Analysis of the accuracy of estimated parameters is an important research direction. In the article, the maximum likelihood estimation is used to estimate CMOS image noise parameters and Fisher information is used to analyse their accuracy. The accuracies of the two parameters are different in different situations. Two applications of it are proposed in this paper. The first one is a guide to image representation. The standard pixel image has higher accuracy for signal-dependent noise and higher error for additive noise, in contrast to the normalised pixel image. Therefore, the corresponding image representation is chosen to estimate the noise parameters according to the dominant noise. The second application of the conclusions is a guide to algorithm design. For standard pixel images, the error of additive noise estimation will largely affect the final denoising result if two kinds of noise are removed simultaneously. Therefore, a divide-and-conquer hybrid total least squares algorithm is proposed for CMOS image restoration. After estimating the parameters, the total least square algorithm is first used to remove the signal-dependent noise of the image. Then, the additive noise parameters of the processed image are updated by using the principal component analysis algorithm, and the additive noise in the image is removed by BM3D. Experiments show that this hybrid method can effectively avoid the problems caused by the inconsistent precision of the two kinds of noise parameters. Compared with the state-of-art methods, the new method shows certain advantages in subjective visual quality and objective image restoration indicators.

Different from a general density estimation, the crime density estimation usually has one important factor: the geographical constraint. In this paper, a new crime density estimation model is formulated, in which the regions where crime is impossible to happen, such as mountains and lakes, are excluded. To further optimize the estimation method, a learning-based algorithm, named Plug-and-Play, is implanted into the augmented Lagrangian scheme, which involves an off-the-shelf filtering operator. Different selections of the filtering operator make the algorithm correspond to several classical estimation models. Therefore, the proposed Plug-and-Play optimization based estimation algorithm can be regarded as the extended version and general form of several classical methods. In the experiment part, synthetic examples with different invalid regions and samples of various distributions are first tested. Then under complex geographic constraints, we apply the proposed method with a real crime dataset to recover the density estimation. The state-of-the-art results show the feasibility of the proposed model.