An apparatus and method are described for texture compression, decompression and filtering. For example, one embodiment of a method comprises: determining distances between each of a plurality of texels of a texture block and each of a plurality of approximation points; generating a decompression matrix comprising a plurality of radial basis function RBF values over the distances using a specified type of RBF; using the decompression matrix to generate a decompression-filtering matrix according to a defined filter function, the decompression-filtering matrix being usable to generate a decompressed and filtered version of the texture block as a result of the filter function being integrated into the decompression-filtering matrix.