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To reconstruct the missing or damaged parts of images from observed incomplete data, some traditional methods have been researched in recent years. The iterative denoising and backward projections(IDBP)algorithm with a simple parameter mechanism have been recently introduced, which solves the typical inverse problem by utilizing the existing 3D transform-domain collaborative filtering denoising algorithm(BM3D). While this algorithm has simple parameter tuning, the collaborative hardthresholding applied to the 3D group is greatly restricted in the procedure of denoising. In this paper, we remedy this deficiency using an iteration reweighted shrinkage denoising method. First, the model is obtained by a Plug and Play(P&P) framework. Then, we solve the optimization problem by using a proposed denoising model based on low rank prior and reweighted shrinkage and obtain a closed-form solution. Finally, the closed-form solution is operated iteratively by using the adaptive backward projection technique. Utilizing this novel strategy, the proposed algorithm not only removes the image noise and effectively recovers the degraded image, but also preserves fine structure and texture information of the image. Experimental results indicate that the proposed algorithm is competitive with some state-of-the-art inpainting algorithms in terms of both numerical evaluation and visual quality. INDEX TERMS Image inpainting, iterative denoising, inverse problem, singular value shrinkage, low-rank prior