Image reconstruction in complex media by the fourth moment wavelet

The discrete wavelet transform (DWT) is generally used in digital image processing to compress or filter images, its operation is based on a quadrature mirror filter that can analyze images in different frequency components. The DWT decomposes images into different sub-matrices representing the original image but in different frequencies analysis. The sub-images obtained is the representation of a low-pass filter and high-pass filter (LL), low-pass filter and high-pass filter (LH), high-pass filter and low-pass filter (HL), finally high-pass filter and high-pass filter (HH). In these sub-images the average noise is zero, but when an image is sent in a wireless channel changes the nature of the image by performing a shift of the mean value. The noise added to images can be eliminated by designing filters with high complexity and high costs, sometimes is diminished the rate of sending and receiving data sent due to the above conditions. Digital images tend to visually impaired decreasing its quality and sometimes tends to lose relevant information about this. By applying the wavelet fourth moment as a mechanism for reconstruction of digital images in noisy environments, together with a reducing estimator of the mean square error, variance and standard deviation, as detector noise in the coefficients of the sub-matrix LH of wavelet decomposition results in simulations showing up to 31 dB for the PSNR.