Block-based image processing methods and apparatus that provide a reduction in block-transform image coding artifacts are described. In various embodiments, the invention is directly incorporated into a decoding process. In such embodiments, transform coefficients are modified in simple but particularly effective ways that reduce or eliminate many of the artifacts that were caused by the quantization of the transform coefficients during encoding and/or by independent block processing during encoding. In other embodiments, the invention is used on an image that has already been decoded. In such embodiments image data values are directly modified in a block-based fashion or a forward block transform is applied and then the methods of the invention for processing transform coefficient blocks are used, followed by an inverse transform operation to generate pixel values from the resulting processed transform coefficient blocks.