The　homodyned-K　(HK)　distribution　model　is　a　generalized　backscatter　envelope　statistical　model　for　ultrasound　tissue　characterization,　whose　parameters　are　of　physical　meaning.　To　estimate　the　HK　parameters　is　an　inverse　problem,　and　is　quite　complicated.　Previously,　we　proposed　an　artificial　neural　network　(ANN)　estimator　and　an　improved　ANN　(iANN)　estimator　for　estimating　the　HK　parameters,　which　are　fast　and　flexible.　However,　a　drawback　of　the　conventional　ANN　and　iANN　estimators　consists　in　that　they　use　Monte　Carlo　simulations　under　known　values　of　HK　parameters　to　generate　training　samples,　and　thus　the　ANN　and　iANN　models　have　to　be　re-trained　when　the　size　of　the　test　sets　(or　of　the　envelope　samples　to　be　estimated)　varies.　In　addition,　conventional　ultrasound　HK　imaging　uses　a　sliding　window　technique,　which　is　non-vectorized　and　does　not　support　parallel　computation,　so　HK　image　resolution　is　usually　sacrificed　to　ensure　a　reasonable　computation　cost.　To　this　end,　we　proposed　a　generalized　ANN　(gANN)　estimator　in　this　paper,　which　took　the　theoretical　derivations　of　feature　vectors　for　network　training,　and　thus　it　is　independent　from　the　size　of　the　test　sets.　Further,　we　proposed　a　parallelized　HK　imaging　method　that　is　based　on　the　gANN　estimator,　which　used　a　block-based　parallel　computation　method,　rather　than　the　conventional　sliding　window　technique.　The　gANN-based　parallelized　HK　imaging　method　allowed　a　higher　image　resolution　and　a　faster　computation　at　the　same　time.　Computer　simulation　experiments　showed　that　the　gANN　estimator　was　generally　comparable　to　the　conventional　ANN　estimator　in　terms　of　HK　parameter　estimation　performance.　Clinical　experiments　of　hepatic　steatosis　showed　that　the　gANN-based　parallelized　HK　imaging　could　be　used　to　visually　and　quantitatively　characterize　hepatic　steatosis,　with　similar　performance　to　the　conventional　ANN-based　HK　imaging　that　used　the　sliding　window　technique,　but　the　gANN-based　parallelized　HK　imaging　was　over　3　times　faster　than　the　conventional　ANN-based　HK　imaging.　The　parallelized　computation　method　presented　in　this　work　can　be　easily　extended　to　other　quantitative　ultrasound　imaging　applications.　©　2023　Elsevier　B.V.