The optimized color space is searched by using the wavelet scattering network in the KTH_TIPS_COL color image database for image texture classification. The effect of choosing the color space on the classification accuracy is investigated by converting red green blue （RGB） color space to various other color spaces. The results show that the classification performance generally changes to a large degree when performing color texture classification in various color spaces, and the opponent RGB-based wavelet scattering network outperforms other color spaces-based wavelet scattering networks. Considering that color spaces can be changed into each other, therefore, when dealing with the problem of color texture classification, converting other color spaces to the opponent RGB color space is recommended before performing the wavelet scattering network.
A new method for reconstructing the compressed sensing color image by solving an optimization problem based on total variation in the quaternion field is proposed, which can effectively improve the reconstructing ability of the color image. First, the color image is converted from RGB （red, green, blue） space to CMYK （cyan, magenta, yellow, black） space, which is assigned to a quaternion matrix. Meanwhile, the quaternion matrix is converted into the information of the phase and amplitude by the Euler form of the quatemion. Secondly, the phase and amplitude of the quatemion matrix are used as the smoothness constraints for the compressed sensing （CS） problem to make the reconstructing results more accurate. Finally, an iterative method based on gradient is used to solve the CS problem. Experimental results show that by considering the information of the phase and amplitude, the proposed method can achieve better performance than the existing method that treats the three components of the color image as independent parts.
In order to classify nonlinear features with a linear classifier and improve the classification accuracy, a deep learning network named kernel principal component analysis network（ KPCANet） is proposed. First, the data is mapped into a higher-dimensional space with kernel principal component analysis to make the data linearly separable. Then a two-layer KPCANet is built to obtain the principal components of the image. Finally, the principal components are classified with a linear classifier. Experimental results showthat the proposed KPCANet is effective in face recognition, object recognition and handwritten digit recognition. It also outperforms principal component analysis network（ PCANet） generally. Besides, KPCANet is invariant to illumination and stable to occlusion and slight deformation.
An algorithm for recovering the quaternion signals in both noiseless and noise contaminated scenarios by solving an L1-norm minimization problem is presented. The L1-norm minimization problem over the quaternion number field is solved by converting it to an equivalent second-order cone programming problem over the real number field, which can be readily solved by convex optimization solvers like SeDuMi. Numerical experiments are provided to illustrate the effectiveness of the proposed algorithm. In a noiseless scenario, the experimental results show that under some practically acceptable conditions, exact signal recovery can be achieved. With additive noise contamination in measurements, the experimental results show that the proposed algorithm is robust to noise. The proposed algorithm can be applied in compressed-sensing-based signal recovery in the quaternion domain.
