Multimedia Digital Signal Processing of Infrared Chemical Remote Sensing Based on Piecewise Linear Discriminant Algorithm
Multimedia Digital Signal Processing of Infrared Chemical Remote Sensing Based on Piecewise...
Gong, Meitao
2021-09-20 00:00:00
Hindawi Advances in Multimedia Volume 2021, Article ID 6337431, 6 pages https://doi.org/10.1155/2021/6337431 Research Article Multimedia Digital Signal Processing of Infrared Chemical Remote Sensing Based on Piecewise Linear Discriminant Algorithm Meitao Gong Jining Normal University, Inner Mongolia, Jining, Key Laboratory of High Speed Signal Processing and Internet of !ings Technology and Application in Jining Normal University, China Correspondence should be addressed to Meitao Gong; jnsygmt@mail.poe.edu.pl Received 8 July 2021; Accepted 20 August 2021; Published 20 September 2021 Academic Editor: Zhendong Mu Copyright © 2021 Meitao Gong. &is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. According to the basic principle of piecewise linear classifier and its application in the field of infrared chemical remote sensing monitoring, the characteristics of unilateral piecewise linear classifier applied to the infrared spectrum identification of chemical agents are studied. With the characteristic of separate transmission, the characteristic recovery with the total observed deviation is used for the model. &e relaxation factors are used to replace the constrained conditions that cannot be optimized into constrained separate line segment calculation conditions. Experiments show that the result of signal recovery is better than traditional Wiener filtering and Richardson–Lucy methods. proposed based on the boundary variation model, and at the 1. Introduction same time, this model is equivalently segmented for cal- Sensors mainly show signals that are fused together with culation and judgment, and the original signal is appro- different factors (noise and ineffective signals), and the priately restored [6]. transmission path is more complicated. Even if a sensor with a higher function is used, the signal results that can be 2. Piecewise Linear Discriminant Algorithm obtained are not ideal. So, it is not easy to obtain the initial signal of a physical characteristic. But deconvolution is a way A multimedia digital signal processing method for infrared to feed back the original signal based on the fused signal. chemical remote sensing is put forward based on piecewise &is method is widely used in different fields such as linear discriminant algorithm. &e principle is shown in communication, radar, voice, and medicine [1–4]. Figure 1, which is divided into two steps: At present, the more advanced technology is the vari- Step 1: the received signal sequence is segmented by ation recovery method of Chan et al. &e partial differential length N, and the energy of each segmented signal gradient projection method is used to carry out the La- N 2 sequence y � |x + i| , N � N N , is calcu- grangian multiplier items to minimize the difference in the j i�1 jN 1 2 lated, which will then be used to obtain the likelihood calculation. &e advantages are fast convergence, stability, ratio of the sequential test. etc., especially suitable for signals with steep edges. For the regular dynamic adaptive calculation method, the calcula- Step 2: calculate the test statistic Λ � λ , y K j j j�1 tion of difference value is also carried out. We published a 1≤ K ≤ N , and compare it with the thresholds A and B variation model of deformation and constraint [5]. Under and make a judgment. If B<Λ < A is always true and this premise, in this article, the restoration of infrared the decision cannot be made, to ensure that the test chemical remote sensing multimedia digital signals is results are obtained within the limited sampling signal 2 Advances in Multimedia Receive signal Segmented energy Probability ratio Sample processing calculation Judgment threshold Test statistics Comparative judgment determination accumulation Result output Figure 1: Block diagram of piecewise linear discriminant algorithm processing. points, piecewise linear discriminant algorithm is used Among them, Normal(μ, σ ) indicates that it obeys the to compare the statistics with the truncation threshold normal distribution, and then the likelihood ratio expression C and make a judgment, namely: can be obtained: ����� � N y − N σ 2 f y |H 1 N j 1 ≥ C, H , w i i 1 ⎝ ⎠ 1 ⎛ ⎞ λ � ln � ln + Λ � λ (1) N j 1 + ρ N + ρ 2 fy |H 2N σ j 0 1 w < C, H . j�1 0 y − N + ρ/2 σ + P j 1 w − . 