Jpeg 图像压缩：量化问题
将原始图像编码为 jpeg 图像时，8x8 数据单元会进行电平移位、使用 2-D DCT 进行变换、量化和霍夫曼编码。
我首先执行了行 DCT，然后执行了列 DCT，并将结果四舍五入为最接近的整数。我将此块发送到量化模块。在量化时，我使用了以下 Q 表。这些表是 IJG 针对品质因数 99 推荐的。
Luma Tables1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 2 2 1
1 1 1 1 1 2 2 2
1 1 1 1 2 2 2 2
1 1 2 2 2 2 2 2
1 2 2 2 2 2 2 2
1 1 1 1 2 2 2 2
1 1 1 1 2 2 2 2
1 1 1 2 2 2 2 2
1 1 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
在量化期间除以“2”时，我将结果舍入到远离零的位置。 示例：11/2 = 6。因此，在解码时的去量化过程中，每个奇数都会添加 +1 的误差。
在另一个设置中，我改变了我的舍入技术。在这里，我将结果四舍五入为零。示例：11/2 = 5。因此，在解码时的去量化过程中，每个奇数都会添加-1 的误差。
在第二种情况下，我得到的文件大小非常小（768x512 图像几乎减少了 100 kb）并且 PSNR 更高。我能够通过说所有在量化为 2 时为“1”的 AC 系数现在将变为 0 而不是 1 来解释较小的文件大小。因此，RLE 使文件大小更小。但我无法解释为什么编码图像质量不断提高。它增加了 2-3 dB，并且我测试的所有图像都发生了这种情况。
我的论点是，因为 DCT 基本上是 A * DCTmatrix，两边的相等误差应该产生相等的损失。但这里的情况并非如此。
While encoding a raw image to a jpeg image, a 8x8 data unit is level shifted, transformed using a 2-D DCT, quantized and Huffman encoded.
I have first performed the Row DCT and then the column DCT and i have rounded the result to the nearest integer. I sent this block to quantization module. While quantizing i have used the following Q Tables. These tables are recommended by IJG for quality factor of 99.
Luma Tables
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 2 2 1
1 1 1 1 1 2 2 2
1 1 1 1 2 2 2 2
1 1 2 2 2 2 2 2
1 2 2 2 2 2 2 2
Chroma Tables
1 1 1 1 2 2 2 2
1 1 1 1 2 2 2 2
1 1 1 2 2 2 2 2
1 1 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
During quantization while dividing by '2' i have rounded the result away from zero.
Example: 11/2 = 6. Hence an error of +1 will be added to every odd number during de-quantization while decoding.
In another set up i have changed my rounding technique. Here i am rounding the result towards zero. Example: 11/2 = 5. Hence an error of -1 will be added to every odd number during de-quantization while decoding.
In the second case i am getting very less file size (less by almost 100 kb for a 768x512 image) and more PSNR. I was able to explain the less file size by saying that all the AC coefficients which are '1' when quantized by 2 will now become 0 instead of 1. Hence RLE makes the file size lesser. But i am unable to explain why the encoding image quality is increasing. It is increasing by a factor of 2-3 dB and it happening for all the images i tested.
My argument is as the DCT is basically A * DCTmatrix equal error on either side should yield equal loss. But this is not the case here.
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