Citation: | Rizwan Sadiq, Muhammad Bilal Qureshi, Muhammad Mohsin Khan. De-convolution and De-noising of SAR Based GPS Images Using Hybrid Particle Swarm Optimization[J]. Chinese Journal of Electronics, 2023, 32(1): 166-176. DOI: 10.23919/cje.2021.00.138 |
Currently synthetic aperture radar (SAR) is comprehensively utilized for the purpose of creating images which are targeted for high quality details [1]. The wavelength of SAR is much higher compared to infra-red (IR) or visible rays as a result it has the ability to see through smoky and cloudy environment when other options unable to work well. The major disadvantage of optical sensors is the inability of collecting the information in cloudy, fogy and dusty environment. On the other hand SAR technology has the ability to perform perfectly even under such unfriendly conditions [2]. Therefore, nowadays application of SAR for such environmental conditions is a hot topic for the researchers. SAR systems are mainly categorized in: mono-static, (situation where same antennas is utilized for both transmission and reception) and bi-static SAR (where separate antennas are utilized) [3]. Based on the research in [4], the authors described a bi-static SAR imaging framwork, which take advantage of reflected global positioning system (GPS) signal wave-forms from target objects on the surface of earth to construct an image of the region of interest along with focus on de-convolution of GPS based SAR imaging. The idea to exploit reflected GPS signals as a tool for remote sensing was first described in 1993 by the European Space Agency [1]. Likewise [5] and [6] also explored the possibility of using the GPS as a bi-static radar illuminator for aerial target detection.
GPS satellites transmit free source of coherent radio waves illuminating the earth surface 24 hours a day which are received and processed by GPS receivers for extracting navigational parameters such as position and velocity. GPS satellite transmits signals that are also reflected from object on the surface of earth. These reflected signals known as multi path signals are one of the major source of error during navigation which requires mitigation during position and velocity calculations. In contrast to this, they can be utilized in variety of remote-sensing applications as they consist of valuable information regarding the reflecting surface. These GPS based images are noisy and can not be used directly in the received form, therefore, various approaches have been employed to remove noise and obtain the real image out of these noisy observations. Most common technique used for this purpose is Wiener filtering [1]. In which power spectral densities of the noisy image and point spread function are used to de-convolve and obtain the real image. Recently, various evolutionary computing algorithms have been established for resolving various global optimization problems, such as particle swarm optimization (PSO) algorithm [7]-[11] which can be explored for the improvement of such noisy images. In this work PSO algorithm is exploited for this purpose and it has been observed that the quality of image can be significantly improved by applying PSO algorithm on the received images. Although PSO algorithm performs well to solve the global optimization problem but still some residue noise remains unveiled in the images due to the local minima. To deal with this residue noise: singular value decomposition (SVD) is proposed for de-noising the resultant image which was achieved after PSO algorithm. This amalgamation of PSO followed by SVD is used for de-convolution and de-noising the noisy observation and to obtain the true target in GPS image. For further refinements, morphological operations like dilation and erosion are utilized to optimize the quality of the restored image. The major contributions of the paper are as below.
• Inverse filtering using Wiener filter is widely used for de-convolution purpose, but in the presence of noisy channel apart from estimating the original signal, Wiener filtering also amplifies the noise component, which ultimately causes reduction in signal to noise ration (SNR). This issue is addressed by using an optimizer which can better estimate target while reducing the noise. We employed PSO algorithm for better de-convolution since it is computationally less expensive and has better tolerance for local minima.
• Under the condition of additive white Gaussain noise (AWGN) channel we know that power spectral density (PSD) of noise is generally uniform as compared to our original signal. By exploiting this property we applied Hybrid PSO algorithm i.e. PSO algorithm followed by SVD, to achieve noticeable improvements in noise reduction.
• For post processing we employed morphological filtering to smooth out any leftovers of noise.
• For the performance analysis the system is simulated and it is shown that step by step application of the proposed technique enhances the quality of image significantly as a result the resultant image is much better than the image de-convolved by using the conventional Wiener filtering.
The rest of the paper is organized as follows. Section II describes the GPS imaging followed by system model and assumptions in Section III. Details of PSO algorithm and SVD are given in Section IV. Section V covers the simulation results. Whereas, the Concluding remarks and future work is presented in Section VI.
The GPS satellite is a modified GPS receiver and its signal detection components (antennas etc.), constitute a bi-static SAR system, which can be employed for passive microwave imaging purposes, where the GPS satellite is used as a transmitter of opportunity. In a real time situation the reflected signals from targets on the surface of the earth will be collected by appropriate hardware setup placed on a object in motion to form the impact of a synthetic aperture and provide the requisite alteration in geometry [6]. Upon the arrival of signal at the target, it is reflected in various directions based on the roughness of surface and the dielectric nature of the target. The reflected signals that are integral for imaging purposes are reflected in a non-specular way. This kind of reflection appears when the signal is spread over a wide angle and imperiled to more attenuation as a function of distance travelled. The complex target surface can be considered as number of point reflectors. In practical environment point reflectors must need to have constrained size and for our research work it is necessary to model these point reflectors as spheres with a diameter equal or close to the resolution of the imaging process [1], [12].
