Answer: The Gemara teaches “one should not Daven in a state of frivolity, idle chat, anger” etc. This includes situations that might cause us to be distracted while davening.According to Halacha, we are not permitted to Daven facing a picture or drawing etc. because it has the potential to divert our attention from the Tefilla. The same holds true regarding a mirror, since there is no difference between a picture or drawing, or the image of the person himself. (Our instant discussion is limited to "davening while facing these images/pictures". In another post, I will discuss whether pictures are at all permitted in a shul).Furthermore, we may not even use a Siddur during davening, which contains pictures , nor are we allowed to daven in a place where there is a Sefer/book with pictures on it. There may be room for leniency in situations where one is accustomed to these pictures, but even then it's preferable to move the pictures away during davening.
If glancing at a picture of the Rebbe while davening, would increase our concentration and focus, would we be permitted to do so?.The Gemara relates the story of R’ Yochanan who had long eyebrows that covered his eyes and obstructed his view. Rav Kahana came to study under R’ Yochanan and challenged him on several statements. R’ Yochanon asked for his eyebrows "to be lifted" in order that he might "see" (who has been challenging him) Rav Kahana. Upon seeing Rav Kahana, R’ Yochanan thought that he was mocking him (Rav Kahana's lips had been split and thus it appeared that he was smiling). Upon seeing Rav Kahana "smile", Rav Yochanan became weak. As a result, Rav Kahana died. (Don't worry, Rav Yochanan was able to revive Rav Kahana).The Maharsha explains that R’ Yochanan’s intent was to empower Rav Kahana, by having him look at his face, based on the Posuk “our eyes will see our teacher”. This concept is explained further by the Radvaz, who writes that when we look at our Rebbe's face or "envision" it, a new spirit of holiness shines down upon us, which empowers us to reach higher levels in our learning and Davening.There is another reason for not davening in front of a picture or image. It might be construed as if we are bowing to the image. Based on this, even a picture of the Rebbe should have the same Din.I heard of a situation where someone went to Daven in front of a Pushkah that had a picture of the Rebbe on it. Rabbi H. Pevzner removed the pushkah.L’halacha: One should not Daven in a place where there are pictures in front of him unless they are higher than his eyes can see, the same holds true about a picture of the Rebbe. There is a concept to look at a picture of the Rebbe before one starts to Daven.Daily inspiration:The human senses take in information from the world around us. As a consequence, we are constantly influenced by our environment and the things we see and hear. The effect of sight leaves a permanent impact on our subconscious mind. As a result, the more pristine an imagery we behold, the more pure our mind and actions will be.
 ברכות ל"א: שוע"ר סי' צ: כ"ב שו"ת רדב"ז ח"א סי' ק"ו עי' שם ומחצית השקל סי' צ סקל"ז עי' שו"ע יו"ד סי' קמ"א:ד ושו"ת דברי מלכיאל ח"ו סי' ב' אות ג-ד ושם סי' י"ג ושו"ת ציץ אליעזר חי"ט סי' ח שוע"ר שם עי' פר"ח סי' צ:כ"ג עי' שו"ת דברי יחזקאל ח"א סי' ט"ו ואגה"ק מהרבי חלק י ע' קלו-ז אגה"ק שם לכאו' אין כאן שייך הדין בשוע"ר שם סעי' כ"ג דזהו רק כשהוא שם בבא קמא קי"ז. חידושי אגדות שם שו"ת ח"ג סי' תע"ב ועי' ס' חסד לאברהם מעין שני נהר ל"גשו"ת רדב"ז ח"א סי' ק"ו פרמ"ג סי' צ' משב"ז סק"ו שו"ת אור לציון ח"ב פ"ז אות י"א עי' שו"ת הנ"ל וערה"ש סי' צ' סעי' כ"ח כך שמעתי מזקיני שליט"א שוע"ר שם ועי' פרמ"ג שם א"א סקל"ז