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Data compression in ViSAR sensor networks using nonlinear adaptive weighting
EURASIP Journal on Wireless Communications and Networking volume 2019, Article number: 264 (2019)
Abstract
Nowadays, industrial video synthetic aperture radars (ViSARs) are widely used for aerial remote sensing and surveillance systems in smart cities. A main challenge of a group of networked ViSAR sensors in an IoTbased environment is low bandwidth of wireless links for communicating big video data. In this research, we propose a nonlinear statistical estimator for adaptive reconstruction of compressed ViSAR data. Our proposed reconstruction filter is based on an adaptively generated nonlinear weight mask of spatial observations. It can strongly outperform several conventional and wellknown reconstruction filters for three different video samples.
Introduction
The interpolation process is one of the most common processes in remote sensing image and video analysis. Some applications of interpolation in order to estimate unknown pixels are image compression, highrate video transmission, image and video watermarking, image reconstruction, restoration, and magnification. For instance in [1], a modified scheme was proposed for converting standarddefinition television (SDTV) frames to highdefinition television (HDTV) standard [2] to be used in video transmission technologies such as DVBT. Researches on interpolation algorithms include a wide range of research on which some details of them are reviewed as follows. Two most famous interpolators are bicubic convolution (mainly abbreviated as BC) and bilinear (BL) [3]. Today, BC and BL are classified into nonadaptive techniques in terms of local edge computation and indeed provide two linear reconstruction filters [4]. Another main point about them is to use both methods in image processing software tools for remote sensing such as ENVI and ERDAS. However, we wish to focus on newer and efficient types of interpolators entitled edgeguided interpolation algorithms. Edgeguided methods are often applicable in image and video reconstruction problems [5]. In [6], a technique has been represented which estimates anything based on an assumption that every image can be modeled as a locally stationary Gaussian process. Based on this assumption, the local covariance coefficients in lowresolution (LR) images are estimated, and then, the interpolation process is performed based on geometric duality between the LR and the highresolution (HR) covariance. A key issue of this method that makes it unsuitable for ViSAR frames is to consider some statistical assumptions which do not exist in practice. In [5], a new scheme was proposed which uses tensor tool for interpolation in order to realize the edgeguided interpolation. This method could outperform some existing methods.
In this research, we want to propose a new edgeguided interpolator based on statistical estimation. Our purposed method uses an adaptive weighting mechanism which makes it edgeguided, nonlinear, and fully greedy. Our scheme is an extension for the method discussed in [7,8,9] for remote sensing applications. In [7], a basic edgeguided interpolation based on linear minimum mean square error estimation (LMMSE) was introduced for benchmark images such that some evaluations about it have been done in [10]. LMMSE includes two phases of directional filtering using a preinterpolator and data fusion of two orthogonal directions. LMMSE scheme for remote sensing images has been discussed in [9]. This interpolator is a relatively adaptive scheme needing a preinterpolator based on linear filtering, e.g., linear or cubic interpolation, for directional filtering. In the current work, we are going to propose a fulladaptive version of LMMSE for remote sensing data of ViSAR whereas our proposed technique does not need any preinterpolator. In fact, if LMMSE can outperform some linear methods like BL or BC, it is completely natural because they have been used as preinterpolator in LMMSE structure (although as two onedimensional components), but our proposed method which is named adaptive LMMSE (ALMMSE) can fuse directional observation without need to any linear preinterpolator and however outperforms the linear interpolators. Our experiments show that it is winner against five conventional techniques among the most popular nonadaptive/linear reconstruction filters.
We can also use the proposed approach for magnifying some multispectral images such as IKONOS and QuickBird images or images related to highresolution optical remote sensing sensors [11,12,13]. In addition, there are many other applications for interpolation algorithms, e.g., data hiding [14,15,16,17,18], interpolationbased image denoising and demosaicking [19,20,21], SDTV to HDTV conversion (SD2HD) [2] in video processing, color processing [22], information fusion [8, 9], and shadow detection [23] which can be assisted by ALMMSE algorithm. As we mentioned, the main focus of this research is towards interpolationbased image/video compression [10, 24]. For compression, we firstly downsample video frames to reduce the information size at the sender side and then reconstruct them using an interpolator at the receiver side. Consequently, ALMMSE can be used in different processes of remote sensing images.
The rest of this paper is organized as follows: in Section 2, we review LMMSE details and some of its applications in digital image processing; then in Section 3, we present our proposed scheme (ALMMSE); and finally, we evaluate it in Section 4. Evaluations show that the use of a locally adaptive estimation in ViSAR frames creates better quality compared to many conventional techniques. The last section is a dedicated conclusion on the work.
Related work