Target detection and imaging based on GPS has the significance that user can take advantage of the expensive GPS infrastructure designed for navigational purposes and no dedicated transmitter is needed. Additionally, the GPS works 24/7 and its signals cover the entire globe. Furthermore, there are more concurrent imaging possibilities, one for each GPS satellite in view. The GPS satellite with optimal geometry in terms of signal strength and visibility can be chosen to capture the direct and reflected GPS signal [13], [14]. We know that the GPS code acquisition (C/A) power spectral density is well below the power spectral density of noise. Therefore by correlation of a locally generated C/A code sequence it is converted to a usable signal to noise ratio (SNR) that results in an effective processing gain to the SNR. The reported GPS C/A code theoretical processing gain is 1023 or 30.1 dB. Low cross-correlation and enhanced auto-correlation values enable a extensive dynamic range for signal acquisition and aid in supplementary image generation [13]. Since the GPS satellites and/or receiver platforms are in continuous movement during the course of integration, the signal collected at the receiver side will be a frequency modulated GPS signal also termed as a chirp signal. The constantly varying Doppler shift can be expressed as:
f(t)=cos(ω0t+πFTt2)−T2<t<T2 |
(1) |
where,
δrange=c2bcos(β/2) |
(2) |
In the above equation
In order to achieve a fair analysis of the system following realistic assumptions are taken into consideration:
• The target is assumed to be fixed point scatter which is based on point target resolution theory.
• Channel is required to be additive white Gaussian noise.
• It is also assumed that the target is reflecting all the signal or the power which is being absorbed by the target is so negligible and it will not affect the analysis that is the reflection coefficient for the system is assumed to be unity.
• Location of the target is set to be the north pole.
• Furthermore, the phase of the carrier is assumed to be locked correctly.
The complete system model block diagram is shown in Fig.1. The received GPS signals are very weak and corrupted due to the effects of channel, additional noise and interference added during the propagation and it is a difficult task to restore the original image from this noisy and corrupted observation. Under these conditions two types of problems need to be addressed for the reconstruction of image. The first is image formation and second one is the de-noising the received observations. The main block diagram has two distinct sub blocks to overcome these both problems; the block with solid lines in Fig.1 represents the whole process of image formation from the GPS signal, whereas the portion with dashed lines covers the image restoration process. In the following subsection both these portions are discussed briefly.
Both direct and reflected signals received from modified GPS receiver are passed to the match filtering block. The Matched filter correlates the direct signal and the reflected signal to maximize the SNR which can be mathematically expressed as follows:
S(fk,τ)=∫Ts2−τ−Ts2Sd(fk,t+τ)∗Sr(fk,t)dt |
(3) |
where,
O(l)=1NpKN0∑n=1K∑k=1S(fk,τn)exp(j4πfkΔR(τn)n)=A0 |
(4) |
The above equation is defined for a single point target as the target points are increased the amplitudes of all scatterer will need to be incorporated and for a m-point target the amplitudes are defined as
A gray scale image having size of
PSF=∫Ts2−τ−Ts2Sr(fk,t+τ)∗Sr(fk,t)dt |
(5) |
where
De-convolution is a way of restoring the original image from degraded measurement of the image [1], [22], [23] which is used in many fields for image processing specially in astronomy, passive imaging, microscopic and medical imaging. In order to remove the deformity caused by PSF conventionally Wiener filter based de-convolution methods [13] are used to improve the image quality [24], [25]. The degradation function combined with an additive noise is applied on the input image,
g(x,y)=h(x,y)∗f(x,y)+η(x,y) |
(6) |
where h(x,y) is the spatial illustration of the degradation function and symbol
G(u,v)=H(u,v)F(u,v)+N(u,v) |
(7) |
The fastest and less computationally extensive method for restoration is direct inverse filtering and is given by:
ˆF=G(u,v)H(u,v) |
(8) |
As a consequence we divide the output with H, however, there exist uncertainty as the output is now convoluted and effected by noise, blurring or both. Inverse filtering will cause undesirable signal amplification and suppression of desired response [21] which drastically degrades the performance of Wiener filtering method. To overcome this problem of Wiener filtering, we propose the application of PSO algorithm for the image estimation from the noisy observations which is discussed in the following section.
