Nonstationary seismic data can be expressed using a linear matrix-vector multiplication system derived from wave theory when anelastic effects of the earth can be quantified by the intrinsic quality factor (or ) and is frequency independent in the seismic bandwidth. On the basis of the linear modeling system and singular value decomposition, we have assessed the stability using weights associated with the left singular vectors, data, and singular values, and we assessed the compensation/resolution limitation of inversion-based deabsorption using the right singular vectors. In addition, a stable inversion-based multitrace deabsorption method was developed by minimizing the -norm of coefficients in the frequency-wavenumber () domain of reflectivity subject to the time-domain nonstationary data misfit. The optimum deabsorption result can be obtained by sequentially solving a series of lasso subproblems until the stopping condition is reached. As the number of solving lasso subproblems increases, the role of magnitude sparsity constraint relative to data misfit gradually decreases. In this way, the proposed method can highlight the spatial continuities and reduce the influence of noise on the updated result during starting iterations due to magnitude sparsity, whereas compensate details including some discontinuities of events and weak reflections during later iterations due to the dominant role of data misfit. We tested the method on a series of data sets, including a synthetic data set, a physical modeling data set, and a field data set. Our results determined that the proposed method can provide stable compensation results, even in the presence of coherent noise and/or strong random noise. Compared with the trace-by-trace -norm regularization deabsorption method, our method performed better in spatial continuity preservation and weak signal compensation.