【摘要】：在信息技術(shù)高速發(fā)展的今天,圖像作為最直觀的信息載體之一,已成為數(shù)據(jù)傳輸?shù)闹髁餍问�。隨著人們對(duì)圖像質(zhì)量的要求不斷提高,對(duì)數(shù)據(jù)的需求量越來(lái)越大,傳統(tǒng)圖像壓縮與傳輸技術(shù)已難以滿足日益增長(zhǎng)的數(shù)據(jù)帶寬需求。壓縮感知(Compressed Sensing,CS)理論應(yīng)運(yùn)而生。該理論突破傳統(tǒng)信號(hào)算法中采樣速率需遵循奈奎斯特采樣定理(Nyquist Sampling Theorem)的約束,根據(jù)信號(hào)的稀疏性或可壓縮性,對(duì)信號(hào)進(jìn)行低速壓縮采樣,采樣頻率遠(yuǎn)低于奈奎斯特采樣定律,并運(yùn)用重構(gòu)算法準(zhǔn)確(針對(duì)稀疏信號(hào))或近似(針對(duì)可壓縮信號(hào))準(zhǔn)確地重構(gòu)出原始信號(hào)。基于壓縮感知理論的圖像壓縮與重構(gòu)算法能夠有效地節(jié)省編碼端采樣和壓縮的資源成本,從而在數(shù)據(jù)量大且冗余度高的圖像信號(hào)壓縮與傳輸領(lǐng)域有著廣闊的應(yīng)用前景,成為該領(lǐng)域?qū)W者的研究熱點(diǎn)。圖像信號(hào)所具備的變換域稀疏性(sparsity)或可壓縮性(compressibility)為壓縮感知理論的應(yīng)用提供了前提保證。傳統(tǒng)CS圖像重構(gòu)算法僅考慮了圖像信號(hào)在小波域等變換域上的稀疏特性或可壓縮特性,但并未充分考慮對(duì)其統(tǒng)計(jì)特性和結(jié)構(gòu)特性的充分利用。圖像的小波稀疏表示形式除稀疏性外,還具有較強(qiáng)的類(lèi)聚性(cluster),這表現(xiàn)在圖像信號(hào)經(jīng)小波變換后,稀疏表示系數(shù)層間呈現(xiàn)的樹(shù)狀結(jié)構(gòu)關(guān)系及層內(nèi)表現(xiàn)出的統(tǒng)計(jì)相依分布。本文針對(duì)圖像小波稀疏表示系數(shù)的特性,從統(tǒng)計(jì)先驗(yàn)角度和結(jié)構(gòu)先驗(yàn)角度分別對(duì)圖像進(jìn)行模型分析及研究,并將結(jié)構(gòu)先驗(yàn)?zāi)Ｐ团c統(tǒng)計(jì)先驗(yàn)?zāi)Ｐ头謩e融入經(jīng)典重構(gòu)算法中,取得了較好的重構(gòu)效果。為進(jìn)一步提高圖像壓縮感知重構(gòu)算法的重構(gòu)質(zhì)量與效率,本文創(chuàng)新性地提出統(tǒng)計(jì)與結(jié)構(gòu)先驗(yàn)聯(lián)合利用的CS圖像重構(gòu)算法,對(duì)圖像信號(hào)的稀疏表示形式進(jìn)行層內(nèi)層間建模,利用多重先驗(yàn)信息對(duì)經(jīng)典重構(gòu)算法進(jìn)行優(yōu)化:針對(duì)圖像小波表示系數(shù)的層內(nèi)層間關(guān)系,利用高斯尺度混合模型對(duì)系數(shù)局部建模,并利用系數(shù)層間樹(shù)結(jié)構(gòu)模型對(duì)其進(jìn)行結(jié)構(gòu)約束,應(yīng)用迭代閾值算法求解稀疏表示系數(shù)估計(jì)值,最終利用少量采樣值實(shí)現(xiàn)高質(zhì)高效的圖像重構(gòu)。本文對(duì)所提算法以及經(jīng)典CS圖像重構(gòu)算法進(jìn)行仿真比較,測(cè)試結(jié)果表明,聯(lián)合利用統(tǒng)計(jì)與結(jié)構(gòu)先驗(yàn)的CS圖像重構(gòu)算法在圖像的重構(gòu)性能上有明顯優(yōu)化。對(duì)于重構(gòu)精度,峰值信噪比較單一模型下的重構(gòu)算法最高提升4dB左右,重構(gòu)速度也有較大提升,是集高效性與實(shí)用性為一體的CS圖像重構(gòu)算法。
[Abstract]:With the rapid development of information technology, image, as one of the most intuitive information carriers, has become the mainstream form of data transmission. With the increasing demand for image quality and the increasing demand for data, the traditional image compression and transmission technology is difficult to meet the increasing demand of data bandwidth. The theory of compressed perception (Compressed Sensing,CS) came into being. This theory breaks through the constraint of Nyquist sampling theorem (Nyquist Sampling Theorem) in the traditional signal algorithm. According to the sparsity or compressibility of the signal, the signal is compressed at low speed and the sampling frequency is much lower than that of Nyquist sampling law. The original signal is reconstructed accurately by using reconstruction algorithm (for sparse signal) or approximate (for compressible signal). The algorithm of image compression and reconstruction based on the theory of compression perception can save the cost of sampling and compression in the coding end effectively, so it has a broad application prospect in the field of image signal compression and transmission, which has a large amount of data and high redundancy. It has become the research hotspot of scholars in this field. The transform domain sparse (sparsity) or compressible (compressibility) of image signal provides a prerequisite for the application of compression sensing theory. The traditional CS image reconstruction algorithm only considers the sparse or compressible characteristics of the image signal in the domain of wavelet transform, but does not fully consider the full use of its statistical and structural characteristics. In addition to sparsity, the wavelet sparse representation of images also has a strong clustering (cluster),. After wavelet transform, the sparse representation shows the tree structure relationship among the coefficient layers and the statistical dependence distribution in the layers. In this paper, according to the characteristics of sparse representation coefficients of image wavelet, the image model is analyzed and studied from the perspective of statistical priori and structural priori, and the structural priori model and statistical priori model are incorporated into the classical reconstruction algorithm, respectively. Good reconstruction effect has been achieved. In order to improve the reconstruction quality and efficiency of the image compression perceptual reconstruction algorithm, a novel CS image reconstruction algorithm based on statistical and structural priori is proposed in this paper, in which the sparse representation of image signals is modeled between layers. The classical reconstruction algorithm is optimized by using multiple prior information. According to the interlayer relationship of image wavelet representation coefficient, Gao Si scale mixed model is used to model the coefficient locally, and the coefficient interlayer tree structure model is used to constrain the coefficient. An iterative threshold algorithm is used to solve the estimation of sparse representation coefficients, and a small number of sampling values are used to achieve high quality and efficient image reconstruction. In this paper, the proposed algorithm and the classical CS image reconstruction algorithm are simulated and compared. The test results show that the combined use of statistical and structural priori CS image reconstruction algorithm has obvious optimization in image reconstruction performance. For the reconstruction accuracy, the peak signal-to-noise ratio (PSNR) algorithm can improve the 4dB and the reconstruction speed greatly. It is a CS image reconstruction algorithm with high efficiency and practicability.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：TP391.41

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本文編號(hào)：2207120