Abstract
This paper proposes a novel methodology for the optimal and simultaneous designs of both Hermitian transforms and masks for reducing the intraclass separations of feature vectors for anomaly detection of diabetic retinopathy images. Each class of training images associates with a Hermitian transform, a mask and a known represented feature vector. The optimal and simultaneous designs of both the Hermitian transforms and the masks are formulated as least squares optimization problems subject to the Hermitian constraints. Since the optimal mask of each class of training images is dependent on the corresponding optimal Hermitian transform, only the Hermitian transforms are required to be designed. Nevertheless, the Hermitian transform design problems are optimization problems with highly nonlinear objective functions subject to the complex valued quadratic Hermitian constraints. This kind of optimization problems is very difficult to solve. To address the difficulty, this paper proposes a singular value decomposition approach for deriving a condition on the solutions of the optimization problems as well as an iterative approach for solving the optimization problems. Since the matrices characterizing the discrete Fourier transform, discrete cosine transform and discrete fractional Fourier transform are Hermitian, the Hermitian transforms designed by our proposed approach are more general than existing transforms. After both the Hermitian transforms and the masks for all classes of training images are designed, they are applied to test images. The test images will assign to the classes where the Euclidean 2-norms of the differences between the processed feature vectors of the test images and the corresponding represented feature vectors are minimum. Computer numerical simulation results show that the proposed methodology for the optimal and simultaneous designs of both the Hermitian transforms and the masks is very efficient and effective. The proposed technique is also very efficient and effective for reducing the intraclass separations of feature vectors for anomaly detection of diabetic retinopathy images. © 2012 IEEE.