Scalable compressive sampling network with progressive hierarchical subspace learning

Traditional compressive sampling does not sufficiently exploit the sparsity of signals to learn the sampling matrix adaptively. Moreover, they do not independently sample different frequency bands, which makes them ineffective in utilizing information from specific frequency bands. The existing deep learning-based compressive sensing methods achieve good performance with high model complexity, which limits their application to devices with low computing resources or small storage space. To address the above issues and improve the compressive sensing performance of natural images, we propose a novel scalable compressive sampling network with progressive hierarchical subspace learning (called SPHSL-CSNet) in an end-to-end mode. Specifically, the progressive hierarchical sampling strategy based on a three-level wavelet transform is presented, achieving band-separated sampling by extracting the low frequency, low-medium frequency, low-mid-second high frequency and the whole wavelet frequency band of the wavelet transform. This enables our model to obtain more image information with fewer sampling measurements and pay more attention to the reconstruction of texture details. The independent sampling of specific frequency bands is realized through the band-aware mask, which effectively reduces the parameter quantity of the sampling matrix and easier to deploy terminal devices in resource-limited scenarios. Extensive experiments on widely used benchmark datasets not only demonstrate that the proposed SPHSL-CSNet outperforms state-of-the-art performance under the premise of being lightweight, but also effective for the multispectral image compression. Furthermore, SPHSL-CSNet achieves excellent performance on antinoise performance with respect to the existing deep learning-based image CS method in most cases. •We propose a progressive hierarchical sampling strategy based on a three-level wavelet transform, which realizes constructing a lightweight compressive sampling matrix, and enables frequency band-separated sampling through band-aware masks.•We present the independent sampling of specific frequency bands strategy, which allows us to focus on the acquisition of important frequency bands at low sampling ratios, and the restoration of image details as the sampling ratio increases.•Extensive experiments demonstrate the effectiveness of our approach, and it is well-suited for deployment terminal devices in resource-limited scenarios.