Image Compressive Sensing Based on Dual-Tree Wavelet Universal Hidden Markov Tree Model

This paper presents an image compressive sensing method based on the dual-tree wavelet universal hidden Markov tree model. This approach integrates dual-tree wavelet transform with universal hidden Markov tree modeling to achieve superior image quality while maintaining high compression rates. The implementation typically involves applying dual-tree complex wavelet decomposition to capture directional image features with approximate shift-invariance, followed by statistical modeling of wavelet coefficients using a universal HMT structure that adapts to different image characteristics. Key algorithmic steps include: 1) Sparse representation through dual-tree wavelet decomposition using filter banks like Kingsbury Q-shift filters, 2) Training a universal HMT model with expectation-maximization algorithm to capture interscale dependencies, and 3) Reconstruction via iterative thresholding or convex optimization methods. Experimental results demonstrate that this method effectively preserves edge information and texture details compared to conventional compressive sensing techniques, with peak signal-to-noise ratio improvements of 2-4 dB across standard test images. The combination of dual-tree wavelets' directional selectivity and UHMT's statistical modeling capabilities makes this approach particularly suitable for medical imaging and remote sensing applications where both compression efficiency and reconstruction quality are critical. Further research directions include optimizing the model for video sequences and exploring hardware implementations for real-time processing.