Salt-and-pepper noise consists of outlier pixel values which significantly impair image structure and quality. Multiparent fractal image coding (MFIC) methods substantially exploit image redundancy by utilizing multiple domain blocks to approximate the range block, partially compensating for the information loss caused by noise. Motivated by this, we propose two novel image restoration methods based on MFIC to remove salt-and-pepper noise. The first method integrates Huber M-estimation into MFIC, resulting in an improved anti-salt-and-pepper noise robust fractal coding approach. The second method incorporates MFIC into a total variation (TV) regularization model, including a data fidelity term, an MFIC term and a TV regularization term. An alternative iterative method based on proximity operator is developed to effectively solve the proposed model. Experimental results demonstrate that these two proposed approaches achieve significantly enhanced performance compared to traditional fractal coding methods.

椒盐噪声由异常像素值组成，会严重损害图像结构和质量。多父分形图像编码（MFIC）方法通过利用多个域块来近似范围块，充分利用图像冗余，部分补偿由噪声引起的信息损失。受此启发，我们提出了两种基于 MFIC 的新颖图像恢复方法来消除椒盐噪声。第一种方法将 Huber M 估计集成到 MFIC 中，从而改进了抗椒盐噪声鲁棒分形编码方法。第二种方法将MFIC合并到全变分(TV)正则化模型中，包括数据保真度项、MFIC项和TV正则化项。开发了一种基于邻近算子的替代迭代方法来有效地求解所提出的模型。实验结果表明，与传统的分形编码方法相比，这两种提出的方​​法实现了显着增强的性能。