本文選題：壓縮感知　切入點：重構算法　出處：《南京郵電大學》2017年碩士論文　論文類型：學位論文

【摘要】：壓縮感知(CS)主要包括稀疏、觀測和重構三個步驟,其中,重構算法的設計影響著信號重構的效果,基于l_0范數的貪婪算法是一類重要的重構算法。為了進一步提高重構的速度和精確度,本文結合梯度優(yōu)化的理論和方法對CS重構算法進行研究,具體的工作內容如下:1.提出了基于PRP共軛梯度的SL_0算法。用雙曲正切函數族近似逼近l_0范數,將最小化l_0范數問題轉化為凸優(yōu)化問題,通過PRP共軛梯度法對函數的極值進行求解。仿真結果表明,該算法的均方誤差比其他基于l_0范數的重構算法更小,重構性能更好。2.提出了基于L-BFGS擬牛頓法的梯度追蹤算法。將最優(yōu)化方法中的L-BFGS擬牛頓法與梯度追蹤算法相結合,通過L-BFGS擬牛頓法對梯度追蹤法中的更新方向進行求解,形成基于L-BFGS擬牛頓法的梯度追蹤算法(L-BFGS Method based Gradient Pursuit,LMGP)。仿真結果表明,該算法的重構時間相較于其他貪婪算法更少,重構效果更好。3.提出了基于PRP共軛梯度改進字典學習的LMGP算法。在稀疏階段用基于PRP共軛梯度的SL0算法對稀疏系數矩陣進行計算,將原始信號進行稀疏表示,形成新的基于PRP共軛梯度法的字典學習方法。接著,用基于L-BFGS擬牛頓法的梯度追蹤算法對視頻幀進行重構。仿真結果表明,該算法在峰值信噪比方面優(yōu)于其他算法,算法的性能更佳。
[Abstract]:Compression sensing (CSS) consists of three steps: sparse, observation and reconstruction, in which the design of reconstruction algorithm affects the effect of signal reconstruction. The greedy algorithm based on L _ 0 norm is an important class of reconstruction algorithms. In order to improve the speed and accuracy of reconstruction, this paper combines the theory and method of gradient optimization to study the CS reconstruction algorithm. The main work is as follows: 1. The SL_0 algorithm based on PRP conjugate gradient is proposed. By using hyperbolic tangent function family to approximate L _ 0 norm, the minimization of l _ 0 norm problem is transformed into a convex optimization problem. The PRP conjugate gradient method is used to solve the extremum of the function. The simulation results show that the mean square error of the algorithm is smaller than that of other reconstruction algorithms based on L _ 0 norm. 2. A gradient tracking algorithm based on L-BFGS quasi-Newton method is proposed. The L-BFGS quasi-Newton method is combined with the gradient tracking algorithm, and the updating direction of the gradient tracking method is solved by L-BFGS quasi-Newton method. A gradient tracking algorithm based on L-BFGS quasi Newton method is formed. The simulation results show that the reconstruction time of the algorithm is less than that of other greedy algorithms. 3. A LMGP algorithm based on PRP conjugate gradient is proposed to improve dictionary learning. In the sparse stage, the sparse coefficient matrix is calculated by SL0 algorithm based on PRP conjugate gradient, and the original signal is represented sparsely. A new dictionary learning method based on PRP conjugate gradient method is proposed. Secondly, the gradient tracking algorithm based on L-BFGS quasi-Newton method is used to reconstruct the video frame. The simulation results show that the proposed algorithm is superior to other algorithms in the aspect of peak signal-to-noise ratio (PSNR). The performance of the algorithm is better.
【學位授予單位】：南京郵電大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN911.7

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