本文選題：非局部均值 + 字典學(xué)習(xí)　； 參考：《東南大學(xué)》2016年博士論文

【摘要】：近來,隨著壓縮感知理論的出現(xiàn),基于稀疏的圖像復(fù)原與圖像重建研究取得了較大的進(jìn)展。壓縮感知理論指出,只要原始信號滿足一定的有限等距性(Restricted Isometry Property, RIP),當(dāng)所采集的信號數(shù)目低于奈奎斯特-香農(nóng)采樣定律(Nyquist-Shannon Sampling Theorem)所規(guī)定的采樣數(shù)目的情況下,仍有極高的可能性恢復(fù)出原始信號。對于稀疏信號的稀疏性的描述,最佳的選擇是l0范數(shù),但是由于其不可導(dǎo)等缺點,壓縮感知理論進(jìn)一步指出基于l1范數(shù)的約束在一定情況下可以近似取代l0范數(shù)。此外,在圖像處理問題中,基于Total Variation (TV)的約束可以看做是一種l1范數(shù)的約束。本文針對稀疏準(zhǔn)則下的約束項做了進(jìn)一步改進(jìn),研究了其在圖像復(fù)原與低劑量計算機(jī)斷層(Computed Tomography, CT)重建問題中的應(yīng)用。具體來講,本文在圖像復(fù)原方面的工作可以歸納為以下兩個方面：(1)提出了一種基于局部與非局部均值誘導(dǎo)的雙重稀疏圖像復(fù)原算法(L-NL)。該算法充分利用了TV圖像復(fù)原模型與逆濾波圖像復(fù)原模型的優(yōu)點,同時融入了非局部均值濾波算法的思想。為了使逆濾波能夠避免噪聲的影響更好地發(fā)揮其復(fù)原性能,本文將逆濾波模型改進(jìn)為無約束優(yōu)化模型,并用非局部均值濾波后的圖像替代模型中的退化圖像。為了提高非局部均值算法的速率,本文對其進(jìn)行了加速改進(jìn),提出了基于相關(guān)加速的快速非局部均值去噪算法。此時,直接使用逆濾波復(fù)原,仍不能達(dá)到理想的復(fù)原效果,因為非局部均值濾波不能完全濾除噪聲且在去噪的過程中引入了新的方法噪聲。于是,本文結(jié)合改進(jìn)的逆濾波優(yōu)化模型與TV模型提出了基于局部與非局部均值誘導(dǎo)的雙重稀疏圖像復(fù)原算法。為了評價所提算法的復(fù)原效果,本文進(jìn)行了大量的實驗,并與其它復(fù)原算法進(jìn)行了對比,根據(jù)Peak Signal to Noise Ratio (PSNR)與Structural Similarity Index Measurement (SSIM)客觀評價指標(biāo)以及視覺效果,證實了所提算法的優(yōu)越性。(2)提出了一種基于局部與字典表示誘導(dǎo)的雙重稀疏的圖像復(fù)原算法(L-DR)。該算法可以看做是對上文所提的基于局部與非局部均值誘導(dǎo)的雙重稀疏算法(L-NL)的進(jìn)一步改進(jìn)。本文首先利用正交匹配追蹤算法與K-Singular Value Decomposition (K-SVD)算法對要復(fù)原的圖像進(jìn)行訓(xùn)練獲得一自適應(yīng)字典,然后基于所學(xué)的字典對要復(fù)原的圖像進(jìn)行濾波,獲得一幅近似的只含模糊退化的圖像。最后結(jié)合逆濾波模型與經(jīng)典的基于TV的圖像復(fù)原模型,提出了基于局部與字典表示誘導(dǎo)的雙重稀疏圖像復(fù)原算法。為了驗證本算法的性能,本文進(jìn)行了大量的實驗,并與其它復(fù)原算法進(jìn)行了對比,根據(jù)P SNR與SSIM客觀度量指標(biāo)以及視覺效果,證實了所提算法的優(yōu)越性。本文在圖像重建方面的工作可以歸納為以下兩個方面：(1)提出了基于Gamma準(zhǔn)則的稀疏角CT圖像重建算法。本文首先分析了基于l0的稀疏準(zhǔn)則模型,基于l1的TV準(zhǔn)則模型以及基于l2的稀疏準(zhǔn)則模型。分析了它們之間的區(qū)別與聯(lián)系,并提出了一個更為通用的的稀疏準(zhǔn)則模型。利用所提的通用模型,結(jié)合Gamma概率分布方面的知識,提出了基于Gamma準(zhǔn)則的稀疏角度重建算法。所提Gamma準(zhǔn)則,成功彌補(bǔ)了l1準(zhǔn)則與l0準(zhǔn)則之間的空白,因此也稱為分?jǐn)?shù)階準(zhǔn)則。為了驗證所提算法有效性,本文基于仿真的Modified Shepp-Logan(MSL)體模與Non-Uniform Rational B-Splines Based Cardiac-Torso(NCAT)體模的稀疏角度投影數(shù)據(jù)以及真實臨床數(shù)據(jù)進(jìn)行了稀疏角度的重建實驗。實驗結(jié)果與基于l2準(zhǔn)則與基于l1準(zhǔn)則方法重建結(jié)果進(jìn)行了對比,依據(jù)PSNR的客觀衡量標(biāo)準(zhǔn)以及視覺效果,證實了所提算法的優(yōu)勢。(2)提出了基于自適應(yīng)Gamma準(zhǔn)則的低劑量CT重建算法�；趯Φ碗娏�(低電壓)情況下投影數(shù)據(jù)中噪聲的分析,以及前文所提出的Gamma準(zhǔn)則,本文提出了基于Gamma準(zhǔn)則的加權(quán)最小方模型。本文首先對Gamma準(zhǔn)則模型中的兩個參數(shù)進(jìn)行了分析,發(fā)現(xiàn)其中的形狀參數(shù)與尺度參數(shù)在Gamma準(zhǔn)則函數(shù)逼近l0函數(shù)的過程中發(fā)揮了相反的作用�；诖�,本文采用固定變量法的設(shè)置策略。然后,依據(jù)兩個參數(shù)的比值與Gamma函數(shù)逼近l0函數(shù)之間的關(guān)系對參數(shù)進(jìn)行自適應(yīng)設(shè)定。為了驗證所提算法的性能,本文基于MSL與NACT體模進(jìn)行了低劑量仿真投影數(shù)據(jù)的重建實驗以及基于Catphan600物理體模的低劑量投影數(shù)據(jù)重建實驗,并與其它重建算法進(jìn)行了對比,根據(jù)PSNR,SNR與SSIM客觀度量指標(biāo)以及視覺效果,證實了所提算法較其它算法在偽影抑制以及噪聲消除方面具有明顯優(yōu)越。
