Lossless and Near-Lossless Compression Algorithms for Remotely Sensed Hyperspectral Images
Abstract
:1. Introduction
- A novel lossless compression technique of remotely sensed hyperspectral images is proposed by employing our recent method of seed generation based on bit manipulation techniques [39]. Four variations are employed in our experiments using the Corpus dataset of HSIs. Our performance results yield an enhancement in data reduction that reaches 29.89% when comparing the corresponding geometric mean value with that obtained by the state-of-the-art ${k}^{2}$-raster method [40].
- A novel near-lossless compression of HSIs is also proposed by incorporating our published quadrature-based square rooting method [39]. A data reduction that varies from 38.90% to 39.73% is realized with a maximum relative error of 0.33 and a maximum absolute error of only 30. Since hyperspectral images with high entropies are hard to losslessly compress due to their reduced correlation, this approach can be applied with a small to negligible impact on the accuracy of the decompressed data.
2. Related Work
3. Lossless Compression
3.1. Computation of the Integral Part
3.1.1. Error Compensation
Algorithm 1. $\mathrm{Calculation}\mathrm{of}\mathrm{the}\mathrm{integer}\mathrm{square}\mathrm{root}\mathrm{of}x\mathrm{by}\mathrm{rolling}\mathrm{back}\mathrm{from}{s}_{0}$. |
Input: $x,{s}_{0}$ Output: $s$$//\mathrm{integer}\mathrm{square}\mathrm{root}\mathrm{of}x$ Initialization: ${s}_{i}\leftarrow {s}_{0}$ $D\leftarrow {s}_{i}^{2}-x$ While $(D0$) Do ${s}_{i}\leftarrow {s}_{i}-1$ $D\leftarrow D-({s}_{i}\ll 1)-1$ End Do $s\leftarrow {s}_{i}$ |
3.1.2. Error Avoidance
3.2. Computation of the Fractional Part
3.3. Preprocessing
3.4. Postprocessing
3.5. Lossless Encoder/Decoder
Algorithm 2. Pseudocode for the compressor part of the proposed lossless compression. |
Input: $x$ // hyperspectral data Outputs: vecRice, // a vector that stores the calculated seed values. vecFrac, // a vector that stores the calculated fractions. vecRLE, // a vector that holds the counts of consecutive runs of zero and nonzero values. vecUnary. // a vector that holds the variable unary codes corresponding to the number of bits of each count. Initializations: ${x}_{0}\leftarrow 0$$,//\mathrm{the}\mathrm{initial}\mathrm{value}\mathrm{to}\mathrm{be}\mathrm{XORed}\mathrm{with}\mathrm{the}\mathrm{first}\mathrm{element}\mathrm{of}x$. ${nZ}_{0}\leftarrow 0$, // initialize the first nonzero value with 0. $cnt\leftarrow 1$, // counts the number of consecutive runs. $PO2\leftarrow 2$, // to calculate the required number of bits for each run. $nVar\leftarrow 11$, // the required number of bits for each run. $n\leftarrow $$\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{bits}\mathrm{required}\mathrm{to}\mathrm{represent}x$. $\mathrm{done}\leftarrow 0$ For all ${x}_{i}$$\mathrm{in}x$ Do 1. Preprocessing $xored\leftarrow {x}_{i}\oplus {x}_{i-1}$ // perform exclusive-or operation. If $xored>0$ Then ${nZ}_{i}\leftarrow 1$ 2. Calculation of the integral part $MSH\leftarrow $$\mathrm{the}\mathrm{leftmost}\lceil n/2\rceil $$\mathrm{bits}\mathrm{of}xored$
