The modulus maxima of a signal's wavelet transform on different levels contain important information of the signal, which can be help to construct wavelet coefficients. A fast algorithm based on Hermite interpolation polynomial for reconstructing signal from its wavelet transform maxima is proposed in this paper. An implementation of this algorithm in medical image enhancement is also discussed. Numerical experiments have shown that compared with the Alternating Projection algorithm proposed by Mallat, this reconstruction algorithm is simpler, more efficient, and at the same time keeps high reconstruction Signal to Noise Ratio. When applied to the image contract enhancement, the computing time of this algorithm is much less compared with the one using Mallat's Alternative Projection, and the results are almost the same, so it is a practical fast reconstruction algorithm.
The quantitative analysis software system for Myocardial Contrast Echocardiography (MCE) conforms to the Digital Imaging and Communications in Medicine (DICOM) standard and can be integrated into the Picture Achiving and Communication System (PACS). The MCE software system can measure the signal intensity of 2-D grayscale images and power Doppler images, draw the time-intensity curves to indicate the variation of the intensity of microbubbles scatting in Subendocardial layer and Subepicardial layer with the varying of myocardial segments, and estimate the hemodynamic parameters by nonlinear regression analysis. So the software brought the quantitative analysis of MCE to success.