8
Compressed Sensing Based Adaptive-Resolution Data Recovery in Underwater Sensor Networks Wenjing Kang, Gongliang Liu, and Bin Hu School of Information and Electrical Engineering, Harbin Institute of Technology, Weihai 264209, P.R.China Emails: {kwjqq, liugl}@hit.edu.cn; [email protected] Abstract With marine development thriving today, underwater acoustic sensor networks have become a vital method in exploring and monitoring the ocean. In this paper, a data recovery scheme with adaptive resolution based on compressed sensing theory is proposed, aiming at acclimating to the atrocious conditions under the water. The fundamental thought of the scheme is to achieve better quality of recovered data at the sacrifice of data resolution. Data resolution adjusting method is raised firstly, then a recovered data quality evaluation algorithm and an adaptive resolution selecting strategy are proposed. The experimental results show that schemes presented are able to evaluate the quality of the recovered data accurately and adaptively select the resolution. Accordingly, recovery resolution is modified triumphantly to achieve higher accuracy on the premise of acceptable data resolution. Index TermsUnderwater sensor networks, compressed sensing, data recovery, adaptive resolution I. INTRODUCTION Oceans are significant sources to maintain the existence of mankind and promote social progress. Wireless sensor networks have become significant facilities helping people to cognize the oceans and exploit marine resources owing to their flexible deployment, low cost and extensive coverage. Nowadays, they’ve played an important role in applications such as scientific data gathering, environmental monitoring and protection, natural undersea resources prospection and disaster monitoring. Underwater Sensor Networks (USNs) consist of sensor nodes with low energy consumption and short communication distance, deployed underwater and networked via wireless communication to collaboratively glean information through various sensors and transmit it to the sink node [1]. Different from terrestrial sensor networks [2], USNs mostly communicate via acoustic wave, which extends the propagation delay substantially. Furthermore, power of acoustic modulator and demodulator is highly larger due to severer propagation attenuation. Difficulty in battery charging makes it important to reduce energy consumption to prolong network lifetime. The Manuscript received August 24, 2015; revised March 9, 2016. This work was supported by the National Natural Science Foundation of China (61371100, 61501139, 61401118), and the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2011114, HIT.NSRIF.2013136) Corresponding author email: [email protected] doi:10.12720/jcm.11.3.317-324 complexity of communication environment such as non- stationary sea noise, alteration of water temperature and pressure and affects of marine organisms induces severe multipath interference and delay jitter, challenging the reliability of communication. Candès , Romberg, Tao and Donoho proposed the theory of Compressed Sensing (CS) [3]-[6] in 2004, which combines signal acquisition process with compression process innovatively. CS theory asserts that signals can be recovered from far fewer samples than traditional methods need, if the signal is sparse in a proper basis [7]. CS exploits the fact that many natural signals are sparse in a proper basis, making it feasible to apply the theory in many practical applications, for instance, wireless sensor networks [8]-[10]. Applying CS theory in USNs not only significantly reduces the data collection quantity, but relieves the pressure of power consumption and bandwidth requirement in data transmission. Besides, low encoding computational complexity of CS theory orientates sensor nodes’ limitation in energy, communication capacity and computing capability. In a word, the CS theory improves the network energy efficiency and prolongs the network lifetime. Under the background of abominable underwater environment, in this paper, an adaptive resolution data recovery scheme based on CS theory is proposed. The essence of this scheme is to achieve better recovery quality at the sacrifice of the resolution. Owing to the instability of underwater acoustic channel, the quantity of received packets may vary acutely, which indicates the probability of the received data packets inadequacy. Without sufficient data packets, more precisely, not enough for success recovery in a high probability, the error of data recovery will increase dramatically. To maintain data recovery accuracy, conventional data collecting system needs to gather more packets, which increases the network burden and energy consumption. However, it is shown that cutting down the recovery resolution will result in reduction of signal sparsity. Taking advantage of this feature, recovery error will decrease by reducing the recovery resolution, when lack of measurements, according to the CS theory. Compared with conventional data gather system, the proposed scheme is more energy efficient and relies less on communication reliability, for conventional schemes are all on the premise of sufficient correct received data 317 Journal of Communications Vol. 11, No. 3, March 2016 ©2016 Journal of Communications

