Hi I am needing some help with the below problem...I'm not grasping what it is asking me to do and I get an error that svd(A) needs to either be a single or double. Use the MATLAB imshow() function to load and display the image A stored in the image.mat file,. For the loaded image, derive the value of k that will result in a compression ratio of . For this value of k, construct the rank-k approximation of the image. My Solution so far: A = load('/MATLAB Drive/Proj 2/MATLAB Image.mat') imshow(A.A) [U, S, V] = svd(A) CR = (3072 * 4608) / (921 * (3072 + 4608 + 1)) A921 = U(:,1:921) * S(1:921, 1:921) * V(:,1:921) Rank(A921) A921 = uint8(round(A921))
Hi I am needing some help with the below problem...I'm not grasping what it is asking me to do and I get an error that svd(A) needs to either be a single or double. Use the MATLAB imshow() function to load and display the image A stored in the image.mat file,. For the loaded image, derive the value of k that will result in a compression ratio of . For this value of k, construct the rank-k approximation of the image. My Solution so far: A = load('/MATLAB Drive/Proj 2/MATLAB Image.mat') imshow(A.A) [U, S, V] = svd(A) CR = (3072 * 4608) / (921 * (3072 + 4608 + 1)) A921 = U(:,1:921) * S(1:921, 1:921) * V(:,1:921) Rank(A921) A921 = uint8(round(A921))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi I am needing some help with the below problem...I'm not grasping what it is asking me to do and I get an error that svd(A) needs to either be a single or double.
Use the MATLAB imshow() function to load and display the image A stored in the image.mat file,. For the loaded image, derive the value of k that will result in a compression ratio of . For this value of k, construct the rank-k approximation of the image.
My Solution so far:
A = load('/MATLAB Drive/Proj 2/MATLAB Image.mat')
imshow(A.A)
[U, S, V] = svd(A)
CR = (3072 * 4608) / (921 * (3072 + 4608 + 1))
A921 = U(:,1:921) * S(1:921, 1:921) * V(:,1:921)
Rank(A921)
A921 = uint8(round(A921))
__________________________________________________________________________________________
![### Problem 3
**Task:**
Use the MATLAB `imshow()` function to load and display the image \( A \) stored in the `image.mat` file. For the loaded image, derive the value of \( k \) that will result in a compression ratio of \( CR \approx 2 \). For this value of \( k \), construct the rank-\( k \) approximation of the image.
**Solution:**
```matlab
A = load('/MATLAB Drive/Proj 2/MATLAB Image.mat')
imshow(A.A)
[U, S, V] = svd(A)
CR = (3072 * 4608) / (921 * (3072 + 4608 + 1))
A921 = U(:,1:921) * S(1:921, 1:921) * V(:,1:921)
Rank(A921)
A921 = uint8(round(A921))
```
**Explanation:**
1. **Loading the Image:**
- `A = load('/MATLAB Drive/Proj 2/MATLAB Image.mat')`: This line loads the image data from the specified `.mat` file.
2. **Displaying the Image:**
- `imshow(A.A)`: This line uses the `imshow` function to display the loaded image \( A \).
3. **Computing the Singular Value Decomposition:**
- `[U, S, V] = svd(A)`: This line computes the Singular Value Decomposition (SVD) of the matrix \( A \), where \( U \), \( S \), and \( V \) are the matrices obtained from the SVD.
4. **Calculating Compression Ratio:**
- `CR = (3072 * 4608) / (921 * (3072 + 4608 + 1))`: This line calculates the compression ratio \( CR \) for a specific rank \( k = 921 \). The compression ratio is approximately 2 as requested in the task.
5. **Constructing Rank-\( k \) Approximation:**
- `A921 = U(:,1:921) * S(1:921, 1:921) * V(:,1:921)`: This line constructs the rank-\( k \) approximation of the image using the first 921 singular values and the corresponding vectors from \( U \) and \( V \).
6. **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf8aa82a-31a1-4382-a30e-3ad6a3174f84%2F50329533-ae3a-4c57-a985-cb8e6695a4ff%2Fe0mffon_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 3
**Task:**
Use the MATLAB `imshow()` function to load and display the image \( A \) stored in the `image.mat` file. For the loaded image, derive the value of \( k \) that will result in a compression ratio of \( CR \approx 2 \). For this value of \( k \), construct the rank-\( k \) approximation of the image.
**Solution:**
```matlab
A = load('/MATLAB Drive/Proj 2/MATLAB Image.mat')
imshow(A.A)
[U, S, V] = svd(A)
CR = (3072 * 4608) / (921 * (3072 + 4608 + 1))
A921 = U(:,1:921) * S(1:921, 1:921) * V(:,1:921)
Rank(A921)
A921 = uint8(round(A921))
```
**Explanation:**
1. **Loading the Image:**
- `A = load('/MATLAB Drive/Proj 2/MATLAB Image.mat')`: This line loads the image data from the specified `.mat` file.
2. **Displaying the Image:**
- `imshow(A.A)`: This line uses the `imshow` function to display the loaded image \( A \).
3. **Computing the Singular Value Decomposition:**
- `[U, S, V] = svd(A)`: This line computes the Singular Value Decomposition (SVD) of the matrix \( A \), where \( U \), \( S \), and \( V \) are the matrices obtained from the SVD.
4. **Calculating Compression Ratio:**
- `CR = (3072 * 4608) / (921 * (3072 + 4608 + 1))`: This line calculates the compression ratio \( CR \) for a specific rank \( k = 921 \). The compression ratio is approximately 2 as requested in the task.
5. **Constructing Rank-\( k \) Approximation:**
- `A921 = U(:,1:921) * S(1:921, 1:921) * V(:,1:921)`: This line constructs the rank-\( k \) approximation of the image using the first 921 singular values and the corresponding vectors from \( U \) and \( V \).
6. **
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