基于小波变换与稀疏傅里叶变换相结合的光场重构方法

Light Field Reconstruction Based on Wavelet Transform and Sparse Fourier Transform

随着计算机图形学和计算机视觉技术的发展,光场开始进入人们的视线并被迅速应用于各个领域.然而光场的获取需要大量的图像,具有数据量大,获取成本高等特点,因此学者们越来越关注如何利用少量的光场数据获取整个光场这一问题,并且做出了大量的工作.针对上述问题,本文将小波变换与稀疏傅里叶变换相结合,利用光场在角度域的稀疏性提出一种新的光场重构方法.首先,利用小波变换多分辨率分析的特点,通过小波变换将原始图像分解为多个不同频率的子图像;然后分别对每个子图像通过傅里叶切片定理恢复其频率位置,从而可以分别得到它们的二维角度谱;最后将每个子图像的二维角度谱合并,进行小波逆变换获得整个光场.本文方法利用小波变换将原图像分解为多个不同频率的子图像分别同时处理,不仅降低了算法的复杂度,大大减少了算法的运行时间,为光场的广泛应用提供了条件,而且相比于单独运用稀疏傅里叶算法重构,本方法有效地抑制了窗口效应,使重构结果更加准确.此外,本文方法将高频信息和低频信息分开重构,可以有效地改善并网恢复中小频率丢失的问题,进一步改进重构结果.最后通过仿真验证了算法的有效性.

With the development of computer graphics and computer vision technology, light field comes into sight and is rapidly applied in various fields. However, the acquisition of the light field needs a large amount of pictures, which has the characteristics of large data and high cost. So how to use a small amount of data to obtain the light field has been paid more and more attention, and a lot of work has been done. To address the above problems, a new method of light field recon- structing is proposed, which combines with wavelet transform and sparse Fourier transform by using sparseness of light field in angle domain. First, we use multi-resolution analysis characteristic of wavelet transform, and the original image can be de- composed into four sub-frequency images through wavelet transform. Then the frequency positions of four sub-frequencies are separately recovered through the Fourier slice theorem, and their two-dimensional angle spectrum are further obtained, re- spectively. Finally, the light field is obtained by combining the two-dimensional angle spectrum of each sub-frequency image and making inverse wavelet transform. In the proposed method, the original image is decomposed into four sub-images by u- sing wavelet transform, and the sub-images are reconstructed respectively. This not only reduces the complexity of our meth- od and greatly reduces the running time of our method, which provides the basis for the wide application of the light field, but also our method effectively inhibits the window effect by comparing to only using sparse Fourier algorithm, so that the reconstruction result is more accurate. In addition, the method can effectively improve problem of small frequency leakage in off-grid recovery by separating high frequency and low frequency information, and further improves the reconstruction re- suits. In the end, the effectiveness of the algorithm is verified by simulation.