VQ is defined as a block coding model which is used to compress images at some loss of information. In VQ, codebook construction is an essential process. Let Y={yij} be the size of raw image with M×M pixels which are partitioned into different block sizes of nxn pixels. In other words, an input vector X=(xi, i=1,2,…,Nb) contains a set of Nb=[Nn]×[Nn] and L indicates n×n. The input vector xi, xi∈RL, is L-dimensional Euclidean space. A codebook C contains L-dimensional code words where C={c1,c2,…,cNc}, cj∈RL, ∀j=1,2,…,Nc. Every input vector is indicated by row vector xi=(xi1, xi2,…,xiL) and the j^th codeword of codebook is denoted as cj=(cj1, cj2,...,cjL). The optimization of C, by means of MSE could be devised as the minimization of distortion function, D. Generally, the minimum value of D implies better C.

(1) D(C)=1Nb∑j=1Nc∑i=1Nbμij⋅‖xi−cj‖2

The above equation is subjected to constraints given in Eqs. (2) and (3)

(2) ∑j=1Ncμij=1,∀i∈{1,2,…,Nb}

(3) μij={1if xi is in the jth cluster0

And Lk≤Cjk≤Uk, k=1,2,…,L, where Lk denotes the lower k^th element in training vector whereas Uk defines a higher k^th element in input vector. The ‖xi−ci‖ shows the Euclidean distance between the vector x and codeword, c.

LBG is defined as a Scalar Quantization (SQ) algorithm and was devised in the year 1957 by Lloyd. By 1980, it was generalized as VQ. It employs two predefined conditions for input vectors to determine the codebook. Let xi, i=1,2,…,Nb be an input vector, distance function d and primary codewords cj(0), j=1,2,…,Nc. The LBG algorithm repeatedly employs two conditions to obtain optimal codebook according to the given procedures:

Divide the input vector into different groups using minimum distance rules. The resultant block is saved in a Nb×Nc binary indicator matrix U, where the components are expressed as follows, (4) μij={1 if d(xi,cj(k))=minpd(xi,cp(k))0 otherwise

The overall operation of the proposed OLBG-LZMA algorithm is illustrated in Fig. 1. The input image should be divided into non-overlapping blocks which then undergo quantization by LBG model. The codebook, which has been deployed using LBG approach, is trained first using GWO method in order to satisfy the needs of global convergence and assures the phenomenon. The index numbers are sent over transmission medium and reconstructed at the destination using decoder. Both reformed index and the corresponding codewords are arranged properly in order to generate the decompressed image size which is almost equal to the given input image. GWO algorithm was developed by Mirjalili et al. [25] in 2016 as a simulation from the hunting behavior of grey wolves. Grey wolves are assumed to be superior predators which often reside in group. Based on its hunting nature, the wolves are divided into alpha (α), beta (β), delta (δ), and omega (ω). The leader wolves are known to be α wolves which decide the place of sleep, hunting destination etc. The decisions taken by α are followed by the remaining members in the group. β is the second level of grey wolves which is referred to be subordinate wolves that guide the α wolves in decision making process. The subordinates can make decision in the absence of dominant wolves. Third level grey wolves are grouped under ω wolves which act as a scapegoat. When the wolves do not come under α, β, or ω, they are known to be subordinate or δ wolves.

These wolves do not dominate α and β wolves, but dominate over ω. Different levels of grey wolf hunting are listed below.

Approaching prey

GWO algorithm is composed of two phases namely, exploration and exploitation. Initially, it is applied to explore the best solutions in local search area. The grey wolf surrounds and attacks the prey when searching for reliable solutions. Secondly, prey is identified by exploring the local space area. While encircling prey, the wolves finds the location of a victim and surrounds it. Hence, encircling prey is expressed as given herewith.

(6) D→=|C→.Xp→(t)−X→(t)|

(7) X→(t+1)=Xp→(k)−A→.D→

where t depicts the present iteration and A→ and C→ are said to be coefficient vectors and position vector of the prey which are represented as Xp→(k). Here, X→ implies the position vector, A→.D→ exhibits the accurate value and X→(t+1) implies element multiplication. The vectors A→ and C→ can be denoted as follows.

(8) A→=2a→.r→−a→

(9) C→=2.r→

where the elements of ~a have been reduced in a linear manner from 2 to 0 during various iterations whereas r1 and r2 define the random vectors in [0, 1].

The default nature of grey wolves is to identify the locations of prey and encircle it. Hunting operation is carried out by α wolf, while β and δ involves in a few scenarios. Also, the numerical simulation of grey wolves is assumed to be α, β and δ which embeds massive aspects in terms of prey location. Thus, the top three solutions are saved which result in improving the position of search agents and is described as depicted in Eq. (10).

D→α=|C→a∗X→α−X→|∗

(10) D→β=|C→b∗X→β−X→|

D→δ=|C→c∗X→δ−X→|

where D→α, D→β and D→δ are the modified distance vectors among α, β and γ locations to alternate wolves and C→a, C→b, and C→c illustrate three coefficient vectors which are applied in distance vector.

X→a=X→α−A→a∗D→α

(11) X→b=X→β−A→b∗D→β

X→c=X→δ−A→c∗D→δ

where X→a represents the newly-attained position vector of α position X→α and the distance vector D→α. X→b implies a novel position vector accomplished using β position X→β and the distance vector D→β. X→v demonstrates the best position vector estimated with the application of δ position X→δ and distance vector D→δ, while A→a, A→b, and A→c are referred to as three coefficient vectors.

