# A New Adaptive Spatial Filtering Method in the Wavelet Domain for Medical Images
## 1 Introduction
### State of the Art
The parameters used are phase, frequency and spatial distribution of features. Electronics and telecommunications domain can also benefit on the adaptive spatial filtering applications. In [40], an analog spatial filtering method is proposed in order to improve the power consumption of a cognitive radio. [PERSON] et al., used the wavelet domain in [41] in order to generate predictive methods based on brain imaging. Their method is able to successfully predict if ADHD (attention deficit hyperactivity disorder) is present or absent. Wavelet transform domain can be used in de-noising both signals and images and this was thoroughly studied in [42] by [PERSON] et al., They compared spatial filtering to Wiener filters and obtained a higher performance of the first one. Document security and privacy can be ensured through watermarking. There are several algorithms for embedding a watermark, but not all of them generate a perfect solution. Based on the wavelet domain, an optimum watermark can be obtained, having high imperceptibility and good robustness [43]. This was also studied by [PERSON] et al., in [44] in the case of blind digital watermarking; also, wavelet domain proved to be a suitable scheme for generating a robust watermark. Super resolution images used in the medical field can be obtained by estimating wavelet coefficients at given high resolutions [45]. These coefficients are then fed into a convolutional neural network in order to reconstruct an image with improved quality. [PERSON] et al., proposed in [46] a hybrid Frequency Wavelet Domain Deconvolution for retrieving the impulse function from terahertz reflection imaging, which is further used to extract the spectroscopy features of the image. B-spline wavelet domain was used in [47] by [PERSON] et al., in order to extract useful exon information from eukaryotes' DNA. Inter-scale correlation of coefficients is used in order eliminate background noise. During decompression of an image, unwanted noise may appear. [PERSON] et al., solve this issue in [48] by using a wavelet-based approximate message passing structure. Using wavelet domain leads to a twice as fast method compared to methods not based on the wavelet domain. Thresholding is also of great importance in the wavelet transforms, especially for de-noising signals. [PERSON] and [PERSON] propose [49] a method of choosing the optimal threshold value for de-noising an electrocardiogram (ECG) signal. X-ray imaging can also benefit from the advantages of wavelet domain. In [50], [PERSON] et al., use a controlled orthonormal wavelet domain for the reconstruction of a tomographic image. Unwanted noise in clinical images and operations can be measured using several techniques [51; 52]. These measurements are useful in assessing the potential denoising power when applying different denoising methods. [PERSON] et al., extended the applications of denoising algorithms to color images through the use of a collaborative Wiener filter [53], based on block-matching fragments of the image into 3-dimensional group arrays (BM3D), thus obtaining very good PSNR (peak signal to noise ratio) results. A fast method for denoising images is the Non-Local Means (NLM) strategy, which was presented in [54], taking into consideration three aspects: noise, quality and MSE (Mean Square Error). This algorithm performed best in the case of textured images. The methods proposed in [53; 54] are applied for noise reduction in images. The results obtained in [53; 54] are good, with applicability for the analysis of macroscopic images, the noise, especially the white Gaussian noise, is significantly reduced, but the contour is degraded. The algorithm proposed in this article represents a first stage in medical image processing, and the results obtained will be used in the development of a sub-pixelation algorithm with neural networks, which will be developed in the second stage. Currently, medical imaging analyzes tumors on a macroscopic level.