[Abstract]:Recently, with the emergence of compressed sensing theory, the research on sparse image restoration and image reconstruction has made great progress. The theory of compressed sensing indicates that as long as the original signal satisfies certain Restricted Isometry Property (RIP), the number of signals collected is lower than the Nyquist Shannon sampling law (Nyquist-Sha In the case of the number of samples given by nnon Sampling Theorem, there is still a high possibility to restore the original signal. The best choice for the sparsity of the sparse signal is the l0 norm, but because of its shortcomings, the compression perception theory further points out that the constraints based on the L1 norm can be approximated to the L in a certain case. 0 norm. In addition, in the problem of image processing, the constraints based on Total Variation (TV) can be considered as a constraint of L1 norm. This paper further improves the constraints under sparse criterion, and studies its application in image restoration and low dose computer tomography (Computed Tomography, CT) reconstruction. The image restoration work can be summed up in the following two aspects: (1) a double sparse image restoration algorithm based on local and non local mean induction (L-NL) is proposed. The algorithm makes full use of the advantages of the TV image restoration model and the inverse filtering image restoration model, and combines the idea of the non local mean filtering algorithm. In this paper, inverse filtering can avoid the influence of noise to better play its recovery performance. In this paper, the inverse filter model is improved to unconstrained optimization model, and the image of non local mean filter is used to replace the degraded image in the model. In order to improve the rate of non local mean algorithm, this paper improves it and proposes the correlation addition. The fast fast non local mean denoising algorithm. In this case, the inverse filtering can not achieve the ideal recovery effect, because the non local mean filter can not completely filter the noise and introduce the new method noise in the process of denoising. Therefore, this paper proposes a local and TV model based on the improved inverse filter optimization model and the model. In order to evaluate the restoration effect of the proposed algorithm, a lot of experiments are carried out and compared with other restoration algorithms. According to the objective evaluation index and visual effect of Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measurement (SSIM), it is proved that The superiority of the proposed algorithm. (2) a double sparse image restoration algorithm based on local and dictionary representation (L-DR) is proposed. This algorithm can be regarded as a further modification of the dual sparse algorithm (L-NL) based on the local and non local mean induction proposed in the previous article. The AR Value Decomposition (K-SVD) algorithm trains the reconstructed image to get a self-adaptive dictionary, then filters the reconstructed image based on the dictionary, and obtains an approximate image containing only fuzzy degradation. Finally, it combines the inverse filter model and the classic image restoration model based on TV, and proposes a local and local based on the image restoration model. In