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Page 1: Compressed Sensing Based Adaptive-Resolution …data recovery scheme with adaptive resolution based on compressed sensing theory is proposed, aiming at acclimating to the atrocious

Compressed Sensing Based Adaptive-Resolution Data

Recovery in Underwater Sensor Networks

Wenjing Kang, Gongliang Liu, and Bin Hu School of Information and Electrical Engineering, Harbin Institute of Technology, Weihai 264209, P.R.China

Emails: {kwjqq, liugl}@hit.edu.cn; [email protected]

Abstract—With marine development thriving today,

underwater acoustic sensor networks have become a vital

method in exploring and monitoring the ocean. In this paper, a

data recovery scheme with adaptive resolution based on

compressed sensing theory is proposed, aiming at acclimating

to the atrocious conditions under the water. The fundamental

thought of the scheme is to achieve better quality of recovered

data at the sacrifice of data resolution. Data resolution adjusting

method is raised firstly, then a recovered data quality evaluation

algorithm and an adaptive resolution selecting strategy are

proposed. The experimental results show that schemes

presented are able to evaluate the quality of the recovered data

accurately and adaptively select the resolution. Accordingly,

recovery resolution is modified triumphantly to achieve higher

accuracy on the premise of acceptable data resolution. Index Terms—Underwater sensor networks, compressed

sensing, data recovery, adaptive resolution

I. INTRODUCTION

Oceans are significant sources to maintain the

existence of mankind and promote social progress.

Wireless sensor networks have become significant

facilities helping people to cognize the oceans and exploit

marine resources owing to their flexible deployment, low

cost and extensive coverage. Nowadays, they’ve played

an important role in applications such as scientific data

gathering, environmental monitoring and protection,

natural undersea resources prospection and disaster

monitoring. Underwater Sensor Networks (USNs) consist

of sensor nodes with low energy consumption and short

communication distance, deployed underwater and

networked via wireless communication to collaboratively

glean information through various sensors and transmit it

to the sink node [1].

Different from terrestrial sensor networks [2], USNs

mostly communicate via acoustic wave, which extends

the propagation delay substantially. Furthermore, power

of acoustic modulator and demodulator is highly larger

due to severer propagation attenuation. Difficulty in

battery charging makes it important to reduce energy

consumption to prolong network lifetime. The

Manuscript received August 24, 2015; revised March 9, 2016.

This work was supported by the National Natural Science

Foundation of China (61371100, 61501139, 61401118), and the Natural Scientific Research Innovation Foundation in Harbin Institute of

Technology (HIT.NSRIF.2011114, HIT.NSRIF.2013136) Corresponding author email: [email protected]

doi:10.12720/jcm.11.3.317-324

complexity of communication environment such as non-

stationary sea noise, alteration of water temperature and

pressure and affects of marine organisms induces severe

multipath interference and delay jitter, challenging the

reliability of communication.

Candès, Romberg, Tao and Donoho proposed the

theory of Compressed Sensing (CS) [3]-[6] in 2004,

which combines signal acquisition process with

compression process innovatively. CS theory asserts that

signals can be recovered from far fewer samples than

traditional methods need, if the signal is sparse in a

proper basis [7]. CS exploits the fact that many natural

signals are sparse in a proper basis, making it feasible to

apply the theory in many practical applications, for

instance, wireless sensor networks [8]-[10]. Applying CS

theory in USNs not only significantly reduces the data

collection quantity, but relieves the pressure of power

consumption and bandwidth requirement in data

transmission. Besides, low encoding computational

complexity of CS theory orientates sensor nodes’

limitation in energy, communication capacity and

computing capability. In a word, the CS theory improves

the network energy efficiency and prolongs the network

lifetime.

