Abstract: A novel incoherent dictionary learning method is introduced based on polar decomposition, which is simple but practical framework for designing incoherent dictionary. The method distinguishes itself from traditional dictionary learning approaches by explicitly taking into account the border condition. In particular, the dictionary approximates the r-tight frame obtained with matrix polar decomposition with respect to Frobenius norm. The minimization of the sum of squared inner product of all atom pairs is taken as an constraint so as to reduce the dictionary coherence and keep the overall dictionary structure similarity before and after the update. Incoherent dictionary learning and optimization are performed based on the steepest gradient descent method and subspace rotation. Experiments on synthetic data and real audio data show that the proposed approach can achieve considerable improvements in trems of approximating equiangular tight frame (ETF) and implementing the maximal sparse coding, and can effective control the trade-off between low sparse representation errors and dictionary coherence in comparison to other methods.