In this paper, two framelet based deconvolution algorithms are proposed. The basic idea of framelet based approach is to convert the deconvolution problem to the problem of inpainting in a frame domain by constructing a framelet system with one of the masks being the given (discrete) convolution kernel via the unitary extension principle of [26], as introduced in [6,9]. The first algorithm unifies our previous works in high resolution image reconstruction and infra-red chopped and nodded image restoration, and the second one is a combination of our previous frame-based deconvolution algorithm and the iterative thresholding algorithm given by [14, 16]. The strong convergence of the algorithms in infinite dimensional settings is given by employing proximal forward-backward splitting (PFBS) method. Consequently, it unifies iterative algorithms of infinite and finite dimensional setting and simplifies the proof of the convergence of the algorithms of [6].