MATLAB Code Implementation for Small Image Denoising

This paper presents a MATLAB implementation for small image denoising using wavelet thresholding techniques. The algorithm begins by calculating the denoising threshold using the formula th=sigma*sqrt(2*log10(L*T)), where sigma represents noise standard deviation, L denotes signal length, and T is a scaling parameter. The implementation then processes high-frequency wavelet coefficients through systematic thresholding operations. The core denoising mechanism involves extracting high-frequency components using indexing operations like ch=c(1,num(4-i,1):num(4-i,3)+step(4-i)-1), followed by applying a customized thresholding function. For coefficients where abs(ch(j))>=th, the algorithm applies a modified soft-thresholding operation: ch(j)=sign(ch(j))*(abs(ch(j))-2*th/(1+exp(m*(ch(j)^2)))). This sophisticated thresholding function incorporates sigmoid modulation (through the exp(m*(ch(j)^2)) term) to create smooth transitions between thresholded and preserved coefficients, effectively reducing noise while maintaining important image features. The MATLAB code implements these operations through loop structures (for j=1:chl) and conditional processing to handle various frequency bands systematically.