2.1. Likelihood Ratio Calculation. According to the central 2 N + ρ σ + P limit theorem, when the segment length N1 is large enough, 1 w the segment energy of the received signal y approaches the (3) normal distribution process (note: “sufficiently large” usu- ally means that N1 must be greater than 0, and the larger N1 &en, the test statistics can be obtained: is, the closer y is to the normal distribution process), namely: 2 4 H : y ∼ NormalN σ , N σ , 0 j 1 1 w w ρ 2 2 2 H : y ∼ NormalN + σ + P, N + ρ σ + P . 1 j 1 1 w w (2) ����� � 2 2 2 2 K K y − N σ y − N + ρ/2 σ + P 1 N j 1 w j 1 w 1 ⎢ ⎥ ⎡ ⎢ ⎤ ⎥ ⎛ ⎝ ⎞ ⎠ ⎢ ⎥ ⎢ ⎥ Λ � ⎣ ⎦ λ � K ln + − . (4) 4 2 1 + ρ N + ρ 2N σ j�1 1 j�1 1 2 N + ρ σ + P 1 w ⎧ ⎪ Eλ |H ≈ −0.5N ρ − ρ, j 0 1 &e obtained Λ is compared with the thresholds A, B, (5) and C, and a judgment is made; then, the test result can be Eλ |H ≈ 0.5N ρ + 0.5ρ. j 1 1 obtained. According to the central limit theorem, the seg- mented energy is approximated in the normal distribution By substituting formula (5) into formula (6), the average process. A very wide probability density distribution capacity samples under the dual hypothesis test conditions function is used for the normal distribution, which not only can be obtained as follows: greatly reduces the computational complexity of the pro- posed algorithm but also is useful for deriving and analyzing αA + (1 − α)B ⎧ ⎪ ⎪ ASN � N E N |H � − , H 1 2 0 0 2 the next spectral perception performance [7]. ⎪ 0.5ρ + ρ/N ⎪ 1 (6) (1 − β)A + βB 2.2. Analysis of Average Sample Size. We derive and analyze ⎪ ASN � N E N |H � . ⎩ H 1 2 1 1 2 the average sample size of the proposed algorithm in a 0.5ρ + 0.5ρ/N complex electromagnetic environment. In this paper, the According to the above analysis, the average capacity average sample size of the proposed algorithm in complex sample ASN, segment length N1, and received signal-to- electromagnetic environment is deduced and analyze (ρ≪ 1) noise ratio of the presented successive inspection algo- and the likelihood ratio of N > 10 is used to calculate the rithm are obtained (ρ). &erefore, in order to obtain the mathematical expectation: Advances in Multimedia 3 best detection performance, the functional relationship of the algorithm is discussed in a complex environment, and the detection performance of the proposed algorithm is deduced [8]. Inference 1. In a complex electromagnetic environment (ρ≪ 1), in the following cognitive wireless network, the average capacity sample ASN of the piecewise linear de- termination algorithm based on piecewise energy processing depends on the false alarm probability α and probability of 1 missed detection of the system implemented as needed. In addition, the received signal-to-noise ratio is shown in proportion to the segment length Ni. Ρ is inversely -6 -4 -2 02 4 6 proportional. Figure 2: Schematic diagram of the probability density distribution &erefore, in order to reduce the average sample size of function of the test statistic. the proposed algorithm, the segment length N1 must be selected as small as possible, but N1 needs to meet the central limit theorem condition. 2 2 0.25 − ρN + ρ N + N 1 1 C � −0.25N ρ + (AB + B) . N N ρ + 1.5ρ 2.3. Discussion on the Best Truncation !reshold. In the 2 1 successive inspection algorithm, the inequality B<Λ < A (9) related to the inspection statistics is always established within a certain inspection time, and there is possibility for &erefore, the sequential inspection algorithm based on no judgment. In order to obtain the inspection result within the proposed infrared chemical remote sensing multimedia the limited inspection time, finally the inspection statistics digital signal processing is executed by performing the are compared with the reduced threshold C to obtain the segmented energy summation processing on the received final judgment result. &e threshold C is analyzed for dis- signal. Sequentially check that the measured likelihood ratio cussion [9]. follows the normal distribution process, which greatly According to the probability density function of the test simplifies the subsequent calculation and theoretical deri- statistics shown in Figure 2, the following inequalities de- vation process. In addition, by introducing the restriction of scribing the false alarm probability and the probability of reduction, it is possible to ensure that the best inspection missed detection of the piecewise linear discriminant al- results can be obtained within a limited inspection time gorithm are true: [10–12]. exp B − 1 ⎧ ⎪ ⎪ α