MTS-CSNet: Multiscale Tensor Factorization for Deep Compressive Sensing on RGB Images

Deep learning based compressive sensing (CS) methods typically learn sampling operators using convolutional or block wise fully connected layers, which limit receptive fields and scale poorly for high dimensional data. We propose MTSCSNet, a CS framework based on Multiscale Tensor Summation (MTS) factorization, a structured operator for efficient multidimensional signal processing. MTS performs mode-wise linear transformations with multiscale summation, enabling large receptive fields and effective modeling of cross-dimensional correlations. In MTSCSNet, MTS is first used as a learnable CS operator that performs linear dimensionality reduction in tensor space, with its adjoint defining the initial back-projection, and is then applied in the reconstruction stage to directly refine this estimate. This results in a simple feed-forward architecture without iterative or proximal optimization, while remaining parameter and computation efficient. Experiments on standard CS benchmarks show that MTSCSNet achieves state-of-the-art reconstruction performance on RGB images, with notable PSNR gains and faster inference, even compared to recent diffusion-based CS methods, while using a significantly more compact feed-forward architecture.