Rate-distortion optimization for compressive video sampling

The recently introduced compressed sensing (CS) framework enables low complexity video acquisition via sub-Nyquist rate sampling. In practice, the resulting CS samples are quantized and indexed by finitely many bits (bit-depth) for transmission. In applications where the bit-budget for video transmission is constrained, rate-distortion optimization (RDO) is essential for quality video reconstruction. In this work, we develop a double-level RDO scheme for compressive video sampling, where frame-level RDO is performed by adaptively allocating the fixed bit-budget per frame to each video block based on block-sparsity, and block-level RDO is performed by modelling the block reconstruction peak-signal-to-noise ratio (PSNR) as a quadratic function of quantization bit-depth. The optimal bit-depth and the number of CS samples are then obtained by setting the first derivative of the function to zero. In the experimental studies the model parameters are initialized with a small set of training data, which are then updated with local information in the model testing stage. Simulation results presented herein show that the proposed double-level RDO significantly enhances the reconstruction quality for a bit-budget constrained CS video transmission system.