1 简介
Decomposition of digital signals and images into other basis or dictionaries than time or space domains is a very common approach in signal and image processing and analysis. Such a decomposition is commonly obtained using fixed transforms (e.g., Fourier or wavelet) or dictionaries learned from example databases or from the signal or image itself. In this work, we investigate in detail a new approach of constructing such a signal or image-dependent bases inspired by quantum mechanics tools, i.e., by considering the signal or image as a potential in the discretized Schroedinger equation. To illustrate the potential of the proposed decomposition, denoising results are reported in the case of Gaussian, Poisson, and speckle noise and compared to the state of the art algorithms based on wavelet shrinkage, total variation regularization or patch-wise sparse coding in learned dictionaries, non-local means image denoising, and graph signal processing.
2 部分代码
% Sample code of the paper:% This script shows an example of calling our denoising algorithm % for signal using Quantum adaptative basis (QAB)function [psi,E] = f_ondes1D(signal,poids)% %the Hamiltonian associates with the signal and the associated eigenvalues% DataN = size(signal,2); % creat space to store datapsi = zeros(N,N); %eigenvectorsE = zeros(N,1); %eigenvalues % Construction of Hamiltonian matrice Hterme_hsm = ones(1,N) * poids;H = diag(signal,0) + diag(terme_hsm,0)*2 ... - diag(terme_hsm(1:N-1),-1) - diag(terme_hsm(1:N-1),1);H(1,N) = -poids;H(N,1) = -poids; % Calculation of eigenvalues and eigenvectors[vectP,valP] = eig(H);valP = diag(valP);vp_min = min(valP);vp_max = max(valP); for g = 1:N % Each iteration finds the "following" eigenvector %(sorts the vectors in ascending order of the associated eigenvalues) [valP_assoc,i_psi] = min(valP); psi(:,g) = vectP(:,i_psi); E(g) = valP(i_psi); valP = [valP(1:(i_psi - 1)) ; valP((i_psi + 1):(N - g + 1))]; vectP = [vectP(:,1:(i_psi - 1)) vectP(:,(i_psi + 1):(N - g + 1))]; endend
3 仿真结果
4 参考文献
[1] Dutta S , Basarab A , Georgeot B , et al. Quantum Mechanics-Based Signal and Image Representation: Application to Denoising[J]. 2021.
博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，相关matlab代码问题可私信交流。
部分理论引用网络文献，若有侵权联系博主删除。