LMMSE is a quartered interpolator for creating a fourtime larger interpolated image and is widely used in different applications such as enlargement (zooming) [7], noise removal (denoising) [19], color demosaicking [20], and image compression [10]. In this technique, each of nonexisting pixels will be computed based on four nearest neighboring pixels which are previously known. Generally, a schematic according to Fig. 1 is used for representing mechanism of LMMSE in two scenarios with orthogonal directions.
The main shortcoming in the design of LMMSE interpolator is to select equal weights for two corresponding pixels which are in the same direction. According to logic of greedy algorithms, LMMSE is not classified into fulladaptive algorithms because it considers a general assumption about generality of images in its computations. However, we can consider it as a partiallyadaptive interpolator compared to linear interpolators such as BL and BC. In our study, the aim is to create a new LMMSEbased interpolator for reconstruction of a kind of compressed remote sensing data without need to any preinterpolation step.
In [21], the authors have proposed an LMMSEbased interpolator for color demosaicking. Demosaicking is a certain type of interpolation which is commonly applicable in some color images, for example Kodak dataset [20]. The demosaicking algorithm in [20] is based on LMMSE and strongly outperforms BL interpolator [3]. Another application of LMMSE is noise reduction. A denoising algorithm is practically a low pass filter which filters high frequency variations of images, or in the other words, it reduces/removes the noises.
Most of the interpolators have mechanisms based on averaging process which is equal to low pass filtering. Therefore, LMMSEbased interpolators can be used in the noise reduction problems. For example in [19], an LMMSEbased denoising algorithm has been proposed for a wide range of digital images. Quality of the scheme is observable. Interpolation in spatial domain is also a way for image compression, for more details about LMMSEbased image compression refer to [10]. Thus, in addition to direct applications of interpolators such as magnification, interpolation is widely used for image restoration and reconstruction. In other researches, interpolationbased data hiding [8, 14, 15, 18, 25] and multispectral image fusion (pansharpening) [9] are carried out using it. For example in [9], LMMSE has been applied as a magnifier for achieving better quality in pansharpening process of Landsat8 images compared to a linear interpolator. Another application for LMMSE is to do denoising for improving classification accuracy in digital images, because noise reduces accuracy of classifiers (a preprocess based on noise reduction algorithms is normally essential before classification).
Proposed method
In the proposed scheme, an interpolation without any assumption regarding estimation weights is applied to reconstruct compressed frames [4]. In fact, there are no default weights, and all of them are computed adaptively. Our proposed scheme adaptively estimates nonexisting pixels to keep edge information in the best way. In this section, we discuss our ALMMSE interpolation method which is an edgeguided scheme and uses four nearest neighbors from two orthogonal directions to estimate targeted pixels; thus, it has suitability for Markov random field (MRF)based neighborhood systems with order of 1 or 2 such as many remote sensing images. An important point about ALMMSE is to be a fulladaptive nonlinear approach that does not need any preinterpolation compared to linear schemes using polynomials (nonadaptive methods) and traditional LMMSE (with a preinterpolator).
In order to compress ViSAR frames using the proposed method, we should make downsampled versions from HR frames (to create LR frames) with lower resolution and then reconstruct the LR frames using our interpolator. To do this, for example, we estimate 75% of the removed pixels through compression (with a downsampling algorithm like Algorithm 1) with using only 25% of the remaining cases (sample pixels). In such experiments, we can reduce the video size to be one fourth of the original version. Therefore, we use ALMMSE as a regular interpolation for a quartered template.
Here, we discuss details of ALMMSE interpolation using a template according to Fig. 2a, as seen in continuation of this section. As per Fig. 2 b, five sample pixels are shown, and for simplicity, we utilize simple notations as Eq. (1):
To calculate the nonexisting pixels in LMMSEbased interpolated frames, i.e., \( {\hat{x}}_h \)(x_{h} is an unknown ideal value and \( {\hat{x}}_h \) is an estimate for x_{h}) and all the same positions, we use a linear combination of original pixels of LR frame. These original pixels are nearest neighbors of the targeted pixel according to Eq. (2) to generate an estimated value (in some scenarios, two of four nearest neighbors are also estimated pixels of a prior step). Although we are using a linear combination, but since all the interpolation weights are specified adaptively and are not fixed, thus, the final reconstruction filter based on ALMMSE will be nonlinear [22]. In [22], the traditional LMMSE has been discussed extensively in order to keep the adaptivity for gray levels in every edge area. As can be followed in [22], a general form of LMMSE (for first/second order MRF system and using the simplest preinterpolator based on two 1D linear estimation (Eq. (3) shows two directional estimates through a kind of bilinear)) can be written as per Eq. (4). The weights in Eq. (4) are according to Eq. (5) and computable through Eqs. (6–8). Therefore, the ALMMSE closed form is similar as per Eq. (9):
