Mobile Information Systems

Volume 2017 (2017), Article ID 2314062, 12 pages

https://doi.org/10.1155/2017/2314062

## Statistical Prior Aided Separate Compressed Image Sensing for Green Internet of Multimedia Things

Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China

Correspondence should be addressed to Jian Jiao

Received 16 December 2016; Accepted 22 February 2017; Published 16 March 2017

Academic Editor: Nan Zhao

Copyright © 2017 Shaohua Wu et al. This 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.

#### Abstract

In this paper, we aim to propose an image compression and reconstruction strategy under the compressed sensing (CS) framework to enable the green computation and communication for the Internet of Multimedia Things (IoMT). The core idea is to explore the statistics of image representations in the wavelet domain to aid the reconstruction method design. Specifically, the energy distribution of natural images in the wavelet domain is well characterized by an exponential decay model and then used in the two-step separate image reconstruction method, by which the row-wise (or column-wise) intermediates and column-wise (or row-wise) final results are reconstructed sequentially. Both the intermediates and the final results are constrained to conform with the statistical prior by using a weight matrix. Two recovery strategies with different levels of complexity, namely, the direct recovery with fixed weight matrix (DR-FM) and the iterative recovery with refined weight matrix (IR-RM), are designed to obtain different quality of recovery. Extensive simulations show that both DR-FM and IR-RM can achieve much better image reconstruction quality with much faster recovery speed than traditional methods.

#### 1. Introduction

As a means of connecting the proliferating embedded devices to the Internet, the Internet of Things (IoT) has drawn extensive attention in recent years. IoT has the great potential to significantly influence our lives and the way we interact with devices including sensors, security/surveillance cameras, mobile phones, home automation/control devices, and vehicle state meters [1]. Different from the traditional wireless sensor networks (WSNs), IoT is envisioned to have a much larger deployment scale and cover a much broader range of services and applications. Therefore, the critical issue of efficient energy utilization in the design of wireless network transmission technologies, including the WSNs, LTE networks [2], cognitive radio networks [3], interference-alignment based networks [4], becomes much more severe for IoT, especially for IoT specialized for multimedia services and applications, which is referred to as “Internet of Multimedia Things” (IoMT) [5].

The multimedia content, for example, image, audio, video, acquired from the physical environment possesses distinct characteristics as compared with the scalar data acquired by typical IoT devices, so the IoMT devices require much higher processing and memory resources. Moreover, the multimedia transmission is more bandwidth hungry as compared with the conventional scalar data traffic in IoT. Considering that the devices are usually low-computation capability devices and may run on battery with limited power, there is a great need for developing special multimedia data processing and transmission technologies that enable green computation and communications, that is, low-power and low-complexity signal processing, and energy efficient transmission. A core module of the multimedia data processing is compression, which aims to reduce the amount of data needed to be transmitted. Traditional compression techniques, such as the JPEG, JPEG 2000 algorithm for image compression, the MPEG, and H.26X algorithm for video compression, are generally too complex for low-cost IoMT devices. In this paper, we focus on the compressed sensing (CS) based image compression and reconstruction methods, aiming to design low-complexity and robust image transmission strategies for green IoMT applications.

The CS technique was first proposed by Candes et al. [6, 7], in which the original data can be accurately reconstructed from only a portion of the sampled data, sampled at rates lower than the Nyquist rate. The key idea of CS is to make use of the sparse or compressible nature of the original data to reduce the size of the sampled/transmitted/stored data. Multimedia data, including images, generally holds this sparse or compressible nature. For example, images are approximately sparse (or compressible) in the wavelet domain. Since its invention, CS has sparked tremendous research interests from related areas such as medical imaging, wireless communication, and image/video compression. This technique lends itself naturally to the IoMT domain, and CS based image compression/reconstruction has become a very hot research topic. In [8], a novel CS based data aggregation mechanism tailored to the application of large-scale air-pollution monitoring with IoT devices was proposed. Their design exploits both the intra- and intersource correlations among air-pollution data using the framework of compressed sensing with side information. In [9], by applying the dictionary learning based denoising method within the approximate message passing (AMP) algorithm framework, a mechanism for efficient communication in IoMT was proposed.

