Probably both are acceptable. However, the version with the article may be preferred, and perhaps especially so in British English.
The question here is whether the noun perspective in the relevant sense is countable or uncountable. If it is countable, then the fact that it appears in the singular means that it normally requires a determiner (an/the/our/that emotional perspective). But if it is uncountable, then if it is meant to be indefinite (as in your sentence), then it should be without a determiner.
Several dictionaries have the useful feature that, as part of the definition provided, they say whether a noun is countable or not.
Cambridge Dictionary says that, in the relevant sense of the word (a particular way of viewing things that depends on one’s experience and personality), the noun perspective is countable in British English, whereas in American English it can be either countable or uncountable.
On the other hand, both Macmillan and Collins dictionaries say that, in the relevant sense, perspective is countable.
Finally, the Oxford English Dictionary does not provide explicit information about countability of nouns, but it does provide examples of usage. For what it's worth, among the examples that are not older than the late 19th century, only two are in the singular and not marked as definite, and both include the indefinite article.
A possible confusion with other senses of the word
A possible source of confusion is that perspective has another meaning in which it is certainly uncountable in both American and British English and according to all dictionaries, namely the meaning relevant to art (the method by which solid objects drawn or painted on a flat surface are given the appearance of depth and distance).
Furthermore, there is yet another sense of the word perspective, which is rather close to the sense relevant to us and according to which it is uncountable: a sensible way of judging how good, bad, important, etc. something is in comparison with other things (e.g. It’s important to keep things in perspective and not dwell on one incident.; Writing as a foreigner gives her a great sense of perspective).
One may speculate that at least some instances of omission of the indefinite article when perspective is used as in your examples stem from confusing that sense with one of the other two in which the word is unambiguously uncountable.