# A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images
## 1 Introduction
### State of the Art
In this manner, they conduct a comparative study on various techniques used for the noise reduction in images, reaching the conclusion that spatial adaptive filters are not only the most efficient ones, but are also the easiest to implement. [PERSON] and [PERSON] implement in [21] an optimal spatial filter design for the classification of motor images derived from BCI (Brain Computer Interface). They propose an innovative extraction of features and consider an additional classification layer linked to the filter through mapping functions, leading to a higher classification accuracy. Spatial filtering was also implemented by [PERSON] et al., in [22] for the training process of a BCI. Another comparison of spatial filters is conducted by [PERSON] in [23] with the purpose of detecting oscillatory patterns in multichannel data from EEG signals. His innovative method is based on eigen decomposition and achieves a maximization of the SNR (signal to noise ratio). As a proof of its vast field of application, eigenvector adaptive spatial filtering was also studied by [PERSON] et al., in [24] for the estimation of a house price, in which they analyzed the spatial heterogeneity and the local variation. Similar techniques were also used in [25] for the trade sector, using a Poisson type regression or in [26] for the unemployment data in Germany. [PERSON] et al., even performed a MATLAB simulation of various adaptive spatial filtering algorithms in [27] for solving the problem of weak satellite signal power subject to strong interferences. They compared three types of adaptive spatial filtering algorithms: LMS (Least Mean Square), RLS (Recursive Least Square) and NLMS (Normalized Least Mean Square). In [28], [PERSON] et al., designed an optimal spatial filter for the preprocessing stage of array signals. They considered a total of five methods, amongst which the one based on the Lagrange multiplier theory proved to be the optimal one. Spatial filtering was also applied in lidar technologies by [PERSON] et al. [29]. Their objective was to remove background solar noise which the lidar instruments are sensitive to, and, therefore, their solution was to implement a voxel-based spatial filtering algorithm. Image capturing equipment can also be affected by transmission errors, atmospheric conditions or camera settings. [PERSON] and [PERSON] solve these issues in [30] by applying spatial filtering algorithms. The many applications of adaptive filtering techniques are further discussed in more depth by [PERSON] et al., in [31]. One of them is related to pattern recognition studied also by [PERSON] and [PERSON] in [32]. They propose a weighted spatial adaptive filtering in which the parameters are automatically detected and estimated. Another situation suitable for using temporal and spatial filtering methods is related to assistive communication and the sensorimotor cortex [33]. Impaired persons can control a prosthetic limb through EEG signals which, of course, are subject to noise and need to be filtered [34]. Through appropriate spatial filtering techniques of the EEG signals, mental workload can be estimated and classified [35]. [PERSON] proposes [36] an innovative solution for solving [PERSON]'s equation by implementing a spatial filtering frequency dependent model for 1D, 2D and 3D dimensions. Medical imaging is also applied in ophthalmology domain, in the study of the retinal fundus [37]. This type of image is mostly affected by Gaussian or Salt & Pepper noise which, can of course be removed through appropriate filtering methods. The most suitable one is concluded to be the adaptive median filter. [PERSON] and [PERSON] conduct an in-depth review [38] related to image denoising using spatial filtering methods. They reach the conclusion that the best method for de-noising, but also preserving image details, is by using the wavelet transform domain. Another type of spatial filtering method was proposed by [PERSON] et al., in [39]. Their filter is coherence-based and it is used to predict stimulus features extracted from brain signals.