Kalifa Jérôme, Mallat Stéphane, Rougé Bernard
Centre de Math. Appliquees, Ecole Polytechnique, Palaiseau, France.
IEEE Trans Image Process. 2003;12(4):446-57. doi: 10.1109/TIP.2003.810592.
The deconvolution of signals is studied with thresholding estimators that decompose signals in an orthonormal basis and threshold the resulting coefficients. A general criterion is established to choose the orthonormal basis in order to minimize the estimation risk. Wavelet bases are highly sub-optimal to restore signals and images blurred by a low-pass filter whose transfer function vanishes at high frequencies. A new orthonormal basis called mirror wavelet basis is constructed to minimize the risk for such deconvolutions. An application to the restoration of satellite images is shown.
利用阈值估计器研究信号的反卷积，该估计器在正交基中分解信号并对所得系数进行阈值处理。建立了一个通用准则来选择正交基，以最小化估计风险。小波基在恢复被低通滤波器模糊的信号和图像方面具有高度次优性，该低通滤波器的传递函数在高频处消失。构造了一种称为镜像小波基的新正交基，以最小化此类反卷积的风险。展示了其在卫星图像恢复中的应用。
