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The striker is currently grappling with his own self-belief, but he's been here before.
The pressure is heightened by the size of the investment Celtic made. Hogh arrived as the club's record signing and was expected to provide an immediate cutting edge at the top end of the pitch. Instead, the Dane has scored in just one of his first 14 appearances, with all three of his goals arriving in a devastating 45-minute burst against Kilmarnock.
Since then, the floodgates many expected to open have remained firmly shut, leaving a striker recruited to solve Celtic's biggest problem still searching for the consistency required to justify his hefty £11m price tag.
It's crystal clear Celtic look a better team with Camilo Duran leading the line and, in truth, even when Chelsea loanee Shim Mheuka is introduced during the closing stages of matches.
But if there is one saving grace, it is that Hogh has been here before, condemned in public before launching a turnaround for the ages.
Not so long ago, Hogh was being ridiculed in his adopted home of Norway despite helping Bodo/Glimt become one of Europe's great overachievers. Former Norway international and TV pundit Carl-Erik Torp famously questioned whether the Dane was good enough for the highest level and delivered the savage verdict that he was "more of a Lada than a Lamborghini".
For many strikers, that sort of public dressing-down can be too much to overcome.
Not for the charismatic Dane.
With doubts swirling over his ability to lead the line in the Champions League, he responded in the only currency that matters to forwards: goals. Big goals.
The criticism reached its peak before a European showdown with Manchester City. Then came the turnaround.
Hogh struck twice on the biggest stage of his career, leaving Torp and the doubters scrambling to reassess their judgement.
He kept scoring and his knack for delivering in the biggest games ultimately led to Celtic splashing the cash in the summer.
The striker who had been branded a clunky runabout suddenly looked every bit the elite frontman Bodo/Glimt believed he could become.
Martin O'Neill insists the man stuck on three goals will score 20 this season and there remain crumbs of comfort when it comes to the striker's future.
The player who missed chances aplenty against Dundee on the opening night of the season still looked razor-sharp despite failing to convert every opportunity.
He then filled his boots at Rugby Park before leading the line impressively against LASK in the first leg of the Champions League play-off.
Then it all went south.
There are no guarantees Hogh won't prove to be a mammoth misfire. However, despite his current woes, Celtic have a player with a proven history of defying the odds and proving his critics wrong.