步抑制负样本，从而产生稀疏的非负解。通过这种方式，算法朝着在最大化稀疏性和最小化重建误差方面取得平衡的解决方案发展。我们在合成信号和完善的人脸和手写图像数据库上的数值和实验结果表明，与最先进的技术相比，所提出的方法具有更高的分类性能。