Under the background of abominable underwater

environment, in this paper, an adaptive resolution data

recovery scheme based on CS theory is proposed. The

essence of this scheme is to achieve better recovery

quality at the sacrifice of the resolution. Owing to the

instability of underwater acoustic channel, the quantity of

received packets may vary acutely, which indicates the

probability of the received data packets inadequacy.

Without sufficient data packets, more precisely, not

enough for success recovery in a high probability, the

error of data recovery will increase dramatically. To

maintain data recovery accuracy, conventional data

collecting system needs to gather more packets, which

increases the network burden and energy consumption.

However, it is shown that cutting down the recovery

resolution will result in reduction of signal sparsity.

Taking advantage of this feature, recovery error will

decrease by reducing the recovery resolution, when lack

of measurements, according to the CS theory. Compared

with conventional data gather system, the proposed

scheme is more energy efficient and relies less on

communication reliability, for conventional schemes are

all on the premise of sufficient correct received data

317

Journal of Communications Vol. 11, No. 3, March 2016

©2016 Journal of Communications

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packets whereas scheme proposed in this paper works

without them. However, there’s a nonnegligible

limitation that decrease of resolution damages the value

of the recovered data. Therefore, a data quality evaluation

method and an adaptive resolution selecting strategy are

proposed afterwards. The proposed data quality

evaluation method exploits the data smoothness in spatial

domain to estimate the reconstruction error. And the

adaptive resolution selecting strategy keeps moderate loss

of resolution to achieve less reconstruction error. Another

adaptive data gathering scheme based on CS was

proposed in [8]. The proposed scheme introduces

autoregressive (AR) model into objective function of

convex optimization, exploiting the local correlation in

sensed data to achieve the local adaptive sparsity.

Furthermore, the recovered data is evaluated according to

temporal correlation between historically reconstructed

data and current reconstruction result, and then the

number of measurement is tuned adaptively. The

difference between [8] and this paper is that we consider

the circumstance that the gathered data is insufficient, in

which circumstance, the sparsity is definite. Only the

resolution decrease can reduce the sparsity then

implement better recovery quality.

The remainder of this paper is organized as follows.

Section II presents the data recovery strategy with

adjustable resolution, based on CS theory. Section III

proposes a recovered data quality evaluation algorithm.

In Section IV, an adaptive resolution selecting strategy is

raised. Experimental results are detailed and discussed in

Section V. Finally, Section VI concludes this paper.

II. DATA RECOVERY WITH ADJUSTABLE RESOLUTION

BASED ON CS THEORY

A. Introduction of Compressed Sensing Theory

Consider a discrete real signal ,x n 1,2, ,n N ,

and an orthonormal basis 1 2, , N N

N R ,

where , 1i i N are columns of the orthonormal

basis . Then x can be expanded in the basis as follows:

1

N

j j

j

x

(1)

where 1{ }N

j j is the coefficient sequence of x in the

basis . can be written as:

T x (2)

If at most k ( k N ) entries of are nonzero, then x

is k-sparse. Only in this case, CS theory is feasible.

Design orthonormal measurement matrix M NR to

sample the signal x to get the measurements y. Moreover,

the sensing matrix defined as CSA must obey the

RIP [11]. Projecting x on obtain measurements y with

M entries: CSy x A (3)

At the receiving end, there’re plenty reconstruction

algorithms, such as Convex Relaxation algorithm [12]

[13] and Greedy Pursuits algorithm [14], [15], to decode y

to get the original signal and x. The CS theory

indicates that when the number of random measurements

M is larger than a constant sN , with the probability at

least 1- MN , the original signal can be reconstructed

uniquely and accurately. sN is defined as

logsN Ck N (4)

where C is a constant irrelevant to N and k [16].