CS based image compression and reconstruction have already shown great potential for IoMP applications. However, there still remain two main problems. First, although the system complexity of “compression-reconstruction” has been greatly shifted from the encoder-end to the decoder-end, the encoding complexity is still too high to be handled by IoMT device when the size of the image is large. Second, although it is commonly assumed that the server node has abundant computation capability for the CS image reconstruction, there exist indeed situations where the decoder-end cannot afford to reconstruct the image, especially for real-time multimedia applications, for example, video surveillance using mobile handset to collect the IoMT packets. For the first problem, one solution is to divide the large image into small blocks and then compress each block sequentially. This method prominently reduces the computation complexity, but block processing destroys the boundary coherence between pixels, leading to obvious reconstruction quality degradation. To overcome this disadvantage, some new methods have been proposed, among which the separable image sensing encoder is the one that not only has affordable computation complexity, but also promises good reconstruction quality [10]. By separable sensing, the original 2D image is directly measured first in the row direction and then in the column direction, instead of being extended to a 1D signal. For reconstruction, one can transform the 2D image recovery problem to a 1D signal recovery by using of Kronecker product [11] or use the 2-dimensionality orthogonal matching pursuit (2D-OMP) algorithm proposed by [12]. However, both the Kronecker reconstruction method and the 2D-OMP algorithm are very computation-consuming; that is, the second problem we note above still exists with these methods.

In our previous work, a separate-combine recovery has been proposed to yield a highly efficient recovery technique for CS image processing [13]. It can process large-sized images that can hardly be handled by existing methods such as the Kronecker reconstruction method or the 2D-OMP algorithm. The expense of the separate-combine recovery method is a slight degradation of the reconstruction quality. Moreover, its computation complexity is still high for practical real-time applications.

In this paper, we aim to propose a reconstruction method that can further reduce the computation complexity and, meanwhile, increase the reconstruction quality. To achieve this goal, statistical information is considered in the recovery method design. By analyzing the image representations in the wavelet domain, the energy distribution of natural images is found to be well fitted by an exponential decay model, which is then used as statistical a priori information in the recovery method. Based on the separate compression image sensing, the recovery process is also composed of two steps: the row-wise (or column-wise) intermediates recovery and the column-wise (or row-wise) final results recovery. The aim of reconstruction in each step is to obtain a solution conform with the statistical prior by introducing a weight matrix. Two recovery strategies are, respectively, designed in this paper: the Direct Recovery strategy with Fixed weight Matrix (DR-FM) and the Iterative Recovery strategy with Refined weight Matrix (IR-RM). The DR-FM strategy is aimed to achieve extremely high computation efficiency by employing the same weight matrixes for the two recovery steps, while, for the IR-RM strategy, the weight matrix for the second step will be iteratively refined, aiming to achieve more accurate recovery results. Extensive simulations and experiments have been conducted, as results show that the proposed recovery method with DR-FM strategy has a much better computational efficiency than traditional methods, while the recovery quality is better; the recovery with IR-RM strategy can achieve the best quality of recovery at the expense of degradation in computational efficiency slightly, yet still faster than the traditional methods.

The remainder of the paper is organized as follows. Section 2 introduces the preliminaries and related work, including the CS basics and its applications to IoMT image transmission. Section 3 describes the separate image sensing and reconstruction methods. In Section 4, the proposed recovery method aided by statistical prior is described in detail. Section 5 presents the simulation results, followed by conclusions in the last section.

#### 2. Preliminaries and Related Work

In this section, we summarize the preliminaries and related work of this paper, including the CS basics, the image transmission in IoMT, and prior aided CS image reconstruction.

##### 2.1. The CS Basics

CS is applied for signal which is sparse or compressible. Under certain bases , a 1D signal can be expressed as . We say is -sparse if it satisfiesorA signal is said to be nearly sparse or compressible if the largest coefficients contribute to most of the signal energy, and the others are small enough to be ignored. Signals in practical systems, including the images, are mostly compressible in a certain domain, so the CS theory can be used widely in natural signal processing.

In CS framework, a spare or a nearly sparse signal (size: ) is measured by a random matrix (size: , where ) to generate a compressed result (size: ):where .

The reconstruction of corresponds to the problem of solving unknown parameters from linear equations, that is, a calculation for an underdetermined system of equations which contains innumerable solutions. Fortunately, , the representation of the original signal under certain basis, is sparse enough, and the solution of the underdetermined system of equations can be achieved by solving the combinatorial optimization problem below:

If the measurement matrix is incoherent with the representation basis , especially when is a random matrix and , satisfies the restricted isometry property (RIP) with enormous probability [14]. The -norm optimization problem in (4) can be replaced by the -norm optimization problem which has the same unique solution; that is,

The original signal can then be obtained as

In conclusion, the crux of CS theory is to reconstruct the sparse representation of the original signal by making good use of the sparsity nature. There are mainly two kinds of reconstruction algorithms.

