The Rate-Distortion Optimized Compressive Sensing for Image Coding

Compressive Sensing (CS) is an emerging technology which can encode a signal into a small number of incoherent linear measurements and reconstruct the entire signal from relatively few measurements. Different from former coding scheme which distortion mainly comes from quantizer, distortion and bit rate are related to quantization and compressive sampling in the compressive sensing based image coding schemes. Moreover, the total number of bits is often constrained in the practical application. Therefore under the given bit rate how to balance the number of measurements and quantization step size to minimization the distortion is a great challenge. In this paper, a fast Lagrange multiplier solving method is proposed for the compressive sensing based image coding scheme. Then using the solved Lagrange multiplier, the optimal number of measurements and quantization step size are determined based on the rate-distortion criteria. Experimental results show that the proposed algorithm improves objective and subjective performances substantially.