Summary: In this study, we investigate the inverse problem of identifying an unknown spacewise-dependent source \(F(x)\) in the one-dimensional advection-diffusion equation \(u_t=Du_{xx}-vu_x+F(x)H(t)\), \((x,t)\in(0,1)\times(0,T]\), based on boundary concentration measurements \(g(t):=u(\ell,t)\). Most studies have attempted to reconstruct an unknown spacewise-dependent source \(F(x)\) from the final observation \(u_T(x):=u(x,T)\), but from an engineering viewpoint, the above boundary data measurements are feasible. Thus, we propose a new algorithm for reconstructing the spacewise-dependent source \(F(x)\). This algorithm is based on Fourier expansion of the direct problem solution followed by minimization of the cost functional by taking a partial \(K\)-sum of the Fourier expansion. Tikhonov regularization is then applied to the ill-posed problem that is obtained. The proposed approach also allows us to estimate the degree of ill-posedness for the inverse problem considered in this study. We then establish the relationship between the noise level \(\gamma>0\), the parameter of regularization \(\alpha>0\), and the truncation (or cut-off) parameter \(K\). A new numerical filtering algorithm is proposed for smoothing the noisy output data. Our numerical results demonstrated that the results obtained for random noisy data up to noise levels of 7% had sufficiently high accuracy for all reconstructions.