1 Introduction

PKB/Akt used in the cell promotion and impediment of cell death [1,2,3,4]. There are three major types of input proteins which lead to cell death/survival: epidermal growth factor (EGF) [5,6,7] and Insulin [8,9,10,11,12,13] were the survival proteins while tumor necrosis factor (TNF) [14,15,16,17] is the protein which leads cell death. Insulin and EGF are the main proteins which activates PKB. There are mainly three different types of AkT: Akt1, Akt2 and Akt3. Phosphorylation of Thr308 and Ser473 activates AkT1 by PDK1. AkT1 and AkT2 were presumed in signal transduction of insulin in adipose tissue, liver skeleton muscle, while AkT3 is not activated by insulin. Figure 1 shows the different steps of PI3K that leads to cell survival/death [2]. As shown in Fig. 1, there are many proteins which on activation/deactivation with PKB leads to cell death/survival like BAD, p53, NFκB are survival proteins while FKHR is an apoptotic protein. There are different pathway which can lead to cell death/survival using EGF/Insulin taking PI3K, PKB as main components. First pathway is EGF/Insulin → PI3K → PKB → BAD (survival pathway). If any of the protein is absent in this path then final result is cell death. Likewise second pathway: EGF/Insulin → PI3K → PKB → p53 (survival pathway), third pathway: EGF/Insulin → PI3K → PKB → NFkB (survival pathway), fourth pathway: EGF/Insulin → PI3K → PKB → FKHR (death), fifth pathway: Insulin → PI3K → mammalian target of rapamycin (mTOR) → IRS (survival pathway). Fifth pathway also leads to protein synthesis.

Fig. 1
figure 1

Illustration of signal communication network triggered by PI3K [2]

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A CAD system was designed using different discrete wavelet filters and different classification techniques.

2 Materials and methods

The work has been carried out on images available from Weiss [3]. The data consists of different images of pAkt: phospho-Akt, AkT, ptAkt: phospho-to-total Akt. A CAD system was designed which can be used as a second opinion tool for radiologists. Figure 2 shows the flow chart of the CAD system designed for PKB.

Fig. 2
figure 2

Proposed CAD system for Protein Kinase B

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For CAD system different steps were taken into consideration: data collection, pre-processing, feature selection, feature extraction, partitioning and classification.

Firstly the data was collected from Weiss [3]. Analysis was done in such a manner so as to remove the redundant/duplicate data. If the data is numeric/continuous the regression analysis was done but if the data is categorical than Chi square test or different data mining techniques was applied.

The pre processing technique was applied which consists of cleaning, transformation etc. We clean the data by filling out the missing values, remove noisy data, remove outliers and resolve whether there was any inconsistency in the data or fill out the missing values. There are different approaches to remove the noise from data like binning method, clustering or regression. The data can be transformed by normalization (min–max, z-normalization, by decimal scaling, euclidean, forbenius), aggregation or generalization (hierarchy climbing).

Feature extraction module: There are two types of feature extraction techniques: shape based and texture based [18,19,20,21,22,23,24,25,26,27] as explained in Fig. 3. In this paper we have used transform domain method which is a part of texture based approach. Discrete wavelet transform (DWT) [28], is one of the part of transform domain method which is used in this paper.

Fig. 3
figure 3

Block diagram representation of different feature extraction methods

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Any signal which we have to decompose is first passed through low pass filter (LPF) and high pass filter (HPF). Approximation (A) decomposition is obtained after LPF and Details (D) decomposition is obtained after HPF. Down sampling of columns has been carried out which gives cA and cD decomposition. Later, down sampling of rows were carried out which yields approximation decomposition (CA) and horizontal decomposition (CH) after decomposing cA while vertical decomposition (CV) and diagonal decomposition (CD) after decomposing cD. It means we will get four decomposition values: CA1, CH1, CV1, and CD1. After decomposing CA1 we get again four parts: CA2, CH2, CV2 and CD2 as shown in Fig. 4. There are different types of wavelet transforms. In this paper we are using ten wavelet transforms such as Haar wavelet: db1, Coiflets wavelet: coif1 and coif2, Symlets wavelet: sym3 and sym5, Biorthogonal wavelet: bior3.1, bior3.3 and bior4.4 and Daubechies wavelet: db4 and db6 filters. For each wavelet transforms we have calculated seven texture feature vectors (TFV). Seven TFV’s are mean, standard deviation (SD), energy, mean + SD, SD + energy, energy + mean, mean + SD + energy.

$${\text{Mean}}\;\mu = \frac{1}{n}\sum\limits_{i\, = \,1}^{n} {x_{i} } ,$$
(1)
$${\text{Standard}}\;{\text{deviation}}\,\sigma = \sqrt {\frac{1}{n}\sum\limits_{i = 1}^{n} {(x_{i} - \mu )^{2} } } ,$$
(2)
$${\text{Energy}}\,E = \int\limits_{ - \infty }^{\infty } {\left| {x(t)} \right|^{2} dt} ,$$
(3)

where xi is the observed value, n is the sample size.