However, under the circumstance of severe channel

condition in USNs, the actual received measurements

may less than sN . Decreasing the data reconstruction

resolution, its sparseness k will decrease, too, illustrate in

Fig. 8 and Fig. 9, then possibly meet the requirement of

success reconstruction.

Fig. 1. Resolution adjustment mechanism

B. Data Recovery Scheme with Adjustable Resolution

This paper basically aims at marine scientific

information, a set of two-dimension data correlated with

latitude and longitude, illustrated in Fig. 1. The entire

figure denotes a sea area. An asterisk represents a sensor

node; solid line grids divide the field into different

regions that hold the same data measured by the sensor

node in its center. The original data 0x is a set of two-

dimension data 0 0

0

N Nx R

whose entries are in one-to-

one correspondence with those grids. It represents

ensemble of data measured by all sensor nodes, with the

amount of 0 0N N N . All data is numbered then

reshaped to a vector 1

1{ }N N

i ix x R

. In each round, the

sink node obtains M measurements, composing a

vector1

1{ }M M

j jy y R

. Every measurement (every

term in y) is a measured value uploaded by a sensor node,

i.e. , , , , 1,2i j i jy x y y x x i j N . Especially,

different i is corresponding to different j, that means

there’re no repeated data packets from same nodes. Here

by, the measurement matrix consists of M rows and N

columns. There’re one “1” and N-1 “0”s in every row.

The number of column with “1” is the same as the

number of the node that upload this data, i.e. , 1i j .

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The basic principle of resolution adjustment is, given a

particular y, reconstructing x in different resolution by

designing different . In brief, the mechanism is to

redraft these grids and layout virtual sensor nodes, as

shown in Fig. 1, too. Those circles represent virtual

sensor nodes, and dash dot lines segment the area into

different ranges that hold the same measured values. If a

virtual grid includes several actual nodes, the measured

value of the virtual node in that grid is the mean value of

those actual nodes’s data. On the contrary, if there’s only

one node in a virtual grid, the measured value of

corresponding virtual node is the same as the actual node.

After data fusion, size of 0x alters from

0 0N N to

' '

0 0N N ; x with N elements turns into x with N

elements, where ' '

0 0N N N . Like the adjustment in

grids, if there’re several data packets come from one

virtual grid, then their mean value forms one new packet.

After data fusion of y, a new measurements vector y

with M elements replaces y. As for new measurement

matrix , it contains M rows and N columns. Due to

variation in number and correspondence of sensor nodes,

the column number with non-zero value in every row

varies too. Reconstruction process proceeds use y and

to get recovered data vector x̂ , then reshape x̂ to

obtain recovered data matrix 0 0

0ˆ N Nx R

.

237.2 237.3 237.4 237.5 237.635.6

35.7

35.8

35.9

36

original data(50*50)

longitude( W)

latitu

de(

N)

12

12.5

13

13.5

Fig. 2. Original data (50×50)

237.3 237.4 237.5 237.6

35.65

35.7

35.75

35.8

35.85

35.9

35.95

36

36.05

longitude( W)

data after reconstruction changing(40*40)

latit

ude(

N)

12

12.5

13

13.5

Fig. 3. Data with adjusted resolution (40×40, 64%)

In this paper, data from online database of Jet

Propulsion Laboratory subordinate to NASA

(http://ourocean.jpl.nasa.gov/) is analyzed. A set of

temperature information of Southern California beachline

is shown in Fig. 2, whose resolution is 50×50. Fig. 3 to

Fig. 5 show dataset after resolution adjustment. These

figures indicate that the temperature data is fairly smooth,

therefore moderate and slight change in resolution won’t

affect its visuality. But sharp decrease in resolution will

result in heavy losses of information it contain.

