## 2 Methodology
### Depthwise Separable Convolution  
Depthwise separable convolutions lessen the number of parameters and computation used in convolutional operations while increasing representational efficacy [54]. This kind of convolution can be applied to information such as spatial, depth dimensions, and the number of channels. While normal convolution deals with a single convolution operation, a depthwise separable convolution separates a kernel into two different kernels that carry out two convolution operations, namely, the depthwise convolution and the pointwise convolution. In the depthwise convolution, a spatial convolution is conducted independently over each channel of the input. It is followed by a pointwise convolution, where a \(1\times 1\) convolution is conducted to map the depthwise channel output into a new channel space [51].  
A standard convolution layer works by applying a convolution kernel to all channels of the input image and takes a weighted sum of the input pixels covered by the kernel sliding across all input channels of the image. This means that for a standard convolution, no matter how many input channels are available, the number of output channels is one.  
Figure 4: Proposed architecture of LDS U-Net.  
However, in depthwise separable convolutions, features are only learned from the input channels. Therefore, the output layer has the same number of channels as the input.  
Suppose in a convolution operation, the input is of size \(P_{f}\times P_{f}\times K\) with the feature map \(f\) and generates an output of size \(P_{g}\times P_{g}\times L\) with the feature map \(g\), where \(P_{f}\) is the spatial width and height of the input feature map; \(K\) is the number of input channels; \(P_{g}\) is the spatial width and height of the output feature map; and \(L\) is the number of output channels. Then, for a conventional convolution operation (Figure 5a) with the convolution kernel \(N\) of size \(P_{n}\times P_{n}\times K\times L\), where \(P_{n}\) is the spatial dimension of the kernel, the computation cost is given by the equation:  
\[G_{c}=P_{n}\.\ P_{n}\.\ K\.\ L\.\ P_{f}\.\ P_{f} \tag{1}\]  
On using the depthwise separable convolution (Figure 5b), the computation cost will be the aggregation of depthwise and pointwise convolutions and is given by the equation:  
\[G_{d}=P_{n}\.\ P_{n}\.\ K\.\ P_{f}\.\ P_{f}+\ K\.\ L\.\ P_{f}\.\ P_{f} \tag{2}\]  
Combining Equations (1) and (2), the reduction in computation can be represented by the equation:  
\[\begin{array}{ll}G&=\frac{G_{d}}{G_{c}}=\frac{P_{n}\.\ P_{n}\.\ K\.\ P_{f}\.\ P_{f}+K\.\ L\.\ P_{f}\.\ P_{f}}{P_{n}\.\ K\.\ L\.\ P_{f}\.\ P_{f}}\\ &=\frac{1}{L}+\frac{1}{P_{n}^{2}}\end{array} \tag{3}\]  
Equation (3) represents the reduction in computation requirements of the depthwise separable convolution compared to the conventional convolution, resulting in considerably lower computing and parameter cost of the network.  
As conventional U-Net, with its few layers, is not deep enough to perform this particular segmentation task, adding more layers directly and making it deeper, may solve the segmentation problem. However, a deeper neural network tends to develop gradient vanishing and redundant computation in network training [55]. To overcome these associated problems, few modifications are required to enhance the learning process of the network.