Fig. 4
figure 4

Two level decomposition

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Figure 5 shows the two level decomposition of one image that how we have decomposed all the images using different wavelet transforms. Figure 6 shows the de-noised image. This also represents the horizontal, diagonal and vertical detailed images.

Fig. 5
figure 5

Two level decomposition of our image

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Fig. 6
figure 6

Denoised Image and its horizontal, vertical and diagonal detailed images

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After feature extraction, partitioning of data is done where data is partitioned into testing and training. There were different approaches for partitioning: holdout (single, repeated), cross validation, boot strap, sampling (re-sampling, stratified sampling) and three way data splits.

Last step is Feature classification module: Classification can be done by two processes supervised learning and unsupervised learning. Basically classification helps in finding the numerical properties of the images and arranges those values into different classes. For classification we divide data into two parts: testing and training set. There are different types of classifiers. In this paper we are using SVM and SSVM classifier. For the execution of SVM classifier LibSVM library has been used [29]. For calculating SSVM classifier, a library was added which was developed by Laboratory of Data Science and Machine Intelligence, Taiwan [30].

3 Results and discussion

A CAD system has been proposed, where different experiments has been carried out to obtain the classification performance which discriminates PKB into cell death/survival using different DWT with SSVM and SVM classifier. The results were depicted in Table 1. For simulation we have used MATLAB 14.7 software. Algorithm for wavelet transform:

Table 1 Classification performance for the seven TFVs using SSVM/SVM classifier
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  • Step 1: Initially different images of AkT, pAkt, and ptAkt were collected from Weiss [3]. Each image consists of sub thirteen sections which explains the time from 0 to 24 h in the interval of 0, 5 min, 15 min, 30 min and 1 h, 1 h 30 min, 2 h, 4 h, 8 h, 12 h, 16 h, 20 h, and 24 h.

  • Step 2: Colored images are converted to gray scale images.

  • Step 3: Computation of first level decomposition (CA1, CH1, CV1, and CD1) for different wavelet transforms using symmetrical mode.

  • Step 4: Computation of second level decomposition (CA2, CH2, CV2, CD2) for different wavelet transforms using symmetrical mode.

  • Step 5: Different features were calculated for different decomposed levels using forbenius normalization. Forbenius normalization of an m by n matrix X is define as

    $$\left\| X \right\|_{F} = \sqrt {\sum\limits_{i = 1}^{m} {\sum\limits_{j = 1}^{n} {\left| {a_{i,\,j} } \right|^{2} } } } .$$
    (4)

The length of the first feature is seven which generates: CH1, CV1, CD1, CA2, CH2, CV2, and CD2, second feature is three: CH1, CV1, CD1, third feature is six: CH1, CV1, CD1, CH2, CV2, and CD2, fourth feature is four: CH1, CV1, CD1, and CD2, fifth feature is four: CH1, CV1, CD1, and CA2, sixth feature is four: CA2, CH2, CV2, and CD2 and seventh feature is three: CH2, CV2, and CD2.

From Table 1, it was observed that maximum accuracy of 80% was obtained using bior 4.4 wavelet transform and db6 wavelet transform for seventh TFV with SSVM classifier. The lowest accuracy (33.33%)was achieved by haar wavelet transform for seventh TFV which consists of length of six features using SVM classifier. A confusion matrix (CM) of the best TFV is shown in Table 2. Table also shows overall classification accuracy (OCA) for present and absent using SSVM classifier.

Table 2 Classification performance for the best TFVs using SSVM classifier
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4 Conclusions

This paper explains a CAD system which helps in classification of PKB using different discrete wavelet transform. From different experiments it was concluded that, for characterization of PKB, bior 4.4 & db6 wavelet transforms yields the best results. These wavelet transforms gives the maximum OCA of 80%. No paper till yet reported such type of work. In future author will try for more DWT and compare the results. Furthermore author can also try for more texture features.