Now in Eq. (9), we should compute four weights of w_{1}, w_{2}, w_{3}, and w_{4}. To do this, there are many ways, but we represent a fulladaptive solution inspired by the traditional LMMSE. Our proposed ALMMSE is indeed a heuristic idea towards extending LMMSE to be fulladaptive (not considering a similar weight for collinear pixels) and with no need to a linear preinterpolator which makes more computational complexity. For eliminating the preinterpolation step, we use an approximate as Eq. (10) to make Eqs. (6–7) more simple and then generate a heuristic expansion on LMMSE weights to achieve ALMMSE weights (Eq. (11)). As shown in Eqs. (12–16), efficient weights of ALMMSE are very similar to LMMSE weights. In fact, we do not consider any equal weights for these four nearest pixels, and therefore, the approach is fully adaptive whereas LMMSE always selects the same weights for the collinear pixels. In addition, LMMSE has to compute some values as directional estimates of each set of collinear pixels. We could consider an adaptive structure which assumes each pixel as separate sample, regardless of collinearity; therefore, the final approach does not need any preestimation for directional estimates that are no longer definable.
The estimation of nonexisting pixels will be repeated to achieve all values of 75% of underestimate pixels, as illustrated in Fig. 2c.
Note that computing of the targeted pixels is firstly based on four nearest neighbors, but in some positions due to the existence of two estimated pixel among four nearest neighbors, practically, the estimation procedure has been performed by six neighbors of which four of these six pixels are not within MRF neighborhood. In the next section, the proposed scheme is evaluated. We will see that the proposed scheme is effective on ViSAR dataset.
Moreover, evaluation is performed based on objective and subjective quality assessment metrics. In addition to the proposed method, a preprocessing step before doing the resampling process exists which contains two blocks of downsampling and upsampling. Suppose that an input image is a typical M × N matrix (for simplicity, M and N are even). Algorithm 1 and Algorithm 2 describe these two blocks.
For more details about impacts of different models of downsampling and upsampling in quartered interpolators, see detailed discussions in [10]. Table 1 provides more qualitative details of LMMSE, ALMMSE, BL, and BC.
Results
For evaluation, some ViSAR frames are used which are observable in Fig. 3. PSNR and SSIM as main metrics are used in all evaluations. PSNR and SSIM definitions are seen in Eq. (17) and Eq. (18), respectively, for two entire 8bit images x and y with the same size N_{1} × N_{2}. In Eq. (18), u_{x} and u_{y} denote mean of images, \( {\sigma}_x^2 \) and \( {\sigma}_y^2 \) show variance of them, and σ_{xy} describes the covariance between them. Resampling is done with the proposed scheme (ALMMSE) and some conventional methods including BL, BC, Lanczos (with parameter of 2 and 3 as an approximation for sinc function), and box kernel [3, 26]. All methods are similar in terms of not having a preinterpolation step, and this makes the evaluations fair. In addition towards fairness, the downsampling processes in all methods are the same, the upsampling in our method is according to Algorithm 2, and the linear methods are according to the MathWork definition.
All simulations have been implemented using MATLAB and show that our scheme is strongly winner against nonadaptive/linear methods. Outputs of PSNR and SSIM with complete details are listed in Tables 2, 3, and 4, and Fig. 4 describes an average for all videos. We observe that the proposed scheme based on a fulladaptive approach causes a suitable impact in real ViSAR dataset and outperforms the other methods.
Conclusions
In the recent years, data processing for IoT became an interesting topic of research [27,28,29,30]. In our study, we proposed ALMMSE interpolation algorithm for the remote sensing ViSAR frames captured by imaging radars in an IoTenabled radar networks of drones and airplanes [31]. This scheme is a new edgeguided interpolator based on nonlinear statistical estimation which has no assumption on local weights and also does not need any preinterpolator. The main feature of the proposed method is to use the most adaptation in comparison to another edgeguided interpolator and conventional interpolation techniques. We compared it with several linear interpolators which do not need any preinterpolator too. All experiments illustrate a clear consequence about superiority of the proposed method. As a future work, we can go ahead to propose a more accurate version of ALMMSE with lower computational complexity. Evaluation of this proposed method for other remote sensing devices may determine some future directions.
Availability of data and materials
All the data and computer programs are available.
Abbreviations
 ALMMSE:

Adaptive LMMSE
 BC:

Bicubic convolution
 BL:

Bilinear
 HDTV:

Highdefinition television
 IoT:

Internet of Things
 LMMSE:

Linear minimum mean square error
 MRF:

Markov random field
 SD2HD:

SDTV to HDTV data conversion
 SDTV:

Standarddefinition television
 ViSAR:

Video synthetic aperture radars
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Acknowledgements
We would like to thank Sandia National Laboratory for ViSAR data used as dataset in this research.
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MK participated in the mathematical design of the proposed method and its computer implementation. SS coordinated the industrial application and raw data preparation, and helped out for the study. MK and SS have completed the first draft of this paper. All authors have read and approved the manuscript.
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Correspondence to Mohammad R. Khosravi.
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Khosravi, M.R., Samadi, S. Data compression in ViSAR sensor networks using nonlinear adaptive weighting. J Wireless Com Network 2019, 264 (2019) doi:10.1186/s136380191577z
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Keywords
 Video synthetic aperture radar (ViSAR)
 Nonlinear reconstruction filter
 Adaptive weighting
 Data compression
 Interpolation
 Internet of Things (IoT)