$$Q\leftarrow {2}^{\u230an/2\u230b}$$
$riceCode\leftarrow \mathrm{m}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{d}\mathrm{R}\mathrm{i}\mathrm{c}\mathrm{e}\left(seed\right)$ $\mathrm{vecRice}.\mathrm{add}(riceCode$) 3. Calculation of the fractional part $m\leftarrow \u2308{\mathrm{log}}_{2}\left(2\cdot seed\right)\u2309$ $Fr\leftarrow xored-{seed}^{2}$ // The fraction encoded as the distance between the xored value and the squared value of the seed If $Fr>0$ Then $Fr\leftarrow Fr-1$ Else $Fr\leftarrow \mathrm{U}\mathrm{n}\mathrm{a}\mathrm{r}\mathrm{y}\left(seed\right)$ $seed\leftarrow 0$ End If ${Fr}_{out}\leftarrow $ $\mathrm{the}\mathrm{rightmost}m$$\mathrm{bits}\mathrm{of}Fr$ $\mathrm{vecFr}.\mathrm{add}({Fr}_{out}$) Else ${nZ}_{i}\leftarrow 0$ End If 4. Run length encoding of $\mathit{n}\mathit{Z}$ If ${nZ}_{i}={nZ}_{i-1}$ Then $cnt\leftarrow cnt+1$ If $cnt=PO2$ Then $PO2\leftarrow PO2\ll $ 1 $nVar\leftarrow nVar+1$ End If Else $\mathrm{vecRLE}.\mathrm{add}(cnt$) $\mathrm{vecUnary}.\mathrm{add}(nVar$) $cnt\leftarrow 1$ $PO2\leftarrow 2$ End If End Do If done Then $\mathrm{vecRLE}.\mathrm{add}(cnt$) $\mathrm{vecUnary}.\mathrm{add}(nVar$) End If |
Algorithm 3. Pseudocode for the decompressor part of the proposed lossless compression. |
Inputs: vecRice, vecFrac, vecRLE, vecUnary. Output: $x$ // reconstructed hyperspectral data. Initializations: $nVar\leftarrow $ the number of bits derived from the next unary code in vecUnary. $cnt\leftarrow $$\mathrm{the}\mathrm{run}\mathrm{length}\mathrm{obtained}\mathrm{by}\mathrm{interpreting}\mathrm{the}\mathrm{next}nVar$ bits from vecRLE. $Flag\leftarrow 0$ For all $cnt$ in vecRLE Do While $cnt>0$ Do If $Flag=0$ Then ${x}_{i}\leftarrow 0$ Else $riceCode\leftarrow $ get the next rice code from vecRice. $seed\leftarrow \mathrm{d}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{d}\mathrm{e}(riceCode$) If $seed=0$ Then $seed\leftarrow $ the value of the next unary code from vecFrac $Fr\leftarrow 0$ Else $m\leftarrow \u2308{\mathrm{log}}_{2}\left(2\cdot seed\right)\u2309$ $Fr\leftarrow $$\mathrm{get}\mathrm{the}\mathrm{next}m$ bits from vecFrac. $Fr\leftarrow Fr+1$ End If
$${x}_{i}\leftarrow {seed}^{2}+Fr$$
$cnt\leftarrow cnt-1$ End Do $Flag\leftarrow \mathrm{n}\mathrm{o}\mathrm{t}Flag$ End Do |
4. Near-Lossless Compression
Algorithm 4. The quadrature-based method to compute the square root value of $x$. |
Inputs: $x,{s}_{0}$ Output $:s$$//\mathrm{square}\mathrm{root}\mathrm{of}x$. Initialization: $BC\leftarrow {s}_{0}$ $CD\leftarrow x/BC$ $M\leftarrow 0.5\times (BC+CD)$ $CM\leftarrow \mathrm{B}\mathrm{C}-\mathrm{M}$ $\mathrm{sin}\theta \leftarrow CM/M$ $\mathrm{cos}\theta \leftarrow $$\mathrm{retrieved}\mathrm{from}\mathrm{a}\mathrm{lookup}\mathrm{table}\mathrm{utilizing}\mathrm{sin}\theta .$ $s\leftarrow \mathrm{cos}\theta \times M$ |