order to verify the performance of the dual sparse image restoration, a dictionary is used to verify the performance of this algorithm. A lot of experiments are carried out in this paper, and compared with other restoration algorithms. The superiority of the proposed algorithm is confirmed according to the objective metrics and visual effects of P SNR and SSIM. The next two aspects are: (1) a sparse angle CT image reconstruction algorithm based on Gamma criterion is proposed. In this paper, the sparse criterion model based on l0, the TV criterion model based on L1 and the L2 based sparse criterion model are analyzed. The difference and connection between them are analyzed, and a more general sparse criterion model is proposed. The general model, combined with the knowledge of Gamma probability distribution, proposes a sparse angle reconstruction algorithm based on Gamma criterion. The proposed Gamma criterion has successfully made up the gap between the L1 criterion and the l0 criterion, so it is also called fractional order criterion. In order to verify the effectiveness of the proposed algorithm, this paper is based on the simulated Modified Shepp-Logan (MSL) body model and No. The sparse angle projection data of the n-Uniform Rational B-Splines Based Cardiac-Torso (NCAT) body model and the real clinical data are reconstructed with sparse angle. The experimental results are compared with the reconstruction results based on the L2 criterion and the L1 criterion method. The proposed algorithm is based on the objective criterion of PSNR and the visual effect. (2) (2) a low dose CT reconstruction algorithm based on adaptive Gamma criterion is proposed. Based on the analysis of the noise in the projection data under low current (low voltage), and the Gamma criterion proposed in the previous article, a weighted least square model based on the Gamma criterion is proposed. First, the paper divides the two parameters in the Gamma criterion model. It is found that the shape parameter and the scale parameter play the opposite role in the process of the Gamma criterion function approximation to the l0 function. Based on this, this paper adopts the setting strategy of the fixed variable method. Then, according to the relation between the ratio of the two parameters and the approximation of the l0 function by the Gamma function, the parameters are adaptively set. The performance of the method is based on the reconstruction experiments of low dose simulation projection data of MSL and NACT body mode, and the experiment of low dose projection data reconstruction based on the physical model of Catphan600, and compared with other reconstruction algorithms. According to the objective metrics of PSNR, SNR and SSIM and visual effect, it is proved that the proposed algorithm is compared with other algorithms. It has obvious superiority in artifact suppression and noise elimination.

【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TP391.41

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