(12) X→(k+1)=∑i=1nX→in

where X→(k+1) is defined as a novel position vector that is calculated as an average of total number of positions attained by applying α, β and δ (n = 3). As mentioned earlier, the grey wolves wait to attack the prey till it becomes idle. To model the approach in a mathematical way, the value of ~a is to be reduced. The random measures of ~A lies in the range of [−1, 1]. There are few steps followed in GWO model as demonstrated in Fig. 2.

Step 1: Initializing parameters: Here, the codebook constructed using LBG approach is declared to be the initial solution whereas the remaining solutions are developed in a random manner. The attained solution refers to a codebook of NC codewords.

Step 2: (Selecting the present best solution): The fitness of each solution is processed using Eq. (1) and the higher fitness location is selected as an optimal result.

Step 3: (Generating novel solution): The position of grey wolves is updated using the location of prey. When an arbitrarily-created number (K) is higher than ~a, then the bad locations are replaced with newly-identified positions and the best location is kept unaltered.

Step 4: Rank the solutions under the application of fitness function and select the better solution.

Step 5: (Termination criteria): Follow the Steps 2 and 3 until the stopping condition is reached.

LZMA coding is used in the compression of generated codebooks. It is used to compress real time data which is generated rapidly. Initially, the sensor nodes observe the physical environment. The sensed value is then tested for anomalies and the label value is appended. Label value is appended by the sensors to every individual sensed data. The labelled value ‘1’ is appended to the sensed data, when the latter differs from actual data i.e., an abnormal value is found. Likewise, the labelled value ‘0’ is appended to the sensed data, when the latter has no deviation from the actual data, i.e., normal value is found. The sensor node appends the label value to sensed data after which the compression is performed. Sensor node runs the LZMA algorithm whereas the compression algorithm compress the labelled data efficiently, irrespective of the label value. LZMA algorithm uses the dictionary, sliding window concept and range encoder to efficiently compress the labelled data. The compressed data is then transmitted to BS. BS receives the compressed data and performs decompression process. As LZMA is a lossless compression technique, the reconstructed data remains the exact replica of original data with no loss of information.

For experimentation, a publicly-available microarray image dataset was employed from Zhong 2017. Besides, the particulars of the dataset is given in Fig. 3 and the sample TMA images are shown in Fig. 4. The dataset contains high resolution Tissue Microarray (TMA) image dataset containing 71 prostate tissue samples of cancer patients digitized by Carl Zeiss Axio Scan.Z1 scanner. The resolution of the image is 7000 × 7000 pixels for a core tissue and is named as *_PTEN_Zesis_7000.jpg. In some cases, 4096 × 4096 resolution is also used and is named as *_PTEN_Zesis_4096.jpg (where * indicates sample id).

Tab. 1 and Figs. 5–8 show the results of PSNR analysis for the proposed algorithm against existing models on the applied images 1–4.

Fig. 9 shows the average PSNR values obtained by different methods under different bit rates. In addition, an average of all the PSNR values attained for the applied test images is tabulated in Tab. 2. For the applied test_image 1, under the least bit rate of 0.1875, the methods used for comparison such as LBG, PSO, QPSO and HBMO attained a PSNR value of 24.0 which was lower than other methods. At the same time, both FF and CS algorithms obtained a PSNR value of 24.1 and 24.3 respectively. However, the newly developed OLBG-LZMA model reached a maximum PSNR value of 25.3. Under a moderate bit rate of 0.3750, the presented algorithm attained the highest PSNR value of 27.1 whereas the CS, FF, HBMO, QPSO, PSO and LBG models achieved the least PSNR values of 26.2, 26.0, 25.9, 25.7, 25.5 and 25.3 respectively. Under the highest bit rate of 0.625, the OLBG-LZMA method yielded significant results with a PSNR value of 33.2 which was much higher than the compared algorithms.

Similarly, for all the applied test images, the proposed OLBG-LZMA algorithm outperformed the existing algorithms in an efficient way. In table values, it is noted that the PSNR values start to rise with an increase in bit rate. This phenomenon can be observed from the PSNR values obtained for the least bit rate of 0.1875 and highest bit rate of 0.625 bit rate. The simulation results portray that the proposed OLBG-LZMA model is an efficient one compared to other algorithms under different codebook sizes.

Experimental validation was performed in Windows 10 operating system while its specifications were Intel(R) Core(TM) i7-7500U and 2.70 GHz CPU with 8 GB RAM. In addition, the execution code was developed and simulated in MATLAB. Tab. 3 and Fig. 10 shows the obtained average CT of various algorithms under different bit rates. The authors used 30 codebooks with 20 iterations. For a codebook of size 8 and a bit rate of 0.1875, the average CT required is shown in the table. From the table, for applied image 1, the highest CT of 977.200 was demanded by CS algorithm. In line with this, both HBMO and FF algorithms showed slightly lower CT values such as 890.254 and 877.123 respectively. The proposed OLBG-LZMA managed well with a moderate CT of 685.246.

But, the existing LBG, PSO and QPSO algorithms achieved effective CT performance with least values of 3.3715, 254.357 and 261.299 respectively. It is clear that the LBG model needs a least CT of 3.3715 s which is highly appreciable. But, its poor performance in PSNR value limits its applications. However, the proposed OLBG-LZMA model has moderate CT and it yielded significant PSNR value which makes it preferable than the CT.