Near-Lossless Encoder/Decoder
Algorithm 5. Pseudocode for the compressor part of the proposed near-lossless compression. |
Input: $x$ // hyperspectral data. Outputs: vecSeed, vecUnary. Initialization: $n\leftarrow $$\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{bits}\mathrm{required}\mathrm{to}\mathrm{represent}x$. For all ${x}_{i}$$\mathrm{in}x$ Do 1. Seed generation $MSH\leftarrow $$\mathrm{the}\mathrm{leftmost}\lceil n/2\rceil $$\mathrm{bits}\mathrm{of}{x}_{i}$ $Q\leftarrow {2}^{\u230an/2\u230b}$ $seed\leftarrow (MSH+Q)\gg 1$ 2. Quadrature-based square rooting $BC\leftarrow seed$ $CD\leftarrow x\u2044BC$ $M\leftarrow 0.5\cdot (BC+CD)$ $CM\leftarrow BC-M$ $\mathrm{sin}\theta \leftarrow CM/M$ 3. Preparing the compressed stream $index\leftarrow {10}^{2}\cdot \mathrm{sin}\theta $ $order\leftarrow $ the corresponding order of the seed value within the lookup table of the index (Table A1). $m\leftarrow $ the number of bits that correspond to index (Table 4). $varCode\leftarrow $$\mathrm{the}\mathrm{least}\mathrm{significant}m$$\mathrm{bits}\mathrm{of}order$. $\mathrm{vecSeed}.\mathrm{add}(varCode$) // add the encoded seed to vecSeed vector. $unary\leftarrow $ the corresponding unary code of the index value. $\mathrm{vecUnary}.\mathrm{add}(unary$) // add unary code to vecUnary vector. End Do |
Algorithm 6. Pseudocode for the decompressor part of the proposed near-lossless compression. |
Inputs: vecSeed, vecUnary Output: $x$ // reconstructed hyperspectral data Initialization: $index\leftarrow $ the index value obtained by interpreting the next unary code in vecUnary For all $index$ Do $m\leftarrow $ the number bits to be read from vecSeed based on index value (Table 4). $order\leftarrow $$\mathrm{get}\mathrm{the}\mathrm{next}m$ bits from vecSeed. $seed\leftarrow $ get the seed value given the index (Table A1). $\mathrm{cos}\theta \leftarrow $ $\mathrm{given}\mathrm{the}\mathrm{index}\mathrm{value}(\mathrm{that}\mathrm{corresponds}\mathrm{to}\mathrm{sin}\theta $ value), retrieve the cosine value from the lookup table. $\mathrm{sin}\theta \leftarrow index/{10}^{2}$ $M\leftarrow seed/(1+\mathrm{sin}\theta )$ $s\leftarrow \mathrm{cos}\theta \times M$ $x\leftarrow s\times s$ End Do |
5. Experimental Results and Discussion
5.1. Dataset Description
5.2. Results of Lossless Compression
Comparison with Other Lossless Methods
5.3. Results of Near-Lossless Compression
Comparison with Other Near-Lossless Methods
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Index | ${\mathit{s}}_{0}$ |
---|---|
0 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255 |
1 | 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224 |
2 | 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 80, 81, 82, 83, 84, 85, 86, 87, 88, 100, 101, 102, 103, 104, 105, 106, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213 |