237.3 237.4 237.5 237.6

35.65

35.7

35.75

35.8

35.85

35.9

35.95

36

36.05

longitude( W)

data after reconstruction changing(30*30)

latit

ude(

N

)12

12.5

13

13.5

Fig. 4. Data with adjusted resolution (30×30,36%)

237.3 237.4 237.5 237.6

35.65

35.7

35.75

35.8

35.85

35.9

35.95

36

36.05

data after reconstruction changing(20*20)

longitude( W)

latit

ude(

N

)

12

12.5

13

13.5

Fig. 5. Data with adjusted resolution (20×20,16%)

Fig. 6. Recovery error distribution

III. RECOVERED DATA QUALITY EVALUATION

Negative effects of resolution reduction make it

necessary to compromise between resolution and

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accuracy. In view of the fact that real data is unavailable,

calculating the conventional error is incapable. However,

the target two-dimension data can be regarded as an

image without texture and boundary, considering its

smoothness. Analysis of recovery error indicates that it

follows the Gauss distribution, shown in Fig. 6, which

accords with the error distribution hypothesis in most of

image noise level estimation algorithms. So it’s feasible

to adopt these algorithms to estimate recovery error.

The recovered data quality evaluation algorithm

proposed is based on [17], using Principal Component

Analysis (PCA).

Firstly, normalize the recovered two-dimension data0x̂ .

Secondly consider the data is a image and decompose the

image into overlapping patches. Thirdly vectorize those

image patches, let 0

ˆix be the vectorized patch

0 0

ˆ =i i ix x n (5)

where 0ix is the original image patch (consider the

original data as a image, too), andin is i.i.d zero-mean

Gaussian noise with variance of 2

n . In our case in is the

recovery error.

According to the column, arrange all the vectorized

image patches0

ˆix to structure a new matrix, whose

covariance matrix is defined as

0ˆ 0 0

1

1ˆ ˆ= ( )( )

PT

x i i

i

x xN

(6)

where P is the quantity of image patch, and is the

mean value of dataset 0 0

ˆ ˆ={ }ix x .

The minimum eigenvalue of the covariance matrix can

be derived as

0 0

2

ˆmin min( )= ( )x x n (7)

where0ˆmin ( )x denotes the minimum eigenvalue of the

covariance matrix formed by recovered data image.

Likewise, 0min ( )x denotes the minimum eigenvalue of

the covariance matrix formed by original data image.

The smooth patches are known to span only low-

dimensional subspace [17], in which case, 0min ( )x is

approximately zero. Them the recovery error err can be

estimated as

0

2

ˆminˆ ( )n xerr (8)

The quality or recovered data is related not only to

recovery error, but data resolution. The less recovery

error, higher resolution, the better quality. We evaluate

the data quality factor (dqf) to estimate the quality of

recovered data.

0ˆ* / ( ') / ( )dqf err sqrt N sprs x (9)

where is a coefficient (in this paper, =500 ), 'N is

the quantity of the recovered data, 0ˆ( )sprs x is its

sparseness.

parameter setting:

thre_score,

step_resl, max_resl, min_resl

thre_sparse, thre_score

iter = 1, resl(iter) = max_res

flag_suc = false

begin

input y

dqf(iter) < thre_score

output

Y

N

iter = iter + 1

resl(iter) = resl(iter-1) - step_resl

reconstruct with resl(iter),

calculate dqf(iter)

reconstruct with resl(iter),

calculate dqf(iter), sparse(iter)

N > 2N

Y

flag1 = sparse(iter-1) < thre_sparse &&

resl(iter-1) > min_res &&

dqf(iter-1) < thre_score &&

dqf(iter-1) < dqf(iter-2) &&

dqf(iter-1) � dqf(iter)

flag1 == true

flag2 = sparse(iter-1) > thre_sparse ||

resl(iter-1) < min_resl

flag2 = = true

Y

N

end

flag_suc = true

flag2_suc = = true

0x

output:fail

to recovery

N

Y

0x

0x

Y N

Fig. 7. Flowchart of the proposed algorithm

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IV. ADAPTIVE RESOLUTION SELECTING STRATEGY

The preceding sections have introduced the

mechanisms of resolution adjusting and recovered data

quality evaluation. In this section, an adaptive resolution

adjustment algorithm is proposed. Fig. 11 illustrates that

under a proper sampling probability, there’s valley point

on the resolution-dqf curve which is the best compromise

between resolution and recovery error. The fundamental

of the proposed algorithm is to find this valley point with

the largest resolution and dqf smaller than a threshold.

