Hi,

you can use JPEG itself! Here is my code, but I make no efforts to optimize it thus it can be really slow. First of all, you need define RGB to

YCbCr transform. I found very nice code

here via Mr.Wizard (up to some small correction):

With[{v1 = Developer`ToPackedArray@{16`, 128`, 128`},

m1 = Developer`ToPackedArray@{{65.481, 128.553,

24.966}, {-37.797, -74.203, 112`}, {112`, -93.786, -18.214}}},

RGBtoYCbCr[a : {_, _, _}?VectorQ] := v1 + m1.a;

RGBtoYCbCr[img_Image] := RGBtoYCbCr@ImageData[img(*,"Byte"*)];

RGBtoYCbCr[a_ /; MatchQ[Dimensions@a, {_, 3}]] :=

Transpose[v1 + m1.Transpose[a]];

RGBtoYCbCr[a_ /; MatchQ[Dimensions@a, {_, _, 3}]] :=

Transpose[v1 + m1.Transpose[a, {2, 3, 1}], {3, 1, 2}];]

Inverse transform:

With[{v1 = Developer`ToPackedArray@{-16`, -128`, -128`},

m1 = Developer`ToPackedArray@

Inverse@{{65.481, 128.553, 24.966}, {-37.797, -74.203,

112`}, {112`, -93.786, -18.214}}},

YCbCrtoRGB[a : {_, _, _}?VectorQ] := m1.(a + v1);

YCbCrtoRGB[a_ /; MatchQ[Dimensions@a, {_, 3}]] :=

Transpose[m1.(Transpose[a] + v1)];

YCbCrtoRGB[a_ /; MatchQ[Dimensions@a, {_, _, 3}]] :=

Transpose[m1.(Transpose[a, {2, 3, 1}] + v1), {3, 1, 2}];]

Then it is necessary to define the Fourier discrete cosine transform.

fnorm = Developer`ToPackedArray@

Normal@SparseArray[{{1, 1} -> 1, {i_, i_} -> Sqrt[2]}, {8, 8}];

bnorm = Developer`ToPackedArray@

Normal@SparseArray[{{1, 1} -> 1, {i_, i_} -> 1/Sqrt[2]}, {8, 8}];

ForwardDCT[matrix_] := fnorm.FourierDCT[matrix - 128, 2].fnorm;

BackwardDCT[matrix_] := 128 + FourierDCT[bnorm.matrix.bnorm, 3];

Please, notice the JPEG uses DCT in slightly different way than Wolfram Mathematica. Next step is to define the quntization tabels for all channels:

DQT["luma"] =

Developer`ToPackedArray@{{16, 11, 10, 16, 24, 40, 51, 61}, {12, 12,

14, 19, 26, 58, 60, 55}, {14, 13, 16, 24, 40, 57, 69, 56}, {14,

17, 22, 29, 51, 87, 80, 62}, {18, 22, 37, 56, 68, 109, 103,

77}, {24, 35, 55, 64, 81, 104, 113, 92}, {49, 64, 78, 87, 103,

121, 120, 101}, {72, 92, 95, 98, 112, 100, 103, 99}};

DQT["chroma"] =

Developer`ToPackedArray@{{17, 18, 24, 47, 99, 99, 99, 99}, {18, 21,

26, 66, 99, 99, 99, 99}, {24, 26, 56, 99, 99, 99, 99, 99}, {47,

66, 99, 99, 99, 99, 99, 99}, {99, 99, 99, 99, 99, 99, 99,

99}, {99, 99, 99, 99, 99, 99, 99, 99}, {99, 99, 99, 99, 99, 99,

99, 99}, {99, 99, 99, 99, 99, 99, 99, 99}};

The last step is the quntization itself:

Quantization[channel_, block_, quality_] :=

BackwardDCT[

quality DQT[channel] Round[

ForwardDCT[block]/(quality DQT[channel])]];

Now, we can start. Import an image and divide it into 8*8 blocks:

horse = Import["http://i.stack.imgur.com/ZhYwB.jpg"]

blocks = Partition[#, {8, 8}] & /@

Transpose[RGBtoYCbCr@horse, {2, 3, 1}];

Then we need to choose the quality of the output.

quality = 2;

Notice that the quality should be large than 1 and quality=1 reduces the size of the output file by factor 1.8. Thus we put a really terrible quality. The next step is quantization of each channel:

luminance[1] =

Join @@ (Join @@@ Transpose[#, {2, 1, 3}] & /@

Map[Quantization["luma", #, quality] &, blocks[[1]], {2}]);

chrominance[1] =

Join @@ (Join @@@ Transpose[#, {2, 1, 3}] & /@

Map[Quantization["chroma", #, quality] &, blocks[[2]], {2}]);

chrominance[2] =

Join @@ (Join @@@ Transpose[#, {2, 1, 3}] & /@

Map[Quantization["chroma", #, quality] &, blocks[[3]], {2}]);

This part works really slow, hence please try to optimize it. The last step is to convert to RGB and save to disk:

SetDirectory[NotebookDirectory[]];

Export["horse.jpg",

Image[YCbCrtoRGB@

Transpose[{luminance[1], chrominance[1], chrominance[2]}, {3, 1,

2}]]]

The size of the output file is 2.2 times smaler then initial one. The Mathematica file is attached to this post.

**Attachments:**