A modified Hopfield neural network model for regularized image restoration is presented. The proposed network allows negative autoconnections for each neuron. A set of algorithms using the proposed neural network model is presented, with various updating modes: sequential updates; n-simultaneous updates; and partially asynchronous updates. The sequential algorithm is shown to converge to a local minimum of the energy function after a finite number of iterations. Since an algorithm which updates all n neurons simultaneously is not guaranteed to converge, a modified algorithm is presented, which is called a greedy algorithm. Although the greedy algorithm is not guaranteed to converge to a local minimum, the l (1) norm of the residual at a fixed point is bounded. A partially asynchronous algorithm is presented, which allows a neuron to have a bounded time delay to communicate with other neurons. Such an algorithm can eliminate the synchronization overhead of synchronous algorithms.