###### 2.1.1. Greedy Algorithms

They are a kind of recovery methods that can find out the locally optimal solution but not the globally optimal solution. Orthogonal matching pursuit (OMP) is a classical greedy method for CS recovery, and it is the base of many later proposed advanced methods, such as CoSaMP [15] and AOMP. The crux of greedy algorithms is to find out columns of the matrix that make significant contributions to the compressed result iteratively.

###### 2.1.2. Convex Optimization Recovery

Different from the greedy algorithms, the convex optimization recovery methods aim to approach the globally optimal solution. The results by convex optimization recovery are usually more accurate, but the expense is more computation resources needed for the reconstruction. Convex optimization recovery can be used in situations where the recovery quality is preferred more than the recovery speed.

##### 2.2. The Image Transmission in IoMT

The IoT will enable connections of a wide variety of things, ranging from small sensors to the cloud of servers (data storage and analysis). With the explosive growth of IoT, the device numbers will increase by several orders of magnitude, resulting in the great requirement for mechanisms that can reduce the computation, power, and communication loads for the end-devices. For the IoMT devices, this requirement becomes especially stringent due to large amount of multimedia data to be processed and transmitted. In addition, for some application scenarios such as security video surveillance, both the device-end and the server-end need to be capable of handling real-time processing.

CS is one promising mechanism that can help to meet all the above requirements. First, CS is naturally a compression technique, so it can reduce the amount of data to be transferred, thus requiring less transmission power and bandwidth. Second, CS compression involves only linear operations, so the encoding complexity is extremely low compared with traditional nonlinear compression. For large image compression, by using methods such as separate sensing, the encoding complexity could further be reduced. Third, since the operation of CS compression is intrinsically global linear projection, every projected result has almost the same amount of information about the whole image. Therefore, CS compression is naturally robust to transmission loss. In other words, it can be regarded as a digital-fountain like erasure-correction codes. In all, the development of new and more efficient CS techniques for IoT is important, and our aim in this paper is to design reconstruction methods with not only low complexity but also high performance for real-time IoMT applications.

##### 2.3. Prior Aided CS Image Reconstruction

In the basic CS framework, only the signal sparsity or compressibility is explored by the reconstruction. In fact, physical signals including IoMT images often show more features other than sparsity or compressibility, such as the structural and statistical features, which can be used as priors to further improve the reconstruction quality or efficiency. For example, the signal wavelet coefficients can be naturally organized into a tree structure, and those significant coefficients that contribute to most of the image energy often cluster along a few branches of this wavelet tree. The condensing sort and select algorithm (CSSA) [16] solving the optimal tree approximation is one of the good methods that can be employed by CS image reconstruction. Another example is the Block-Matching and 3D (BM3D) collaborative filtering model utilized to exploit the nonlocal self-similarity among pixels in global positioned patches [17].

Besides structural prior exploration, statistical prior could also be used. In [18], recovery method adopting statistical information as prior knowledge was proposed to achieve a higher quality for the 1D sparse signals. Reference [19] proposed an innovative recovery method that achieves an estimation of the original signal by a series of iterations. In each iteration, a weight matrix which contains statistical a priori information of the original signal is used. However, the method involved numerous computation for an excess of iterations. A self-adapting statistical model of image expressed in wavelet domain is proposed by [20] to reduce noise in image storage. This method was not combined with compressed image sensing but still provides some inspiration for the next step research on CS. In [21], the Gaussian scale mixtures (GSM) model, which has been shown to effectively capture the local dependencies of intrascale wavelet coefficients [22], was incorporated into the proposed BLS-GSM recovery method using the Bayes least-square estimation. The BLS-GSM recovery has shown good performance, but the computation complexity is still too high to be affordable for IoMT devices. In summary, the development of low-complexity high-performance CS image reconstruction methods for IoMT image transmission systems remains an open problem requiring further investigation, which is just the aim of this paper.

#### 3. Separate Image Sensing and the Reconstruction Methods

In this section, we will illustrate how the 2D images in IoMT applications can be compressed through the low-complexity separate sensing method and describe the existing corresponding reconstruction methods.

##### 3.1. Separate Sensing for 2D Image Compression

To reduce the computation complexity of compressed image sensing, the 2D separate compression has been proved to be an effective method [10], especially for large-sized images. Let the original image signal be , whose size is , and let the random compression matrix be , whose size is (). The original signal is measured column-wise by and row-wise by , respectively, where is the transposition of . So the compressed signal can be expressed as , as is shown in Figure 1. The size of compressed signal has been changed to from , after the compression.