The conventional Cohen’s distribution can’t meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we embark on blending time-frequency operators and coordinate operator fractionizations to formulate the definition of the joint fractionizations metaplectic Wigner distribution (JFMWD), based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen’s distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the JFMWD domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including the classical Gaussian filter, the Cohen’s distribution filtering methods with fixed kernel functions, the classical Wiener filter, the adaptive generalized linear canonical convolution-based filtering method, the adaptive Cohen’s distribution filtering method, the adaptive JFMWD-based Cohen’s distribution filtering method, and the adaptive generalized metaplectic convolution-based Cohen’s distribution filtering method in noise suppression.

Due to their simplicity and efficiency, the margin-based Softmax losses are proposed to enhance feature discrimination in face recognition. Recently, the strategy of hard sample mining is incorporated to the margin-based Softmax losses for focusing the misclassified samples and achieves superior performance. However, the current mining-based Softmax losses indicate the sample difficultness only from the perspective of the negative cosine similarity, which is local and not robust. To obtain more discriminative deep face features, a novel adaptive hardness indicator Softmax (AHI-Softmax) loss is proposed in this paper to fully exploit the hardness information of samples. Our AHI-Softmax firstly defines a global sample hardness indicator function that integrates three difficultness factors to robustly indicate the level of “hardness” in numerical form. Then, a training stage indicator is incorporated to avoid the convergence issue. Finally, a novel sample-related modulation coefficient of the negative cosine similarity which combines the global and local hardness indicator will be defined to further enhance the differentiation of constraints imposed on samples. The experimental results on general face datasets, including LFW, AgeDB-30, CFP-FP, CALFW, CPLFW, MegaFace, IJB-B and IJB-C, show that our method can obtain more discriminative features and achieve superior verification and recognition results.