1. Introduction

Figure 1. A) RDA with squint angle = 0 B) RDA with accurate SRC. C) RDA with approximate SRC.

Figure 1. A) RDA with squint angle = 0 B) RDA with accurate SRC. C) RDA with approximate SRC.

2. Methodology

• Range compression: In this step, the transferring of the received signal to the frequency domain of the panel and accompanied by the reference signal. The two signals are sent after multiplying them, and then we return the signal to the time domain.

  $$s_0(f_{\tau },\eta )=A_0{\omega }_r\left({\displaystyle \frac{f_{\tau }}{K_r}}\right){\omega }_a(\eta -{\eta }_0)\mathrm{e}\mathrm{x}\mathrm{p}(-j4\pi f_0{\displaystyle \frac{{f_{\tau }}^2}{K_r}})\mathrm{e}\mathrm{x}\mathrm{p}(-j4\pi (f_0+f_{\tau }){\displaystyle \frac{R(\eta )}{c}}$$

  (2)

  $$H_r\left(f\right)=rect({\displaystyle \frac{f}{KT}})\mathrm{e}\mathrm{x}\mathrm{p}(j\pi {\displaystyle \frac{f^2}{K^2}})$$

  (3)

2.

Fourier transform stage: In this step, the Fourier transform of the signal is performed.

$$s_1(\tau ,f_{\eta })=A_1{p}_r\left(\tau -{\displaystyle \frac{2∆R\left(f_{\eta }\right)}{C}}\right){\omega }_a({\displaystyle \frac{f_{\eta }}{K_a}})\mathrm{e}\mathrm{x}\mathrm{p}(-j4\pi f_0{\displaystyle \frac{R_0}{C}})\mathrm{e}\mathrm{x}\mathrm{p}(j\pi \left({\displaystyle \frac{{f_{\eta }}^2}{K_a}}\right)\exp \left(-j2\pi f_{\eta }{\eta }_0\right)$$

(5)

3.

CORRECTING THE PLATE MIGRATION: as the target is a point in the coordinates ($R_0,{\eta }_0$), so after compressing the plate the signal must be compressed at point ${\displaystyle \frac{2R_0}{C}}$ but as is clear. In addition, another delay duration was obtained whose cause varies with the:

$${s_1(\tau ,f_{\eta })=A}_1{p}_r\left(\tau -{\displaystyle \frac{2∆R\left(f_{\eta }\right)}{C}}\right){\omega }_a({\displaystyle \frac{f_{\eta }}{K_a}})\mathrm{e}\mathrm{x}\mathrm{p}(-j4\pi f_0{\displaystyle \frac{R_0}{C}})\mathrm{e}\mathrm{x}\mathrm{p}(j\pi \left({\displaystyle \frac{{f_{\eta }}^2}{K_a}}\right)\exp \left(-j2\pi f_{\eta }{\eta }_0\right)$$

(6)

4.

COMPRESSION STAGE: Lateral pressure after adjusting the RCM can be done in the same way as the pressure in the direction the plate is completed, and repeat the same for the side direction, so we have:

$$s_3(\tau .f_{\eta })=A_1{p}_r\left(\tau -{\displaystyle \frac{2∆R\left(f_{\eta }\right)}{C}}\right){\omega }_a({\displaystyle \frac{f_{\eta }}{K_a}})\mathrm{e}\mathrm{x}\mathrm{p}(-j4\pi f_0{\displaystyle \frac{R_0}{C}})\exp \left(-j2\pi f_{\eta }{\eta }_0\right)$$

(7)

5.

INVERSE FAST FOURIER TRANSFORM (IFFT): the aspect of the above relationship, it is enough to take the form of the Fourier transform to obtain the final expression. We assume that the envelope of the signal in the side direction instead of the (5) relationship is rectangular as follows:

$${\omega }_a\left(\eta \right)=rect({\displaystyle \frac{\eta }{T_a}})$$

(8)

3. Proposed Algorithm

Spectroscopic Separation

Raw pixels mean pixels made up of only one material. However, the mixed pixels as shown in the figure contain more than one single material.

Figure 2. Pure Pixel and Mixed Pixel.

Figure 2. Pure Pixel and Mixed Pixel.

Spectral algorithms transform mixed pixel cells into end members and relative frequency. The end-members are actually spectral signatures present in the present and the relative frequency is the ratio of the end-members in each pixel cell. The relative frequency must be positive for each end member.

There are different assumptions about the type of mixture of electromagnetic spectra. Based on these assumptions, different mixture models have been presented that fall into two main categories, linear and nonlinear.

