【摘要】：壓縮感知利用信號的稀疏性,無損地從低維測量信號中恢復高維度稀疏信號。然而,目前存在的測量矩陣中大多存在元素相關性高等問題,無法保證恢復效果的精確性,大大制約了它們的應用前景。針對此問題,通過引入切比雪夫混沌系統(tǒng),提出一種基于采樣列化的切比雪夫混沌感知測量矩陣(SC3M)。不同于經典的相對獨立取值的構造方法,SC3M矩陣通過對切比雪夫混沌序列作采樣列化及歸一化處理等操作來確保矩陣的低列相關性,以優(yōu)化重構效果;進一步,結合Johnson-Lindenstrauss引理嚴格證明了其滿足約束等距特性(restricted isometric property,RIP),給提出的測量矩陣的應用提供了扎實的理論依據。實驗仿真表明,提出的混沌測量矩陣能確保良好的信號和圖像重構精度,明顯優(yōu)于純隨機矩陣、伯努利矩陣和高斯矩陣等其他經典測量矩陣。
[Abstract]:Compression perception utilizes the sparsity of the signal to recover the high dimensional sparse signal from the low dimensional measurement signal. However, there are many problems in the measurement matrix, such as high correlation of elements, which can not guarantee the accuracy of the recovery effect, which greatly restricts their application prospects. To solve this problem, a Chebyshev chaotic sensing measurement matrix (SC3M) based on sampling listing is proposed by introducing Chebyshev chaotic system. In order to optimize the reconstruction effect, the SC3M matrix, which is different from the classical construction method of relatively independent values, can ensure the low column correlation of the matrix by sampling and normalizing the Chebyshev chaotic sequence. In combination with Johnson-Lindenstrauss Lemma, it is strictly proved that it satisfies the constraint isometric characteristic (restricted isometric propertyn RIP), which provides a solid theoretical basis for the application of the proposed measurement matrix. Experimental results show that the proposed chaotic measurement matrix can ensure good signal and image reconstruction accuracy, and is superior to other classical measurement matrices such as pure random matrix, Bernoulli matrix and Gao Si matrix.
【作者單位】： 廣州大學松田學院;廣東農工商職業(yè)技術學院;中國移動通信集團廣東有限公司;
【基金】：廣東省省級課題資助項目(GDYJSKT16-08) 廣東省高等職業(yè)教育教學改革立項課題(201401154)
【分類號】：TN911.7

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