Abstract
A measurement matrix and sensing dictionary are the basic tools for signal compression sampling and reconstruction, respectively, which are important aspects in the field of compression sensing. Previous studies which have divided the measurement matrix and sensing dictionary into two separate processes did not make full use of their inherent intercorrelations. In case of which could be fully utilized, the mutual coherence of the atoms of measurement matrix and sensing dictionary can be further reduced under the premise of ensuring that the original signal information is stored, which could improve the accuracy of signal recovery. The present study attempted to reduce the mutual coherence between the sensing dictionary and measurement matrix by proposing the t-average mutual coherence coefficient as an evaluation index for the sensing dictionary. A mathematical model for co-constructing a measurement matrix and sensing dictionary is firstly proposed. Then, the measurement matrix and sensing dictionary cooperative construction(MSCA)algorithm is proposed to solve the model at a faster rate. The simulated results for sparse signal and binary image show that the proposed algorithm has faster computing speed and higher solution precision than the state-of-the-art construction algorithms.
Highlights
IntroductionAutomatic dependent surveillance and broadcast (ADS-B) (automatic dependent surveillance and broadcast) is an important technology for monitoring aircraft operations
Automatic dependent surveillance and broadcast (ADS-B) is an important technology for monitoring aircraft operations
This study proposes a measurement matrix and sensing dictionary cooperative construction algorithm (MSCA) to improve the accuracy of the original sparse signal by utilizing a sensing dictionary
Summary
ADS-B (automatic dependent surveillance and broadcast) is an important technology for monitoring aircraft operations. By constructing a sensing dictionary that has the same dimensions and a low mutual coherence with the measurement matrix, the sensing dictionary included in the reconstruction algorithm can achieve a better sparse approximation to the original signal. It improves the accuracy of signal recovery. The basic idea is to first set up the inner product between φi and εi equal 1, according to Eq (3), and calculate G' = ∑TΦ and tighten the non-diagonal elements so that they gradually approach 0 using a greedy algorithm until μt(∑, Φ) satisfies threshold t After these steps are finished, a pair of Φ and ∑ can be constructed. The optimization routine can be described as follows: 1) Define the cost function as C 1⁄4 kΦT Φ−Hk2F ; 2) Calculate the gradient of the cost function:
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