The recorded spectra often suffer noise and band overlapping, and deconvolution methods are always used for spectral recovery. However, during the process of spectral recovery, the details cannot always be preserved. To solve this problem, two regularization terms are introduced and proposed. First, the conditions on the regularization term are analyzed for smoothing noise and preserving detail, and according to these conditions, φHL regularization is introduced into the spectral deconvolution model. In view of the deficiency of φHL under noisy condition, adaptive φHL regularization (φAHL) is proposed. Then semi-blind deconvolution methods based on φHL regularization (SBD-HL) and based on adaptive φHL regularization (SBD-AHL) are proposed, respectively. The simulation experimental results indicate that the proposed SBD-HL and SBD-AHL methods have better recovery, and SBD-AHL is superior to SBD-HL, especially in the noisy case.