The Unreasonable Effectiveness of JPEG: A Signal Processing Approach

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Chapters:
00:00 Introducing JPEG and RGB Representation
2:15 Lossy Compression
3:41 What information can we get rid of?
4:36 Introducing YCbCr
6:10 Chroma subsampling/downsampling
8:10 Images represented as signals
9:52 Introducing the Discrete Cosine Transform (DCT)
11:32 Sampling cosine waves
12:43 Playing around with the DCT
17:38 Mathematically defining the DCT
21:02 The Inverse DCT
22:45 The 2D DCT
23:49 Visualizing the 2D DCT
24:35 Introducing Energy Compaction
26:05 Brilliant Sponsorship
27:23 Building an image from the 2D DCT
28:20 Quantization
30:23 Run-length/Huffman Encoding within JPEG
32:56 How JPEG fits into the big picture of data compression
The JPEG algorithm is rather complex and in this video, we break down the core parts of the algorithm, specifically color spaces, YCbCr, chroma subsampling, the discrete cosine transform, quantization, and lossless encoding. The majority of the focus is on the mathematical and signal processing insights that lead to advancements in image compression and the big themes in compression as a whole that we can take away from it.
Animations created jointly by Nipun Ramakrishnan and Jesús Rascón.
References/Additional Resources:
www.red.com/red-101/video-chr... - great resource on different types of chroma subsampling
weitz.de/dct/ - play around with the DCT
www.cse.iitd.ac.in/~pkalra/co... - paper referenced in video
www.ee.ic.ac.uk/hp/staff/dmb/c... - a more rigorous signal processing approach to the DCT
www.impulseadventure.com/phot... - great landing point for learning more about how huffman codes work in the context of JPEG
• Everything You Need to... - a great playlist I recommend that dives deep into actually implementing a JPEG decoder
This video wouldn't be possible without the open source library manim created by 3blue1brown and maintained by Manim Community.
The Manim Community Developers. (2021). Manim - Mathematical Animation Framework (Version v0.11.0) [Computer software]. www.manim.community/
Here is link to the repository that contains the code used to generate the animations in this video: github.com/nipunramk/Reducible
All music in the video is from Aakash Gandhi