PSO algorithm is a common technique for the optimization of objective or cost functions and is recently being utilized for the de-convolution of images [2], [10], [11]. In order to achieve the goal of image restoration, we use PSO algorithm with more than one degraded observations of true image retrieved at varying time slots. These correlated images of multiple observations aids in diversity and facilitate in attaining the enhanced results which are embedded in the degraded observations using PSO based de-convolution technique. In PSO algorithm usually we proceed by setting up a group of random “particles” or “solutions” and determine the optimal among them by updating every generation. At the end of every iteration, we get two optimum or best values from our generated particles or solutions. We call this best value as local minima or
For execution, PSO needs an objective function to be minimized for the purpose of obtaining the optimal solution. Objective function acts as the criteria for minimization and when achieved, it also works like a stopping condition. Mean square error (MSE) or absolute difference among two signals is taken as natural objective function i.e.
MSE=1MNM−1∑x=0N−1∑y=0(ˆf(x,y)−f(x,y))2 |
(9) |
The primary objective of the optimization problem is the minimization of the MSE. Once the objective function is defined it is followed by executing the PSO algorithm by random setting of the population. Every particle makes an effort to reach the solution by minimizing the objective function, since the image is in a matrix form. To employ PSO it is transformed to a vector form of
vi,j(k+1)=wvi,j(k)+c1rand1(.)(Pbi,j(k)−pi,j(k))+c2rand2(.)(Gbi,j(k)−pi,j(k)) |
(10) |
where
pi,j(k+1)=pi,j(k)+vi,j(k+1) |
(11) |
The updated velocity is directly proportional to the distance from local minima and global minima, greater the distance between them faster the particle tends to converge towards best solution [27]. In order to limit the change in particle velocity a parameter
If
The performance of each particle is measured using a fitness function. In this paper we used MSE as the fitness function. The fitness function of particle
Fitness(pi,j(k))=11+epi,j(k) |
(12) |
Here
Pbi(k+1))={pbi(k), if pbi(k)>f(pbi(k+1)pbi(k+1), otherwise |
(13) |
Gbi(k+1))=max(f(pbi(k+1))),1≤i≤N |
(14) |
From the above equations it can be seen that in order to update the local best particle first the updated particle
Although PSO performed very well under the noisy conditions but still some noise can be observed. To overcome this residue noise we propose the implementation of singular value decomposition which further refines the results of PSO processed image and this amalgamation of both techniques gives a significant improvement in recovering the real image.
Even the goal of focusing the targets in the image was achieved using PSO, however, further image processing is imperative to reduce the residue noise components. For de-noising we use SVD which has been used for image enhancement [28], in this process we calculate singular (or principal components) values of image matrix and extract the necessary information from these values. Noisy image matrix can be decompose by utilizing SVD through the given relationship:
F=USV |
(15) |
where
g=gsig+gn |
(16) |
g=nl∑n=1snunvn+N+K−1∑n=nlsnunvn |
(17) |
where
As a final step of de-noising we used dilation and erosion [29] as our post processing method. Dilation expands all noise values along with original signal rendering them prominent by adding the pixels at the boundary. The Erosion process thereafter reduces the sizes of objects and removes small disruptions by subtracting objects with a radius less than the kernel by removing pixels at the boundaries. In this manner the small anomalies which are highlighted by dilation process are easily removed from the image. This process was performed by choosing a
To validate the performance of PSO algorithm for the improvement in the reconstruction of GPS based SAR images different simulations are performed. The aim of the simulations is to compare the results achieved the conventional Wiener filtering based processing and by the proposed methodology. From the simulations it was observed that the proposed methodology compared to the conventional system found to be superior in restoring the imaged with better quality. For the simulation purposes following subsection discusses the set of parameters.
The simulation is divided into two separate parts for a purpose: the responsibility of first part is to synthesize the signal originating from the analog to digital converter of the GPS front end, whereas the role of second part is to construct an image. It is carefully ensured that only digitized GPS signal information is available to the reconstruction engine which contains globally available data (satellite ephemerids) and the receiver location. The reconstruction engine splits the area of interest in an array of square bins and makes an effort to coherently correlate the received signal with an single method chirp which is exclusive to every bin. The model for directly received signal is represented as follows:
Sdir=ddir(t)ejwLt |
(18) |
where
Sref=dref(t)ejwLt |
(19) |
where
Fig.4 shows the search area in which targets can be positioned. The position [0, 0, 6378001] is fixed in the middle of the search region in ECEF coordinate system. These are actually the north pole coordinates used to make coordinate transformations easier. For computational improvements the calculations were carried out on vectors as opposed to multi-dimensional arrays. The spatial resolution is set at 1 meter, which is suitable for a point target simulation. The test signals were generated with the help of a Borland C++ based GPS direct and reflected signal generator [18], some of the important parameters are summarized in Table 1. In order to apply PSO we need multiple observations, therefore, we generated multiple images by varying the integration time during SAR reconstruction algorithm. Experimental observations have revealed to select a value of 2, 4, 6 and 8 seconds to resolve the targets with acceptable spatial resolution as shown in the Figs.5 and 6 for single point target and 4-point target respectively. After 8 seconds no significant change is observed in the acquired image.