3 | 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 24, 25, 29, 30, 31, 43, 44, 45, 46, 47, 48, 49, 50, 51, 85, 86, 87, 88, 89, 90, 91, 97, 98, 99, 100, 101, 102, 103, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206 |
4 | 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 23, 24, 25, 45, 46, 47, 48, 49, 50, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 193, 194, 195, 196, 197, 198, 199, 200 |
5 | 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 24, 47, 48, 93, 94, 95, 96, 97, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195 |
6 | 6, 7, 8, 9, 13, 14, 15 |
7 | 5, 6, 7, 8, 9 |
8 | 4, 6, 7, 8 |
9 | 3, 5, 6, 7, 8 |
10 | 5, 7, 8 |
11 | 2, 4, 6, 7 |
12 | 6, 7 |
13 | 4, 6 |
14 | 3 |
15 | 4 |
17 | 4 |
18 | 3 |
20 | 2 |
21 | 3 |
25 | 3 |
27 | 2 |
33 | 1 |
50 | 1 |
$\mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{S}0=\mathrm{L}\mathrm{U}\mathrm{T}$ $\mathrm{X}=0:2^16-1;$ $\mathrm{\%}\mathrm{S}\mathrm{E}\mathrm{E}\mathrm{D}\mathrm{G}\mathrm{E}\mathrm{N}\mathrm{E}\mathrm{R}\mathrm{A}\mathrm{T}\mathrm{I}\mathrm{O}\mathrm{N}\mathrm{O}\mathrm{F}\mathrm{s}0\mathrm{B}\mathrm{A}\mathrm{S}\mathrm{E}\mathrm{D}\mathrm{O}\mathrm{N}\mathrm{B}\mathrm{I}\mathrm{T}\mathrm{M}\mathrm{A}\mathrm{N}\mathrm{I}\mathrm{P}\mathrm{U}\mathrm{L}\mathrm{A}\mathrm{T}\mathrm{I}\mathrm{O}\mathrm{N}$ $\mathrm{n}\mathrm{B}\mathrm{i}\mathrm{t}\mathrm{s}=\mathrm{m}\mathrm{a}\mathrm{x}(1,\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}(\mathrm{l}\mathrm{o}\mathrm{g}2\left(\mathrm{X}\right))+1);$ $\mathrm{n}\mathrm{S}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{s}=\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}(0.5\ast \mathrm{n}\mathrm{B}\mathrm{i}\mathrm{t}\mathrm{s});$ $\mathrm{M}\mathrm{S}\mathrm{H}=\mathrm{b}\mathrm{i}\mathrm{t}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}(\mathrm{X},-\mathrm{n}\mathrm{S}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{s});$ $\mathrm{s}0=\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}(0.5\ast (\mathrm{M}\mathrm{S}\mathrm{H}+2.^\mathrm{n}\mathrm{S}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t}\mathrm{s}\left)\right);$ $\mathrm{\%}\mathrm{Q}\mathrm{U}\mathrm{A}\mathrm{D}\mathrm{R}\mathrm{A}\mathrm{T}\mathrm{U}\mathrm{R}\mathrm{E}-\mathrm{B}\mathrm{A}\mathrm{S}\mathrm{E}\mathrm{D}\mathrm{S}\mathrm{Q}\mathrm{U}\mathrm{A}\mathrm{R}\mathrm{E}\mathrm{R}\mathrm{O}\mathrm{O}\mathrm{T}\mathrm{I}\mathrm{N}\mathrm{G}$ $\mathrm{B}\mathrm{C}=\mathrm{s}0;$ $\mathrm{C}\mathrm{D}=\mathrm{X}./\mathrm{B}\mathrm{C};\mathrm{C}\mathrm{D}\left(\mathrm{i}\mathrm{s}\mathrm{n}\mathrm{a}\mathrm{n}\right(\mathrm{C}\mathrm{D}\left)\right)=0;\mathrm{\%}\mathrm{H}\mathrm{A}\mathrm{N}\mathrm{D}\mathrm{L}\mathrm{I}\mathrm{N}\mathrm{G}\mathrm{D}\mathrm{I}\mathrm{V}\mathrm{I}\mathrm{S}\mathrm{I}\mathrm{O}\mathrm{N}\mathrm{B}\mathrm{Y}\mathrm{Z}\mathrm{E}\mathrm{R}\mathrm{O}$ $\mathrm{M}=0.5.