Image deconvolution is an ill-posed problem thatusually requires prior knowledge for regularizing the feasiblesolutions. In the literature, iterative methods estimate an intrinsic image, minimizing a cost function regularized by specific priorinformation. However, it is difficult to directly minimize the constrained cost function, if a nondifferentiable regularization (e.g.,the sparsity constraint) is employed. In this paper, we proposea nonderivative image deconvolution algorithm that solves the under-constrained problem (i.e., a non-blind image deconvolution) by successively solving the permuted subproblems. The subproblems, arranged in permuted sequences, directly minimize the nondifferentiable cost functions. Various L p-regularized (0 < p ≤ 1, p = 2) objective functions are utilized to demonstrate the pixel-wise optimization, in which the projection operator generates simplified, low-dimensional subproblems for estimating each pixel. The subproblems, after projection, are dealt within the corresponding hyperplanes containing the adjacent pixels of each image coordinate. Furthermore, successively solving the subproblems can accelerate the deconvolution process with a linear speedup, by parallelizing the subproblem sequences. The image deconvolution results with various regularization functionals are presented and the linear speedup is also demonstrated with a parallelized version of the proposed algorithm. Experimental results demonstrate that the proposed method outperforms the conventional methods in terms of the improved signal-to-noise ratio and structural similarity index measure.