Description | Value |
Ts (Sampling time) | 10 s |
Attenuation factor | 0.5 |
GPS L1 Frequency | 1575.42 MHz |
tt (signal transit time) | 70 ms |
C/A code chip rate | 1023000 |
Receiver start position (x) | 1000 |
Receiver start position (y) | 1000 |
Receiver start position (z) | 6378300 |
Receiver velocity (x) | 200 m/s |
Receiver velocity (y and z) | 0 |
Spatial resolution | 1 m |
Total atmospheric loss | 2 dB |
Satellite antenna gain | 13.4 dB |
Polarization mismatch loss | 3.4 dB |
To effectively minimize the shortcomings of the standard Wiener filter we have proposed a hybrid technique for image de-noising and de-convolution. Figs.7 and 8 show a comparison between the conventional Wiener filter model and proposed model for both single point and 4 point targets respectively. Both figures contain the images after application of the proposed technique and clearly it is observable that after every step the quality of image gets better and better. a) In Figs.7 and 8 contains the de-convolved image by the Wiener filter whereas, b) in Figs.7 and 8 there contains the image de-convolved by using proposed PSO technique. After applying PSO, the targets are better in terms of visibility and the presence of excessive noise is noticeably decreased as compared to Wiener filtering. Even though the noise is significantly decreased but still there is some noise which can be observed around the target. To further refine the target SVD followed by morphological filters i.e. dilation and erosion are applied to remove this background anomalies. The resultant image is shown in (c) and (d) of Figs.7 and 8 and finally a threshold is applied to remove small noise components and conclude the task of image restoration as shown in (e) of Figs.7 and 8.
Some measures are available in image processing domain to find out or ascertain quality of image such as the sharpness or resolution. In order to evaluate the proposed technique based on MSE, peak signal to noise ratio (PSNR), improved signal to noise ratio (ISNR), following equations are utilized:
PSNR=10log10(1MSE) |
(20) |
ISNR=10log10∑Mm=1∑Nn=1(f(m,n)−g(m,n))2∑Mm=1∑Nn=1(f(m,n)−ˆf(m,n))2 |
(21) |
where
The Fig.9 and Fig.10 contain a comparison of conventional and proposed method for de-convolution of GPS based SAR images in case of a single point target and 4 point target respectively. They also depict the response after de-noising. It can be deduced that Wiener filter is unable to reduce the noise from degraded observation. However, in case of PSO based de-convolution noise is reduced as we are using multiple observations which is not the case in Wiener based model. By acquiring multiple observations more information about our desired signal is available which helps us in exploiting image diversity.
The Table 2 and Table 3 summarize the performance evaluation of restored images by using different techniques such as wiener filter, standard PSO algorithm and proposed methodology for a single point and 4-point target respectively. These methods have been applied for the restoration of GPS based SAR image for single and four point targets based scenario. It can be observed that these restoration techniques perform better for fewer point targets. Another aspect that can be inferred and verified is that the SVD based technique offers better results as compared to wiener filter or standard PSO algorithm.
Method | MSE | ISNR(dB) | PSNR(dB) |
Before filtering | − | − | 15 |
Wiener filter | 1.2563E−004 | 0.0433 | 89.8217 |
P.S.O | 2.1396E−006 | 5.6123 | 130.5489 |
After SVD | 2.1479E−007 | 8.6047 | 153.5361 |
Method | MSE | ISNR(dB) | PSNR(dB) |
Before filtering | − | − | 35 |
Wiener filter | 6.9146E−005 | 0.2091 | 95.7931 |
P.S.O | 3.9290E−006 | 4.8717 | 124.4711 |
After SVD | 3.9823E−007 | 7.8680 | 147.3622 |
De-convolution based on PSO algorithm is proposed to achieve a better quality image by using GPS based SAR images. The quality is further enhanced by incorporating SVD which turns out to be an efficient and more reliable approach to restore the original image and address the de-convolution and de-noising problem. This work can be extended for a specific shape based image rather than a point target. The proposed algorithms have been applied on images obtained by simulated GPS signals, however, with the help of suitable hardware actual GPS data can be acquired and SAR based reconstruction algorithms can be used for the detection of real life targets and image generation. The proposed SVD based PSO algorithm can be used for the restoration of actual smeared and noisy images. Moreover, the feature extraction and classification tools can also be applied for target shape and symmetry.
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