\ast (\mathrm{B}\mathrm{C}+\mathrm{C}\mathrm{D});$ $\mathrm{C}\mathrm{M}=\mathrm{a}\mathrm{b}\mathrm{s}(\mathrm{B}\mathrm{C}-\mathrm{M});$ $\mathrm{i}\mathrm{d}\mathrm{x}=\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}\left(\right(\mathrm{C}\mathrm{M}./\mathrm{M}).\ast 10^2)+1;\mathrm{\%}\mathrm{I}\mathrm{N}\mathrm{D}\mathrm{E}\mathrm{X}\mathrm{I}\mathrm{N}\mathrm{G}\mathrm{S}\mathrm{T}\mathrm{A}\mathrm{R}\mathrm{T}\mathrm{S}\mathrm{A}\mathrm{T}\left(1\right)$ $\mathrm{i}\mathrm{d}\mathrm{x}\left(\mathrm{i}\mathrm{s}\mathrm{n}\mathrm{a}\mathrm{n}\right(\mathrm{i}\mathrm{d}\mathrm{x}\left)\right)=1;$ $\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{i}=1:51\mathrm{\%}\mathrm{S}\mathrm{T}\mathrm{E}\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{Z}\mathrm{E}\mathrm{O}\mathrm{F}0.01$ $\mathrm{I}=\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{d}(\mathrm{i}\mathrm{d}\mathrm{x}==\mathrm{i});$ $\mathrm{S}0\left\{\mathrm{i}\right\}=\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{e}\left(\mathrm{s}0\right(\mathrm{I}\left)\right);$ $\mathrm{e}\mathrm{n}\mathrm{d}$ $\mathrm{e}\mathrm{n}\mathrm{d}$ |
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Reference | Method | Category | Type | Year |
---|---|---|---|---|
[40] | ${k}^{2}$-raster | Compact Data Structure | Lossless | 2020 |
[45] | HCCNet | Deep Learning | Lossy | 2023 |
[44] | Autoencoders | Deep Learning | Lossy | 2021 |
[43] | SVR | Machine Learning | Lossy | 2020 |
[42] | RNN | Deep Learning | Lossless | 2019 |
[41] | CNN | Deep Learning | Lossy | 2019 |
[48] | HyperLCA | Transform-Based | Lossy | 2022 |
[22] | HW-HyperLCA | Transform-Based | Lossy | 2019 |
[49] | 3D-WBTC | Transform-Based | Lossy | 2019 |
[51] | Spectral Graph Transform | Transform-Based | Lossless | 2019 |
[50] | 3D-DCT | Transform-Based | Lossy | 2018 |
[52] | Tensor-Robust CUR | Tensor-Based | Lossy | 2023 |
[54] | Tucker Decomposition | Tensor-Based | Lossy | 2021 |
[59] | Optimized CS | Compressed Sensing | Lossy | 2020 |
[58] | CACS | Compressed Sensing | Lossy | 2019 |
[57] | SHSIR | Compressed Sensing | Lossy | 2019 |
[56] | BlockSparse Dictionary | Compressed Sensing | Lossy | 2018 |
[60] | B-CRLS | Recursive Least-Squares | Lossless | 2018 |
[61] | SuperRLS | Recursive Least-Squares | Lossless | 2018 |
[61] | BSuperRLS | Recursive Least-Squares | Lossless | 2018 |
${\mathit{s}}_{0}$ | Fractional Bits |
---|---|
${2}^{0}$ | 1 |
${2}^{1}$ | 2 |
${2}^{1}<{s}_{i}\le {2}^{2}$ | 3 |
${2}^{2}<{s}_{i}\le {2}^{3}$ | 4 |
${2}^{3}<{s}_{i}\le {2}^{4}$ | 5 |
${2}^{4}<{s}_{i}\le {2}^{5}$ | 6 |
${2}^{5}<{s}_{i}\le {2}^{6}$ | 7 |
${2}^{6}<{s}_{i}\le {2}^{7}$ | 8 |
${2}^{7}<{s}_{i}\le {2}^{8}$ | 9 |
$\mathit{x}$ | ${\mathit{s}}_{0}$ | Integer Bits | Fractional Bits |
---|---|---|---|
1 | 1 | 0000 | 0 (unary) |
2 | 1 | 0001 | 0 |
3 | 1 | 0001 | 1 |
4 | 2 | 0000 | 10 (unary) |
5 | 2 | 0010 | 00 |
6 | 2 | 0010 | 01 |
7 | 2 | 0010 | 10 |
