In this paper, we propose a convex optimization method of prefilters for image coding. JPEG, which is the de facto image coding method, generally produces some errors, e.g., blocking artifacts, under the low bit rate case. The undersampled time-domain lapped transform (TDLT) can efficiently reduce the errors. To improve the performance of the undersampled TDLT, its prefilter is determined by minimizing the errors between the original image and the image upsampled from the downsampled one. This approach enhances the performance but there exists a room for further improvements since the image derived by the prefilter would not become a smoothed image whose charactaristic is important for image coding. To resolve the problem, we consider to minimize a cost function with ℓ₁ regularization defined on the frequency domain of the downsampled image. It can be solved by using a convex optimization algorithm; the alternating direction method of multipliers. Some experimental results show the validity of our method.