After data gather process of every round, recovered

data is constructed in max resolution max_resl , then dqf

is evaluated at the sink node. If dqf is less than a

presupposed threshold thre_score, the data reconstruction

succeed, and resolution adjustment is unnecessary.

Otherwise, subtract presupposed step_reslu from

resolution, then data reconstruction and evaluation are

processed again. The iteration continues until specific

conditions are satisfied. As mentioned above, the process

aims at finding a valley point, therefore in every iteration,

whether the last iteration reconstruction is successful is

decided.

A successful reconstruction should meet four

requirements:

1) Sparseness requirement: the sparseness proportion

of recovered data should be less than thre_sparse;

2) Resolution requirement: the resolution of recovered

data should be greater than min_reslu;

3) Data quality requirement: the dqf of recovered data

should be less than thre_score;

4) Valley point requirement: the point on resolution-

dqf curve should be a valley point.

If one recovered data meets these requirements, the

iteration would stop with a successful recovery. On the

contrary, if in an iteration, the resolution of the recovered

data is less than min_reslu or the sparseness proportion is

greater than thre_sparse, then the iteration would stop

with a fail. The detail of the algorithm is illustrated in Fig.

7.

V. EXPERIMENTAL RESULTS

A. Influence of Resolution Adjustment

Firstly, we examine the influence of resolution

changing on sparsity. We selecting 100×100 dataset and

frequency domain as sparse domain. In frequency domain,

quantity of coefficients whose energy is over 99.95% of

the total energy is regarded as the sparseness. As seen in

Fig. 8, the sparseness decreases with the decreasing of

resolution. Thus, according to the CS theory and equation

(4), the probability of accurate reconstruction increases.

However, Fig. 9 indicates that the proportion of non-zero

coefficients increase with the decreasing of resolution. So

that resolution reduction is finite. Excessively low

resolution leads to invalidation of sparsity feature, and

then CS theory become invalid.

0 2000 4000 6000 8000 100000

50

100

150

200

250

300resolution - sparsity

data number

spars

ity

Fig. 8. Sparseness varies with resolution

0 2000 4000 6000 8000 100000.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

resolution - sparsity ratio

data number

spars

ity r

atio

Fig. 9. Sparse level varies with resolution

Secondly, we test the influence of resolution changing

on the recovery error with different sampling probability.

Size of dataset is 50×50; frequency domain is sparse

domain; reconstruction algorithm is OMP [12]; Monte-

Carlo simulation 50 times.

Simulation results are shown in Fig. 10. In Fig. 10, the

right-most value of every curve is the error of original

resolution reconstruction. It illustrates that with lower

resolution, the reconstruction error is relatively lower in

temperate sampling probability, which demonstrates the

feasibility of proposed resolution adjusting scheme.

When the sampling probability equals to 0.1, the error

curve is evidently higher than other curves. It indicates

that received data is not adequate to reconstruction in any

resolution. With comparatively high sampling probability,

the reconstruction error is generally constant and along

with the decrease of resolution, there’s a tendency to

increase.

B. Quality Estimation of Recovered Data

Firstly, we test the quality estimation with different

resolution of original data. Fig. 11 shows that with the

decrease of resolution, dqf of the data increases. More

precisely, the dqf increases gently at first, sharply at last.

It accords with the fact that low resolution results in poor

data quality.

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Fig. 11. The dqf of original data with different resolution

Fig. 12. Error estimation

Fig. 13. Quality estimation of recovered data

Secondly, we consider the quality estimation of

recovered data with resolution variation. The image patch

size is 5×5; other simulation conditions are the same as

simulations above. Simulation results are presented in Fig.