8 | 2 | 0010 | 11 |
9 | 3 | 0011 | 00 |
... | ... | ... | ... |
16 | 4 | 0000 | 110 (unary) |
17 | 4 | 0100 | 000 |
18 | 4 | 0100 | 001 |
19 | 4 | 0100 | 010 |
20 | 4 | 0100 | 011 |
21 | 4 | 0100 | 100 |
22 | 4 | 0100 | 101 |
23 | 4 | 0100 | 110 |
24 | 4 | 0100 | 111 |
25 | 5 | 0101 | 0000 |
... | ... | ... | ... |
Index | $\mathbf{Variations}\mathbf{of}{\mathit{s}}_{0}$ | Number of Bits |
---|---|---|
0 | 157 | 8 |
1 | 111 | 7 |
2 | 83 | 7 |
3 | 66 | 7 |
4 | 52 | 6 |
5 | 31 | 5 |
6 | 7 | 3 |
7 | 5 | 3 |
8 | 4 | 2 |
9 | 5 | 3 |
10 | 3 | 2 |
11 | 4 | 2 |
12 | 2 | 1 |
13 | 2 | 1 |
14 | 1 | 0 |
15 | 1 | 0 |
17 | 1 | 0 |
18 | 1 | 0 |
20 | 1 | 0 |
21 | 1 | 0 |
25 | 1 | 0 |
27 | 1 | 0 |
33 | 1 | 0 |
50 | 1 | 0 |
$\mathit{x}$ | ${\mathit{s}}_{0}$ | Index |
---|---|---|
29 | 5 | 7 |
12,317 | 112 | 0 |
22,556 | 152 | 1 |
31,003 | 185 | 4 |
5403 | 74 | 0 |
1818 | 44 | 3 |
21,017 | 146 | 0 |
61,974 | 249 | 0 |
15,125 | 123 | 0 |
10,260 | 104 | 2 |
Imager | Scene | Data Type | Dimensions | C\U * | Bit Rate |
---|---|---|---|---|---|
AIRS | gran9 | u16 | 1501 × 135 × 90 | U | 12 |
gran16 | 1501 × 135 × 90 | ||||
gran60 | 1501 × 135 × 90 | ||||
gran82 | 1501 × 135 × 90 | ||||
gran120 | 1501 × 135 × 90 | ||||
gran126 | 1501 × 135 × 90 | ||||
gran129 | 1501 × 135 × 90 | ||||
gran151 | 1501 × 135 × 90 | ||||
gran182 | 1501 × 135 × 90 | ||||
AVIRIS | Hawaii | u16 | 224 × 512 × 614 | U | 16 |
Maine | 224 × 512 × 680 | ||||
Yellowstone (sc00) | 224 × 512 × 680 | ||||
Yellowstone (sc03) | 224 × 512 × 680 | ||||
AVIRIS | Yellowstone (sc00) | s16 | 224 × 512 × 677 | C | 16 |
Yellowstone (sc03) | 224 × 512 × 677 | ||||
Yellowstone (sc10) | 224 × 512 × 677 | ||||
Yellowstone (sc11) | 224 × 512 × 677 | ||||
Yellowstone (sc18) | 224 × 512 × 677 | ||||
CRISM | sc182 | u16 | 545 × 450 × 320 | U | 12 |
sc214 | 74 × 2700 × 64 | ||||
CASI | t0477f06 | u16 | 72 × 1225 × 406 | U | 12 |
t0180f07 | 72 × 2852 × 405 | ||||
Hyperion | Cuprite | u16 | 242 × 1024 × 256 | U | 12 |
ErtaAle | 242 × 3187 × 256 | ||||
LakeMonona | 242 × 3176 × 256 | ||||
MtStHelens | 242 × 3242 × 256 | ||||
M3 | globalA | u16 | 86 × 512 × 320 | U | 12 |
globalB | 86 × 512 × 320 | ||||
targetA | 260 × 512 × 640 | ||||
targetB | 260 × 512 × 640 | ||||
targetC | 260 × 512 × 640 | ||||
SFSI | Mantar | u16 | 240 × 140 × 496 | U | 12 |
Scene | Original Sparsity | Sparsity after Decorrelation | Average Bit Rate | CR |
---|---|---|---|---|
Hawaii (U) | 01.45% | 25.84% | 12.87 | 1.2 |
Maine (U) | 0% | 25.90% | 12.86 | 1.2 |
Yellowstone (sc00, C) | 0% | 30.80% | 12.07 | 1.3 |
Yellowstone (sc00, U) | 01.19% | 19.86% | 13.82 | 1.2 |
Yellowstone (sc03, C) | 0% | 00.19% | 16.97 | 0.9 |
Yellowstone (sc03, U) | 02.65% | 24.69% | 13.05 | 1.2 |
Yellowstone (sc10, C) | 0% | 00.18% | 16.97 | 0.9 |
Yellowstone (sc11, C) | 07.68% | 35.58% | 11.31 | 1.4 |
Yellowstone (sc18, C) | 02.03% | 27.12% | 12.66 | 1.3 |
Scene | Original Sparsity | Sparsity after Decorrelation | Average Bit Rate | CR |
