Abstract: The 3-dimensional helical cone-beam CT has many advantages of fast scanning，high resolution imaging，and becomes an important development direction of modern CT technology.Katsevich proposes exact FBP algorithm，which promotes access to a breakthrough in 3-dimensional cone-beam CT studies.With the complexity of the algorithm，the application has been limited.An integration CT reconstruction algorithm based on Katsevich algorithm and approximate inverse algorithm is proposed.The filtering operation is constituted by the Hilbert kernel function.The Katsevich algorithm is rewritten into the form of approximate inverse，and the specific forms of reconstructed kernel are given.

Key words: approximate inverse, reconstructed kernel, cone-beam helical CT reconstruction, Katsevich algorithm

摘要： 三维螺旋锥束CT以扫描速度快、成像分辨率高等诸多优点成为现代CT技术的一个重要发展方向。Katsevich精确FBP算法的提出，使得三维锥束CT研究获得了突破性进展。由于该算法的复杂性，应用中受到了限制。研究了Katsevich算法在检测板上沿滤波线展开的形式，其滤波运算由Hilbert核函数构成，利用近似逆的思想提出了融合的CT重建算法。该算法将Katsevich公式改写成近似逆的形式，得到了重建核的具体形式。

关键词: 近似逆, 重建核, 锥束螺旋CT重建, Katsevich算法