12 and Fig. 13. Fig. 12 shows that the error estimation

curve basically fits the error curve in Fig. 10. The PCA

algorithm is applicable in reconstruction error estimation.

Fig13 illustrates the recovered data quality evaluation. It

shows that there’re valley points on dqf curves with

temperate sampling probability. On the left side of the

valley points, the dqf increases due to low resolution.

Conversely on the right side, the dqf increases due to

large reconstruction error. Similar to Fig 10, when the

sampling probability is extremely low, like 0.1,

successful reconstruction is unable to reach. When

sampling probability is comparatively high (0.35-0.4),

due to low reconstruction error, the dqf curve is gentle,

there’s no obvious valley point. Particularly, although dqf

is relatively low, it’s not proper to adopt extremely low

resolution (400-800), owing to severe information loss.

C. Reconstruction with Adaptive Resolution

To evaluate the success of the scheme proposed,

calculate the recovery resolution according to the

flowchart presented in Fig. 7. Meanwhile, calculate

recovery error (Pe) in each iteration, too. If the error

corresponding to the chosen resolution is the smallest one

among all the errors calculated in overall iterations, then

the choice is correct. Using Monte Carlo simulation with

100 times, the result is shown in Fig. 14. It illustrates that

with the increase of sampling probability, the success rate

of the proposed scheme increases, too. The overall

success rate is over 70%, so, given consideration to the

randomness of every measured dataset, the proposed

scheme is capable of choosing the best recovery

resolution. Fig. 15 and Fig. 16 show the improvement of

Pe and resolution modify rate of every sampling

probability. For instance, when the sampling probability

is 0.21, applying the proposed scheme, the Pe decreases

7.53% at the sacrifice of 16.18% resolution. It’s shown

that when the sampling probability increases, the

improvement of accuracy decreases, due to better

recovery quality in original resolution. Meanwhile, the

resolution reduction drops either.

Fig. 14. Success rate

Fig. 15. Pe improvement

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Fig. 16. Resolution modify

VI. CONCLUSIONS

This paper proposed an adaptive resolution data

recovery scheme based on CS theory, aiming at

accommodating to the features like enormous energy

consumption and low communication reliability in USNs.

In the circumstances of insufficient measured data, the

presented scheme is able to achieve better recovery

quality at the sacrifice of data resolution. The

experimental results show that the proposed scheme

evaluates recovery quality accurately and achieves

adaptive adjustment of resolution and compromises

properly between resolution and recovery accuracy.

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Wenjing Kang received the B.S., M.Eng.

and Ph.D. degrees in measuring &

control technology and instrumentations

in 2001, 2003 and 2007, respectively, all

from Harbin Institute of Technology,

Harbin, China. She is now with the

Harbin Institute of Technology at Weihai

as an lecture. Her current interests

include underwater sensor networks, moving target tracking and

image processing.

Gongliang Liu received the B.S. degree

in measuring & control technology and

instrumentations, and the M.Eng. and

Ph.D. degrees in electrical engineering in

2001, 2003 and 2007, respectively, all

from Harbin Institute of Technology,

Harbin, China. He is now with the

Harbin Institute of Technology at Weihai

as a professor. His current interests include satellite

communications and underwater sensor networks.

323

Journal of Communications Vol. 11, No. 3, March 2016

©2016 Journal of Communications

Page 8: Compressed Sensing Based Adaptive-Resolution …data recovery scheme with adaptive resolution based on compressed sensing theory is proposed, aiming at acclimating to the atrocious

Bin Hu received the B.S. and M.Eng.

degrees in 2013 and 2015, respectively,

all from Harbin Institute of Technology.

Her current interest include underwater

sensor networks and communication

systems.

324

Journal of Communications Vol. 11, No. 3, March 2016

©2016 Journal of Communications