IEEE Trans Image Process. 2018 Aug;27(8):3753-3765. doi: 10.1109/TIP.2018.2823546.
Sparse representation leads to an efficient way to approximately recover a signal by the linear composition of a few bases from a learnt dictionary based on which various successful applications have been achieved. However, in the scenario of data compression, its efficiency and popularity are hindered. It is because of the fact that encoding sparsely distributed coefficients may consume more bits for representing the index of nonzero coefficients. Therefore, introducing an accurate rate constraint in sparse coding and dictionary learning becomes meaningful, which has not been fully exploited in the context of sparse representation. According to the Shannon entropy inequality, the variance of Gaussian distributed data bound its entropy, indicating the actual bitrate can be well estimated by its variance. Hence, a globally variance-constrained sparse representation (GVCSR) model is proposed in this paper, where a variance-constrained rate term is introduced to the optimization process. Specifically, we employ the alternating direction method of multipliers (ADMMs) to solve the non-convex optimization problem for sparse coding and dictionary learning, both of them have shown the state-of-the-art rate-distortion performance for image representation. Furthermore, we investigate the potential of applying the GVCSR algorithm in the practical image set compression, where the optimized dictionary is trained to efficiently represent the images captured in similar scenarios by implicitly utilizing inter-image correlations. Experimental results have demonstrated superior rate-distortion performance against the state-of-the-art methods.
稀疏表示通过从基于学习的字典中线性组合几个基来近似恢复信号，这是一种有效的方法，基于此已经实现了各种成功的应用。然而，在数据压缩的情况下，其效率和普及性受到阻碍。这是因为稀疏分布系数的编码可能需要更多的位来表示非零系数的索引。因此，在稀疏表示的背景下，引入准确的速率约束在稀疏编码和字典学习中变得有意义，但这一点尚未得到充分利用。根据香农熵不等式，高斯分布数据的方差限制其熵，这表明实际比特率可以通过其方差很好地估计。因此，本文提出了一种全局方差约束稀疏表示（GVCSR）模型，其中在优化过程中引入了方差约束的速率项。具体来说，我们采用交替方向乘子法（ADMMs）来求解稀疏编码和字典学习的非凸优化问题，它们在图像表示方面都表现出了最先进的率失真性能。此外，我们研究了将 GVCSR 算法应用于实际图像集压缩的潜力，其中通过隐式利用图像间相关性，优化后的字典被训练来有效地表示在类似场景中捕获的图像。实验结果表明，与最先进的方法相比，该方法具有优越的率失真性能。
