In my opinion your specimens should be Thalassiosira proschkinae considering the processes pattern, general aspect, size, morphology of the fultoportulae, etc. Nevertheless, you should consider the literature for confirming.
Firstly I think that those diatoms belong to T. spinulata. According to Takano (1981) that species has 3 satellite pores (see first attached text) as diatoms on photos. After that I've found in Park et al. (2009) that Makarova (1988) reclassified that species to T. proschkinae var. spinulata (see second attached text). And finally I look into Algaebase and found that now it is a synonym of T. proschkinae.
For me is "spinulata" - it is very different for typical "proschkinae"! But in case, that you have not taxonomical; study - and the eco;ogy is similar, give it as species "proschkinae"! It is a pity, because the best taxonomists of Thalassiosira (Ira Makarova and Greta Hasle) have not any followers....There are a lot of "gaps" in more centric genera!! Success!
Iraida Makarova has a comment in her 1988 book. She wrote that she found intermediate forms between T. proschkinae and T. spinulata. They differ from T. proschkinae by the presence of tiny spinula on areolae ribs (as on photo), and they differ from T. spinulata by the presence of tangential ribs between areolae (as on photo). Also founded speciments has 3 satellite pores as T. spinulata. So I don't know how to correctly name founded diatoms. They more belongs to T. spinulata - if it is a correct taxonomic name.
You have possibility to determine it as "spinulata", I have seen also - that there are different dimensions? as well as - the structure of the areolae is different,isn't it? I have seen this comment of Makarova (1988) - and I agree, that this is not the same form - as "proschkina"! Is there any new determination?
To determine it as "spinulata" we need to check, can "proschkinae" develop spunula on areolae ribs during its ontogenic cycle or can not? If it can, it is a morphotype of "proschkinae", if it cann't - it is a separate species "spinulata".