Oversampled Inverse Complex Lapped Transform Optimization

When an oversampled FIR filter bank structure is used for signal analysis, a main problem is to guarantee its invertibility and to be able to determine an inverse synthesis filter bank. As the analysis scheme corresponds to a redundant decomposition, there is no unique inverse filter bank and some of the solutions can lead to artifacts in textured image filtering applications. In this paper, the flexibility in the choice of the inverse filter bank is exploited to find the best-localized impulse responses. The design is performed by solving a constrained optimization problem which is reformulated in a smaller dimensional space. Application to seismic data clearly shows the improvements brought by the optimization process.