Efficient Parameter Optimization For Example-Based Design Of Nonseparable Oversampled Lapped Transform

This paper proposes an efficient design method of nonseparable oversampled lapped transform (NSOLT). NSOLT is a multidimensional redundant transform which satisfies the nonseparable, symmetric, real-valued, overlapped, compact-supported and perfect reconstruction property. A typical example-based design approach, which consists of sparse coding and parameter optimization, is applicable to NSOLT. In the previous implementation, however, the parameter optimization stage dominated the computation. The main reason is that the quasi-Newton method with numerical gradient of the objective function was adopted. To reduce the computational cost, the analytical gradient is derived and introduced. For further acceleration, the quasi-Newton method is replaced by stochastic gradient descent. Through some experiments, the significance of the proposed method is verified.