基于小波基向量的改进FRIT去噪方法

An Improved FRIT Denoising Method Based on Wavelet Base Vector

计算小波变换的Mallat算法需要逐级分解和重构,而本文通过矩阵变换方法,给出不需逐级计算的小波分解和重构矩阵的构造方法,并给出9/7小波的分解和重构矩阵的基向量及波形图。另外,本文改进了一种新型的图像方向性表示方法———有限域Ridgelet变换(FRIT),通过折叠分块和增加零行的方法克服了原FRIT需要构造素数长度的小波基的缺点,使小波变换的基向量可直接应用于FRIT中,计算方法和计算量都得到简化。实验表明,在对具有直线特征的图像去噪方面其性能优于FRIT。

Successive decomposition and reconstruction is necessary in Mallat computational algorithm of wavelet. Through matrix transform method, the paper developed method to construct wavelet decomposition and reconstruction ma trices without successive decomposition. A concrete example for 9/7 wavelets is provided including decomposition reconstruction base vectors and waveforms. Moreover, a new image directional representation method--FRIT （Finite ridgelet transform） is improved. By means of folded blocking and adding zero rows, the shortcoming of original FRIT, wavelet bases for prime length, is overcome. So the base vectors of wavelet transform could bc directly applied into FRIT. Both the algorithm and computational complexity can be simplified and reduced simultaneously. Simulation has shown that the performance of this algorithm is better than that of original FRIT in denoising images with linear singularities.