4. Look at Previous Methods

4.5. Spatial Energy Algorithm

This spatial energy approach is proposed to extract the spatial spectral endmember of hyperspectral images.

SENMAV (Spatial ENergy prior constrained MAximum simplex Volume) examines spatial information from the perspective of the spatial energy of a former Markov Random Field (MRF), which is used as a regularization expression for the traditional maximum-volume single model to constrain the selection of endmembers in both spatial and spectral domains. New light on endmember extraction on a spectral-spatial basis because SENMAV parallelizes the accuracy of end-member extraction and the spatial feature requirements of the end-members are well-matched. First, we reduced the original HSI to low dimensionality using the PCA method.

We then cluster the dimensionally reduced HSI (Hyper Spectral Image) into a class map via k-means clustering, which captures the spatial energy before the end-member candidates, and the end-member candidates can be randomly selected from the centroids derived from the clustering step. Act Based on the previously limited singular volume framework of space energy, the end members can finally be searched

Until the maximum values of the objective function form. [13]

Figure 3. SENMAV diagram.

Figure 3. SENMAV diagram.

5. Algorithms Based on Thin Architecture

5.1. Orthogonal Matching Pursuit OMP

The basis of this algorithm is to use the optimization problem in such a way that it remains the same.

The y - Axi is obtained as the concatenated set of $x^i$ and the estimate of x in the $i^{th}$ iteration of the algorithm.

In the first iteration, the initial residual is equal to the observed spectrum of the pixel, the zero relative frequency vector is selected, and the given matrix is empty of end members.

Then, in each iteration, the algorithm searches for the member A that has the best relationship with the true residual, adds this member to the finite member matrix, updates its value, and calculates an estimate of x using the components of the given finite members.

The algorithm stops at some point. The stopping criterion is met when the actual residual value is less than a predetermined threshold and member A cannot be selected more than once because the residual ratio is zero for members who have already been selected. [14]

5.3. Alternating Direction Method of Multipliers ADMM

Convex optimization problems are common in hyperspectral separation, examples of which are constrained least squares (CLS) and fully constrained least squares (FCLS), problems of this class used to calculate relative frequency in linear mixtures with known spectra.

The CBP finite basis tracing problem, which is used to find tight smoothness, for example with a few non-zero elements, uses linear mixtures of spectra available in large libraries.

The constrained baseline tracking denoising (CBPDN) problem, a generalization of BP, admits modeling errors. In this method, two new algorithms are introduced to effectively solve optimization problems based on multiple alternative methods, one of which is the complete Lagrangian family presented. [16]

6. Results and Conclusion

6.3. RDA Method

First, we begin by creating an image of the RDA method, the steps of which are summarized in the diagram below. According to the book, the return signal, which is called raw SAR data, is as follows, where the parameter $A_0$ is the value of the back-scattering reflectivity .

$$S_{rec}\left(\tau ,\eta \right)=A_0.{\omega }_a\left(\eta -{\eta }_0\right).S_{pulse}(\tau -{\displaystyle \frac{{2R}_0}{C}})$$

(12)

Figure 4. RDA follow-chart.

Figure 4. RDA follow-chart.

The amounts in the table below can be used to make one pixel in this way:

Table 1. Parameters for simulation to one Pixel.

Table 1. Parameters for simulation to one Pixel.

The name of the parameter	Parameter Symbol	parameter value
Pulse repetition frequency	PRF	600 Hz
Radar platform speed	v	200 m/sec
Carrier frequency	$f_0$	300M
The length of the antenna along the side	$L_a$	0.6 m
Range Swath	$R_{swath}$	400 m
The distance from the platform to the center Range Swath	$R_{center}$	20 Km
flight height	h	14142 m
The width of the transmitted chirp pulse	$T_r$	2.5 µsec
Chirp rate sent	$k_r$	4x${10}^{13}$Hz/sec
Sampling frequency	$F_s$	200 MHz

First, the unprocessed raw data is produced as follows, then the processing steps are performed on it and the result is obtained as follows:

Figure 5. Pure data.

Figure 5. Pure data.

Figure 6. creating a Pixel using RDA.

Figure 6. creating a Pixel using RDA.

In a fuzzy cloud image, each pixel describes a certain radian of the corresponding position. Due to the lack of specific solutions for hyperspectral images, one pixel often covers several different materials. Therefore, this special spectrum is the combination of the results of several substances according to their distribution and formation. The goals of these combinations are to identify the presence of substances distributed in this area and estimate their parts. To do this, advanced hybrid and non-hybrid models have become vital.

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