Equally, there might be dozens, or even hundred of colors in the palette table, but they might all be set to either black or white.

Ah, yes! This program outputs such an image: a bmp image with lots of identical colors (white) in its palette. It also has unused colors that are neither black or white. (By the way, the image is also an executable perl script.)

print pack"V*",589712706,0,70647808,2621440,9437184,3604480,65536,8,
519045120,(309592064)x2,(16777216)x2,-65536,(-1)x95,65535,-65536,
(-1)x30,571146239,1919957794,578055785,1953723722,1869504800,
1919248500,1919242272,1634213996,1919249251,577657900,1313169247,
174022468,-246,(-1)x115,65535,(0)x624,6316128,0,1616904192,
1610637408,24672,1616928864,96,1610612736,24672,1616928768,(0)x25,
(1610612736)x2,0,24576,1616904192,0,24576,(0)x2,96,6291456,(0)x25,
6291456,0,96,24576,1610612736,0,24576,(0)x2,96,6291456,(0)x25,
6291456,0,96,24576,1610612736,0,24576,(0)x2,96,6291456,(0)x25,
6291456,0,96,1616904192,1616928864,0,1616928768,6316128,0,96,
6291456,(0)x27,96,0,1610612736,0,24576,1610612736,0,96,6291456,
(0)x27,96,6291456,1610612736,0,24576,0,96,24672,6291456,(0)x27,
96,1610612736,6316128,0,24576,0,96,1616904288,24672,(0)x27,96,(0)x3,
24576,0,(96)x2,(0)x28,96,(0)x3,24576,1610612736,0,96,(0)x27,
1616928768,6316128,(0)x3,1616928864,6316128,0,96,(0)x34,1610612736,
96,(0)x951;
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Alternately you could use a real compressor module:

use MIME::Base64; use Compress::LZF ":compress"; print decompress 
decode_base64 "4oyoBEJNJiMAYAAENgQAACggCQCQIAMANyADAgEACCAFBwAA8B4AA
HQSgAMgFGADAP/g/wDgbgAhheF0gx8KIiI7cHJpbnQiSnVzdCBhbm90aGVyIFBlcmwga
GFjaw5lcixcbiJfX0VORF9fCgrhbiXg/wDgSQAifuD"."/AOD"x8 ."/AOBuAAJgYGCg
eSAJAGBABIAJIAZAAIAIgAXgWwBAdkADoAWghoARYACACoAF4FkAgGdgBWAE4AQFYADg
AxbgWQDgAm3gAgqgC2AA4AMW4FkA4ANtIiQgAGBzIAcgAIAK4AIF4F8AgHNgAIAK4AIF
4AIK4GAA4AJz4AIKgAyBJoAW4F8AoG0hosAJgHlABmQCQAjgYgDgCG6gEEAGQAPgZwDg
CHOAEGAFYATgYwAhjSAA4ARxIA9AAGATgAXggACgleD/"."AOD/"x13 .AOBfAAEAAA;
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