Abstract: Compressive sensing has received much attention in the signal processing field for it can reconstruct a signal or image from surprisingly few samples.In this paper,the author investigates the wavelet domain image reconstruction problem and proposes a weighted  li  minimization algorithm to reconstruct the images.The proposed method utilizes not only the sparsity of signals,but also incorporates the structure information of images in wavelet domain.Hence,compared with the classical compressive sensing algorithm,the proposed method has better recoverability.Simulation results show that the proposed method has achieved the same equality image from few samples,which demonstrates the validity of the proposed method.

Key words: compressive sensing, image reconstruction, wavelet, basis pursuit