---|---|---|---|---|
Hawaii (U) | 04.74% | 43.05% | 5.56 | 1.4 |
Maine (U) | 11.77% | 53.51% | 4.72 | 1.7 |
Yellowstone (sc00, C) | 14.28% | 54.23% | 4.66 | 1.7 |
Yellowstone (sc00, U) | 04.43% | 43.82% | 5.49 | 1.5 |
Yellowstone (sc03, C) | 00.96% | 27.52% | 6.80 | 1.2 |
Yellowstone (sc03, U) | 06.53% | 44.91% | 5.41 | 1.5 |
Yellowstone (sc10, C) | 01.33% | 28.85% | 6.69 | 1.2 |
Yellowstone (sc11, C) | 14.12% | 52.40% | 4.81 | 1.7 |
Yellowstone (sc18, C) | 05.80% | 47.85% | 5.17 | 1.5 |
Rice Code | AIRS-1D | AIRS-2D | AVIRIS-1D | AVIRIS-2D |
---|---|---|---|---|
0.0 | 0 | 0 | 0 | 0 |
0.1 | 3 | 3 | 1 | 1 |
10.0 | 2 | 2 | 2 | 2 |
10.1 | 1 | 1 | 15 | 3 |
110.0 | 5 | 5 | 3 | 5 |
110.1 | 7 | 7 | 7 | 15 |
1110.0 | 15 | 15 | 5 | 7 |
1110.1 | 4 | 4 | 14 | 4 |
11110.0 | 10 | 11 | 10 | 10 |
11110.1 | 14 | 10 | 4 | 11 |
111110.0 | 6 | 6 | 6 | 6 |
111110.1 | 11 | 14 | 11 | 14 |
1111110.0 | 9 | 8 | 9 | 8 |
1111110.1 | 13 | 9 | 13 | 9 |
11111110.0 | 8 | 13 | 8 | 13 |
11111110.1 | 12 | 12 | 12 | 12 |
Imager | Scene | Entropy (Bits) | ${\mathit{k}}^{2}$-Raster | Proposed (1D XOR, Rice) | Proposed (2D XOR, Rice) | Proposed (1D XOR, Mapped Rice) | Proposed (2D XOR, Mapped Rice) |
---|---|---|---|---|---|---|---|
AIRS | gran9 | 11.2 | 21% | 22% | 23% | 25% | 26% |
gran16 | 11.1 | 24% | 24% | 24% | 26% | 26% | |
gran60 | 11.5 | 19% | 18% | 20% | 20% | 22% | |
gran82 | 11.0 | - | 29% | 27% | 32% | 30% | |
gran120 | 11.2 | - | 25% | 25% | 27% | 27% | |
gran126 | 11.5 | 20% | 20% | 21% | 22% | 24% | |
gran129 | 11.1 | 28% | 31% | 29% | 34% | 31% | |
gran151 | 11.6 | 21% | 23% | 23% | 26% | 25% | |
gran182 | 11.6 | 19% | 19% | 20% | 22% | 22% | |
AVIRIS | Hawaii | 8.6 | - | 58% | 57% | 59% | 57% |
Maine | 9.1 | - | 58% | 57% | 58% | 57% | |
Yellowstone (sc00, U) | 12.6 | 25% | 19% | 22% | 22% | 25% | |
Yellowstone (sc03, U) | 12.3 | 27% | 22% | 25% | 24% | 27% | |
AVIRIS | Yellowstone (sc00, C) | 10.3 | 40% | 39% | 43% | 41% | 44% |
Yellowstone (sc03, C) | 9.9 | 41% | 40% | 44% | 43% | 46% | |
Yellowstone (sc10) | 8.6 | 52% | 53% | 52% | 55% | 55% | |
Yellowstone (sc11) | 9.8 | 45% | 46% | 48% | 47% | 49% | |
Yellowstone (sc18) | 10.2 | 39% | 39% | 44% | 41% | 46% | |
CRISM | sc182 | 11.2 | 16% | 35% | 27% | 37% | 29% |
sc214 | 9.9 | - | 60% | 52% | 61% | 53% | |
CASI | t0477f06 | 10.4 | - | 24% | 23% | 27% | 25% |
t0180f07 | 10.7 | - | 15% | 17% | 18% | 19% | |
Hyperion | Cuprite | 9.4 | - | 44% | 37% | 46% | 40% |
ErtaAle | 9.5 | 35% | 43% | 36% | 45% | 38% | |
LakeMonona | 9.9 | 35% | 43% | 36% | 45% | 38% | |
MtStHelens | 9.3 | 34% | 40% | 33% | 42% | 36% | |
M3 | globalA | 9.4 | - | 44% | 37% | 46% | 43% |
globalB | 9.3 | - | 45% | 38% | 47% | 45% | |
targetA | 8.7 | - | 55% | 48% | 56% | 51% | |
targetB | 9.7 | - | 52% | 45% | 53% | 48% | |
targetC | 8.8 | - | 61% | 54% | 62% | 56% | |
SFSI | mantar | 7.2 | - | 47% | 40% | 50% | 45% |
Geometric Mean | 28.40% | 34.45% | 33.13% | 36.89% | 35.72% | ||
