压缩感知技术及其在数字图像取证中的应用研究

发布时间：2018-05-04 04:10

本文选题：压缩感知 + 稀疏表示　；参考：《北方工业大学》2012年硕士论文

【摘要】：传统的信号采样方法遵守香农采样定理：信号的采样频率必须要至少是信号最高频率的两倍。近年来迅速发展的压缩感知技术突破了该定理的限制,利用测量矩阵方法将采样和压缩的步骤统一起来,从而利用较少的采样经过一定的优化算法就可以将原信号恢复。该理论建立在信号的稀疏性的基础之上,且信号稀疏表示理论在近十几年来也得到了长足的发展。由信号的傅里叶变换,离散余弦变换,小波变换等正交变换得到稀疏系数,发展到在冗余字典上进行稀疏表示,从而扩展了正交基的概念,使得信号得到更好的自适应性和稀疏性的表示。该理论颠覆了以往数据获取的思路,力求从尽量少的数据获取尽量的信息。因此也已经在图像压缩,图像处理,信息安全,计算机视觉,模式识别,人脸识别,通信等大量的应用科学中取得了大量的进展,尤其在图像去噪,人脸识别等领域得到了惊人的突破。本文将压缩传感和稀疏表示方法应用到信号处理和图像取证等方面,主要做了一下几个方面的工作： 1)基于压缩感知的秘密图像分存。该算法将把这一解决方案应用于秘密图像分存中去,利用图像稀疏度的限制和现有算法的局限性,将图像分存问题转化为压缩信号恢复问题,该方案简单灵活且安全高效。 2)基于稀疏表示和偏微分方程的图像压缩与重建研究。该算法首先提取图像的角点,得到图像在空域上的稀疏表示,利用测量矩阵进行采样后得到压缩数据。反过来利用重建算法可以恢复空域数据,再利用偏微分扩散方程就可以重建原始图像。 3)基于压缩感知的图像脆弱水印算法。该算法的核心思想是压缩感知中的稀疏重建的技术可以从含有噪音的信号测量中恢复信号,从而可以将图像在DCT频域中的稀疏信号看做噪声,水印看做原始信号,对水印进行测量后加到频域中去实现嵌入,但是对于图像进行攻击后,水印将无法正确提取出来,从而达到脆弱水印的效果。 4)基于稀疏和冗余表示的立体声音频去噪。该算法首先对双通道数据进行冗余采样,在样本基础上训练得到冗余字典。利用该字典对噪音信号进行稀疏表示,从而可以恢复出去噪信号,该算法对高斯噪音效果显著。
[Abstract]:The traditional signal sampling method obeys Shannon's sampling theorem: the sampling frequency of the signal must be at least twice the maximum frequency of the signal. In recent years, the rapid development of compression sensing technology has broken through the limitation of the theorem, using the method of measurement matrix to unify the steps of sampling and compression, so that the original signal can be recovered by using a certain optimization algorithm with less sampling. The theory is based on the sparsity of signals, and the theory of sparse representation of signals has been greatly developed in recent ten years. The sparse coefficients are obtained from orthogonal transforms such as Fourier transform, discrete cosine transform and wavelet transform of signals, which are developed to sparse representation in redundant dictionaries, thus extending the concept of orthogonal basis. It makes the signal more adaptive and sparse. This theory overturns the idea of data acquisition and tries to obtain as much information as possible from as few data as possible. Therefore, a great deal of progress has been made in the fields of image compression, image processing, information security, computer vision, pattern recognition, face recognition, communication and so on, especially in image denoising. Face recognition and other fields have made an amazing breakthrough. In this paper, compression sensing and sparse representation are applied to signal processing and image forensics. 1) secret image sharing based on compressed perception. The algorithm will apply this solution to secret image sharing. By taking advantage of the limitation of image sparsity and the limitation of existing algorithms, the problem of image sharing is transformed into a problem of compressed signal recovery. The scheme is simple, flexible and safe and efficient. 2) Image compression and reconstruction based on sparse representation and partial differential equations. The algorithm firstly extracts the corner of the image and gets the sparse representation of the image in the spatial domain. The compressed data is obtained by sampling the image using the measurement matrix. In turn, the reconstruction algorithm can be used to recover the spatial data, and then the partial differential diffusion equation can be used to reconstruct the original image. 3) Image fragile watermarking algorithm based on compression perception. The core idea of the algorithm is that the sparse reconstruction technique in compression perception can recover the signal from the noisy signal measurement, so that the sparse signal of the image in the DCT frequency domain can be regarded as noise, and the watermark as the original signal. The watermark is measured and embedded in the frequency domain. However, after attacking the image, the watermark will not be extracted correctly, so that the fragile watermark can be achieved. 4) Stereo audio denoising based on sparse and redundant representation. In this algorithm, the dual channel data is sampled and the redundant dictionary is trained on the basis of the sample. The dictionary is used to represent the noise signal sparsely, so the noise signal can be recovered, and the algorithm has remarkable effect on Gao Si noise.
【学位授予单位】：北方工业大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TP391.41;D918.2

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