本文選題：壓縮感知 + 稀疏表示　； 參考：《北方工業(yè)大學(xué)》2012年碩士論文

【摘要】：傳統(tǒng)的信號采樣方法遵守香農(nóng)采樣定理：信號的采樣頻率必須要至少是信號最高頻率的兩倍。近年來迅速發(fā)展的壓縮感知技術(shù)突破了該定理的限制,利用測量矩陣方法將采樣和壓縮的步驟統(tǒng)一起來,從而利用較少的采樣經(jīng)過一定的優(yōu)化算法就可以將原信號恢復(fù)。該理論建立在信號的稀疏性的基礎(chǔ)之上,且信號稀疏表示理論在近十幾年來也得到了長足的發(fā)展。由信號的傅里葉變換,離散余弦變換,小波變換等正交變換得到稀疏系數(shù),發(fā)展到在冗余字典上進(jìn)行稀疏表示,從而擴(kuò)展了正交基的概念,使得信號得到更好的自適應(yīng)性和稀疏性的表示。 該理論顛覆了以往數(shù)據(jù)獲取的思路,力求從盡量少的數(shù)據(jù)獲取盡量的信息。因此也已經(jīng)在圖像壓縮,圖像處理,信息安全,計算機(jī)視覺,模式識別,人臉識別,通信等大量的應(yīng)用科學(xué)中取得了大量的進(jìn)展,尤其在圖像去噪,人臉識別等領(lǐng)域得到了驚人的突破。本文將壓縮傳感和稀疏表示方法應(yīng)用到信號處理和圖像取證等方面,主要做了一下幾個方面的工作： 1)基于壓縮感知的秘密圖像分存。該算法將把這一解決方案應(yīng)用于秘密圖像分存中去,利用圖像稀疏度的限制和現(xiàn)有算法的局限性,將圖像分存問題轉(zhuǎn)化為壓縮信號恢復(fù)問題,該方案簡單靈活且安全高效。 2)基于稀疏表示和偏微分方程的圖像壓縮與重建研究。該算法首先提取圖像的角點(diǎn),得到圖像在空域上的稀疏表示,利用測量矩陣進(jìn)行采樣后得到壓縮數(shù)據(jù)。反過來利用重建算法可以恢復(fù)空域數(shù)據(jù),再利用偏微分?jǐn)U散方程就可以重建原始圖像。 3)基于壓縮感知的圖像脆弱水印算法。該算法的核心思想是壓縮感知中的稀疏重建的技術(shù)可以從含有噪音的信號測量中恢復(fù)信號,從而可以將圖像在DCT頻域中的稀疏信號看做噪聲,水印看做原始信號,對水印進(jìn)行測量后加到頻域中去實(shí)現(xiàn)嵌入,但是對于圖像進(jìn)行攻擊后,水印將無法正確提取出來,從而達(dá)到脆弱水印的效果。 4)基于稀疏和冗余表示的立體聲音頻去噪。該算法首先對雙通道數(shù)據(jù)進(jìn)行冗余采樣,在樣本基礎(chǔ)上訓(xùn)練得到冗余字典。利用該字典對噪音信號進(jìn)行稀疏表示,從而可以恢復(fù)出去噪信號,該算法對高斯噪音效果顯著。
[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.
【學(xué)位授予單位】：北方工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TP391.41;D918.2

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