This paper studies an inverse source problem for a time fractional diffusion equation with the distributed order Caputo derivative. The space-dependent source term is recovered from a noisy final data. The uniqueness, ill-posedness and a conditional stability for this inverse source problem are obtained. The inverse problem is formulated into a minimization functional with Tikhonov regularization method. Further, based on the series representation of the regularized solution, we give convergence rates of the regularized solution under an a-priori and an a-posteriori regularization parameter choice rule. With an adjoint technique for computing the gradient of the regularization functional, the conjugate gradient method is applied to reconstruct the space-dependent source term. Two numerical examples illustrate the effectiveness of the proposed method.

This paper studies a backward problem for a time fractional diffusion equation, with the distributed order Caputo derivative, of determining the initial condition from a noisy final datum. The uniqueness, ill-posedness and a conditional stability for this backward problem are obtained. The inverse problem is formulated into a minimization functional with Tikhonov regularization. Based on the series representation of the regularized solution, we give convergence rates under an a-priori and an a-posteriori regularization parameter choice rule. With a new adjoint technique to compute the gradient of the functional, the conjugate gradient method is applied to reconstruct the initial condition. Numerical examples in one- and two-dimensional cases illustrate the effectiveness of the proposed method.

Abstract-In this paper, a feature fusion algorithm is proposed for automatic target recognition based on High Resolution Range Profiles (HRRP). The proposed algorithm employs Convolution Neural Network (CNN) to extract fused feature from the time-frequency features of HRRP automatically. The time-frequency features used include linear transform and bilinear transform. The coding of the CNN's largest output node is the target category, and the output is compared with a threshold to decide whether the target is classified to a pre-known class or an unknown class. Simulations by four different aircraft models show that the proposed feature fusion algorithm has higher target recognition performance than single features.

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