基于非线性压缩感知和自适应字典学习的相位恢复与图像重建方法研究

项目名称： 基于非线性压缩感知和自适应字典学习的相位恢复与图像重建方法研究

项目编号： No.61471313

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 无线电电子学、电信技术

项目作者： 练秋生

作者单位： 燕山大学

项目金额： 80万元

中文摘要： 相位恢复的目标是仅根据图像二维傅立叶变换或菲涅耳变换的幅值或部分幅值精确地复原丢失的相位信息，而图像先验是决定相位恢复质量的关键因素。最近发展的稀疏相位恢复和可压缩相位恢复方法利用图像空域的稀疏性或某种固定变换的稀疏性来代替传统的图像支撑先验，图像表示的稀疏程度对相位恢复和图像重建质量具有至关重要的影响。本项目以非线性压缩感知理论为基础，根据综合稀疏和解析稀疏两种模型，利用测量的高度不完备非线性幅值信息，结合字典约束条件和图像固有的非局部相似性及边缘稀疏性等多种先验信息学习能对重建图像本身进行最优表示的个性化字典，并根据这种自适应表示的稀疏性及结构稀疏性进行单像面和多像面相位恢复和图像重建。该方法有望突破现有相位恢复方法的诸多限制，在低采样率下实现高精度、抗噪性能强的相位恢复与图像重建。本项目将促进非线性压缩感知、自适应稀疏表示理论和相位恢复技术的发展，具有重要的理论意义和应用价值。

中文关键词： 压缩感知；图像重建；稀疏表示；相位恢复；字典学习

英文摘要： The accurate recovery of the loss phase information is the goal of phase retrieval only based on the full or partial magnitude of the 2D Fourier transform or Fresnel transform. However, the image priors are the key factor to guarantee the quality of phase retrieval. The sparsity of the images in spatial field or some fixed transform domain, rather than the traditional support priors on images, is exploited by the recent developmental methods of sparse phase retrieval and compressive phase retrieval. The sparse degree of the represented images has crucial effect on the phase retrieval and the quality of image reconstruction. On the base of the nonlinear compressive sensing theory, this project aims to learn adaptive dictionary via the highly incomplete nonlinear amplitude information based on synthesis sparse and analysis sparse model. Moreover, the dictionary constraint conditions and the multiple inherent priors of images including non-local similarity, edge sparsity and others are exploited to learn the adaptive dictionary which can perform optimal representation on the reconstruction image itself, further more, this project aims to propose robust single-plane and multi-plane phase retrieval and image reconstruction based on the sparsity and structural sparsity of the adaptive representation. It is expected to break through the limitations of the existing phase retrieval methods, which can obtain high accuracy, noise robust phase retrieval and image reconstruction at low sampling rate. This project will promote the development of the nonlinear compressive sensing, adaptive sparse representation theory and phase retrieval technology, which has an important theoretical significance and application value.

英文关键词： Compressed sensing;image reconstruction;Sparse representation;Phase retrieval;Dictionary learning