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How does a predictive coding aid in lossless compression?
Lossless Video Compression PipelineCompressing normally distributed dataHow can GIF compression be lossless if the maximum # of colors is 256?Hash for verifying both compressed and uncompressed data?Can random suitless $52$ playing card data be compressed to approach, match, or even beat entropy encoding storage? If so, how?Arithmetic coding and “the optimal compression ratio”How does adaptative Huffman coding (Vitter algorithm) work?Universal Lossless Compression?Is von Neumann's randomness in sin quote no longer applicable?Algorithm for estimating lossless compression factor
$begingroup$
I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
asked 1 hour ago
Liam F-ALiam F-A
211
$endgroup$
add a comment |
$begingroup$
I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
asked 1 hour ago
Liam F-ALiam F-A
211
$endgroup$
add a comment |
$begingroup$
I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
asked 1 hour ago
Liam F-ALiam F-A
211
$endgroup$
I'm working on this lab where we need to apply a lossless predictive coding to an image before compressing it (with Huffman, or some other lossless compression algorithm).
From the example seen below, it's pretty clear that by pre-processing the image with predictive coding, we've modified its histogram and concentrated all of its grey levels around 0. But why exactly does this aid compression?
Is there maybe a formula to determine the compression rate of Huffman, knowing the standard deviation and entropy of the original image? Otherwise, why would the compression ratio be any different; it's not like the range of values has changed between the original image and pre-processed image.
Thank you in advance,
Liam.
image-processing data-compression huffman-coding
image-processing data-compression huffman-coding
asked 1 hour ago
Liam F-ALiam F-A
211
asked 1 hour ago
Liam F-ALiam F-A
211
asked 1 hour ago
Liam F-ALiam F-A
211
asked 1 hour ago
Liam F-ALiam F-A
211
asked 1 hour ago
Liam F-ALiam F-A
211
211
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
$endgroup$
add a comment |
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1 Answer
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$begingroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
$endgroup$
add a comment |
$begingroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
$endgroup$
add a comment |
$begingroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
$endgroup$
Huffman coding, as usually applied, only considers the distribution of singletons. If $X$ is the distribution of a random singleton, then Huffman coding uses between $H(X)$ and $H(X)+1$ bits per singleton, where $H(cdot)$ is the (log 2) entropy function.
In contrast, predictive coding can take into account correlations across data points. As a simple example, consider the following sequence:
$$
0,1,2,ldots,255,0,1,2,ldots,255,ldots
$$
Huffman coding would use 8 bits per unit of data, whereas with predictive coding we could get potentially to $O(log n)$ bits for the entire sequence.
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
answered 1 hour ago
Yuval FilmusYuval Filmus
196k15184349
196k15184349
add a comment |
add a comment |
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