## 3 System Model
\[\rm HV=Y \tag{5}\]  
By choosing the best combinations of {V*, a*i, b*i, i = 1, 2,..., L}, the discrepancy between forecasts and targets can be reduced, as shown in Equation (6). \[\parallel\mathbf{H}(a^{*},\ldots,a^{*},b^{*},\ldots,b^{*})\mathbf{V}^{*}-\mathbf{Y} \parallel=\min(\parallel\mathbf{H}(a_{1},\ldots,a_{L},b_{1},\ldots,b_{L}) \mathbf{V}-\mathbf{Y}\parallel)_{a,ib,\mathbf{V}} \tag{6}\]  
Following gradient-descent-based algorithms, the minimization process modifies weights, as well as biases, through iterations of backward propagation. The equation for this method is represented in Equation (7). \[W_{k}=W_{k-1}-\eta\frac{\delta E(W)}{\delta W} \tag{7}\]  
where \(E\) is the error that remains, after each prediction iteration, with the learning rate \(\eta\). For the vast majority of problems, these gradient-descent-based techniques perform admirably. These algorithms are typically slow since they involve iterative learning stages. Additionally, they have issues with overfitting, which is frequently used to find local minima as opposed to global ones. By increasing the likelihood of visible units, which is represented by the joint probability distribution of visible-hidden unit pair in Equation (8), the ideal set of parameters can be determined. \[P(v,h)=\frac{e^{-E(v,h)}}{\sum_{v^{\prime}}\sum_{v^{\prime}}e^{-E(v^{\prime},h^ {\prime})}} \tag{8}\]  
which has all the possible pairings of visible hidden units as its denominator. The probability of a visible unit is in Equation (9), after marginalizing the space of concealed units. Figure 1:0  
Tensor A \(\in\) RN1 \(\times\) N2 \(\times\) N3, each of which is N2 \(\times\) N3 in size. By Equation (10) A is decomposed according to Tucker  
Figure 1:1  
All images in the y- and x-directions are based on columns of U\({}^{(2)}\) and U\({}^{(3)}\), respectively. For a particular i\({}_{1}\), one large part of the leading S\({}^{(1)}\)(i\({}_{1}\), i\({}_{2}\), i\({}_{3}\))i\({}_{2}\),i\({}_{3}\) is picked As a result, the approximation of picture Ai1 is represented by {U(2) i2 \(\circ\) U(3) i3}i2, i3, {S(1)(i1, i2, i3), (i2, i3) \(\in\) I2,3 i1}. Equation (11) provides the covariance between two vectors. Figure 1:2  
Additionally, the average of all the pixels is given by Equation (12). Figure 1:3  
It is calculated to produce a diagonal matrix D of eigenvalues and a matrix V of corresponding eigenvectors. The detailed coefficients' m\({}_{1}\) and m\({}_{2}\) are likewise evaluated in a similar manner. Weights for the fusion rule are the average of all these m1 and m2, which are given by Equation (13). Figure 1:4  
Regarding the fused image, it is represented by Equation (14). Figure 1:5With the DWT being used as a dyadic sample with parameters x and y, which depend on powers of x = 2j and y = k * 2j; when j, k2Z are replaced with formula (15), the outcome is waves. Figure 1:6  
DTW is given by Equation (16). Figure 1:7  
The wavelet coefficients are represented by the notation dj, k, where k stands for location and j stands for level. This process is classified as the first level, for example: (A2, D2) and (A3, D3). In the following part, a statistical formula was used after obtaining these features. As a result, each signal has 2184 features as a result of the statistical functions being applied, in addition to the signal's class. Watermarking and data hiding away for double images can be arranged by one of the accompanying installing strategies: text line, word, or character moving, fixed partitioning of the image into blocks, limit modifications, adjustment of character features, change of run-length examples, and adjustments of halftone images. Information is implanted in text records by moving lines and words separating just barely (1/150 inch.) For example, a text line can be moved to encode a =1\({}^{\prime}\) or down to encode a =0\({}^{\prime}\); a word can be moved left to encode a =1\({}^{\prime}\) or right to encode =0\({}^{\prime}\).