Reduction Enhancement | NA | 21.30% | 16.65% | 29.89% | 25.77% |
Imager | Scene | Proposed (1D XOR, Rice) | Proposed (2D XOR, Rice) | Proposed (1D XOR, Mapped Rice) | Proposed (2D XOR, Mapped Rice) | ${\mathit{k}}^{2}$-Raster (DACs) | gzip | bzip2 | xz |
---|---|---|---|---|---|---|---|---|---|
AIRS | gran9 | 9.37 | 9.23 | 9.03 | 8.92 | 9.49 | 10.16 | 7.42 | 7.90 |
gran16 | 9.16 | 9.13 | 8.82 | 8.83 | 9.12 | 9.82 | 7.15 | 7.66 | |
gran60 | 9.89 | 9.63 | 9.56 | 9.33 | 9.72 | 10.53 | 7.71 | 8.23 | |
gran126 | 9.65 | 9.47 | 9.33 | 9.16 | 9.61 | 10.33 | 7.64 | 8.10 | |
gran129 | 8.25 | 8.57 | 7.94 | 8.26 | 8.65 | 9.50 | 6.68 | 7.22 | |
gran151 | 9.23 | 9.24 | 8.91 | 8.93 | 9.53 | 10.31 | 7.43 | 7.97 | |
gran182 | 9.72 | 9.60 | 9.39 | 9.29 | 9.68 | 10.64 | 7.79 | 8.33 | |
AVIRIS | Yellowstone (sc00, U) | 12.94 | 12.41 | 12.51 | 12.07 | 11.92 | 12.39 | 9.99 | 10.61 |
Yellowstone (sc03, U) | 12.46 | 11.95 | 12.11 | 11.63 | 11.74 | 11.98 | 9.54 | 10.23 | |
AVIRIS | Yellowstone (sc00, C) | 9.83 | 9.18 | 9.47 | 8.90 | 9.61 | 10.12 | 7.51 | 8.04 |
Yellowstone (sc03, C) | 9.53 | 8.89 | 9.15 | 8.57 | 9.42 | 9.59 | 7.10 | 7.62 | |
Yellowstone (sc10) | 7.55 | 7.62 | 7.15 | 7.18 | 7.62 | 7.41 | 5.30 | 5.73 | |
Yellowstone (sc11) | 8.72 | 8.38 | 8.45 | 8.11 | 8.81 | 9.04 | 6.65 | 7.07 | |
Yellowstone (sc18) | 9.80 | 8.91 | 9.48 | 8.65 | 9.78 | 10.00 | 7.45 | 7.95 | |
CRISM | sc182 | 7.83 | 8.81 | 7.57 | 8.53 | 10.11 | 10.90 | 8.53 | 7.90 |
Hyperion | ErtaAle | 6.82 | 7.67 | 6.57 | 7.40 | 7.76 | 8.69 | 6.41 | 6.73 |
LakeMonona | 6.84 | 7.73 | 6.56 | 7.43 | 7.82 | 8.69 | 6.46 | 6.74 | |
MtStHelens | 7.18 | 7.95 | 6.93 | 7.69 | 7.91 | 8.26 | 6.28 | 6.48 |
Imager | Scene | Data Reduction (%) | MRE | MAE |
---|---|---|---|---|
AIRS | gran9 | 39.4242 | 0.0667 | 30 |
gran16 | 39.7075 | 0.0038 | 30 | |
gran60 | 39.5578 | 0.3333 | 30 | |
gran82 | 39.6562 | 0.0038 | 30 | |
gran120 | 39.5115 | 0.0667 | 30 | |
gran126 | 39.5593 | 0.0667 | 30 | |
gran129 | 39.6236 | 0.0038 | 30 | |
gran151 | 39.5363 | 0.3333 | 30 | |
gran182 | 39.5240 | 0.0667 | 30 | |
AVIRIS | Yellowstone (sc00, U) | 39.7314 | 0.0667 | 30 |
Yellowstone (sc03, U) | 39.7106 | 0.0667 | 30 | |
CRISM | sc182 | 39.4889 | 0.3333 | 30 |
CASI | t0477f06 | 39.6337 | 0.3333 | 30 |
t0180f07 | 38.9011 | 0.3333 | 30 |
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Altamimi, A.; Ben Youssef, B. Lossless and Near-Lossless Compression Algorithms for Remotely Sensed Hyperspectral Images. Entropy 2024, 26, 316. https://doi.org/10.3390/e26040316
Altamimi A, Ben Youssef B. Lossless and Near-Lossless Compression Algorithms for Remotely Sensed Hyperspectral Images. Entropy. 2024; 26(4):316. https://doi.org/10.3390/e26040316
Chicago/Turabian StyleAltamimi, Amal, and Belgacem Ben Youssef. 2024. "Lossless and Near-Lossless Compression Algorithms for Remotely Sensed Hyperspectral Images" Entropy 26, no. 4: 316. https://doi.org/10.3390/e26040316