Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Pretoria 0028, South Africa.
Council for Scientific and Industrial Research, Pretoria 0001, South Africa.
Sensors (Basel). 2023 May 17;23(10):4843. doi: 10.3390/s23104843.
A measurement matrix is essential to compressed sensing frameworks. The measurement matrix can establish the fidelity of a compressed signal, reduce the sampling rate demand, and enhance the stability and performance of the recovery algorithm. Choosing a suitable measurement matrix for Wireless Multimedia Sensor Networks (WMSNs) is demanding because there is a sensitive weighing of energy efficiency against image quality that must be performed. Many measurement matrices have been proposed to deliver low computational complexity or high image quality, but only some have achieved both, and even fewer have been proven beyond doubt. A Deterministic Partial Canonical Identity (DPCI) matrix is proposed that has the lowest sensing complexity of the leading energy-efficient sensing matrices while offering better image quality than the Gaussian measurement matrix. The simplest sensing matrix is the basis of the proposed matrix, where random numbers were replaced with a chaotic sequence, and the random permutation was replaced with random sample positions. The novel construction significantly reduces the computational complexity as well time complexity of the sensing matrix. The DPCI has lower recovery accuracy than other deterministic measurement matrices such as the Binary Permuted Block Diagonal (BPBD) and Deterministic Binary Block Diagonal (DBBD) but offers a lower construction cost than the BPBD and lower sensing cost than the DBBD. This matrix offers the best balance between energy efficiency and image quality for energy-sensitive applications.
测量矩阵对于压缩感知框架至关重要。测量矩阵可以建立压缩信号的保真度，降低采样率需求，并增强恢复算法的稳定性和性能。为无线多媒体传感器网络（WMSN）选择合适的测量矩阵是具有挑战性的，因为必须在能量效率和图像质量之间进行敏感的权衡。已经提出了许多测量矩阵来提供低计算复杂度或高图像质量，但只有一些同时实现了这两个目标，甚至更少的已经得到了毫无疑问的证明。提出了一种确定性部分典型身份（DPCI）矩阵，它具有最低的传感复杂度，同时提供比高斯测量矩阵更好的图像质量。最简单的传感矩阵是所提出矩阵的基础，其中随机数被替换为混沌序列，并且随机置换被替换为随机采样位置。新的构造大大降低了传感矩阵的计算复杂度和时间复杂度。DPCI 的恢复精度低于其他确定性测量矩阵，如二进制置换块对角（BPBD）和确定性二进制块对角（DBBD），但与 BPBD 相比，它的构建成本更低，与 DBBD 相比，它的传感成本更低。对于节能敏感型应用，该矩阵在能量效率和图像质量之间提供了最佳的平衡。
