# A Novel Implicit Neural Representation for Volume Data
## 2 Related Work
### Implicit Neural Representation  
As the memory consumption of discrete voxel grids increases cubically, the Ref. [5] suggests an implicit organ segmentation network, using continuous implicit neural representations. As the IOSNET is a continuous function, it is completely independent of spatial resolution. Because of its continuity, high-resolution medical images can be processed quickly using IOSNET. The Ref. [6] suggests DeepSDF as a fully continuous and implicit representation for generative 3D modelling. DeepSDF is based on Sign Distance Function, but it uses a generative model to produce 3D continuous interfaces. DeepSDF reduces memory consumption in comparison with its counterparts. The suggested auto-encoder in DeepSDF needs explicit optimization which consumes more time during inference. In the Ref. [7] they introduced an encoder-decoder neural architecture to losslessly compress truncated signs in distance fields (TSDF) in a 3D voxel grid. Their deep network architecture is block-based that is trained end-to-end. The main limitation of their model architecture is that the blocks are independent and identically distributed. Ignoring this limitation may help to increase the rate of compression. A lossless compression technique (MedZip) using Long Short-Term Memory (LSTM) was introduced by the Ref. [8]. Their work predicts the next intensity value using LSTM in a set of the voxels' neighbourhood concept. MedZip is the first lossless compression technique that uses LSTM for volumetric MRI and CT.  
In the Ref. [9] the authors suggested a technique to synthesize new views of a volumetric scene using implicit neural representation as a continuous function. Their technique represents a volume using a deep fully connected network with five inputs and four outputs. The network encodes the spatial location and direction to RGB and opacity. NeRF is time-consuming and its capability in complex images is not considerable. Following this work, the Ref. [1] demonstrates that using periodic activation functions outperforms ReLU-MLPs. They also suggest sinusoidal representation networks (SIRENs) that use periodic activation functions in implicit neural representation. This technique fits complex signals and natural images. In the Ref. [10] a 3D representation technique is presented to reduce the memory footprint. In their design, they use a neural network to predict the occupancy function to obtain a continuous volume. The Ref. [11] presents a compression technique using an implicit neural network (COIN) to compress natural images. It uses multi-layer perceptron (MLP) to encode geometric inputs. COIN's results are weaker than state-of-the-art compression techniques. The Ref. [12] suggests an adversarial generation of continuous images using INRs. Their model is constituted of two techniques, multi-scale INRs and factorized multiplicative modulation (INR-GAN). With this architecture, it is possible to represent high-resolution images. Because high sensitivity of INR-based techniques to high-frequency features, it leads to cause artefacts. The Ref. [13] introduces an implicit neural representation technique with prior embedding to reconstruct sampled medical images [14] suggests a generative network based on implicit neural network representation to reconstruct new viewpoints by learning from different viewpoints from input images taken. The Ref. [15] suggests using Fourier features in MLP. As a standard MLP is slow in convergence, they suggest passing the inputs of the network through a simple Fourier feature mapping. By this technique, the network can learn high-frequency functions and improve the MLPs' performance.