compressive sensing

Question

Reconstruct the image from projections using Lasso, with regularization parameter 𝛼 obtained by 5-fold cross validation. Store your fitting result in rgr_lasso.

Answer 1

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To reconstruct an image from projections using Lasso regression and determine the regularization parameter alpha by 5-fold cross validation in Python, you can follow these steps:

1. Import the required libraries:

   import numpy as np
   import matplotlib.pyplot as plt
   from sklearn.model_selection import KFold
   from sklearn.linear_model import LassoCV
   

2. Load the projections data and store it in a variable:

   projections = ... # load your projections data here
   

3. Create a variable to store the reconstructed image:

   reconstructed_image = np.zeros((...)) # specify the shape of the image
   

4. Define the number of folds for cross-validation:

   n_folds = 5
   

5. Split the projections data into training and testing sets using KFold:

   kf = KFold(n_splits=n_folds)
   

6. Iterate over the folds and perform Lasso regression:

   for train_index, test_index in kf.split(projections):
    # Split into training and testing sets
    X_train, X_test = projections[train_index], projections[test_index]
    
    # Initialize Lasso regression model with cross-validated regularization parameter
    lasso_cv = LassoCV(cv=n_folds)
    
    # Fit the model
    lasso_cv.fit(X_train, X_test)
    
    # Reconstruct the image using the fitted model
    reconstructed_image[:, test_index] = lasso_cv.predict(X_test)
   

7. Store the reconstructed image in the variable rgr_lasso:

   rgr_lasso = reconstructed_image
   

Note: In the above code, make sure to fill in the appropriate shapes and values according to your data.

After running this code, the variable rgr_lasso will contain the reconstructed image obtained using Lasso regression with the regularization parameter alpha determined by 5-fold cross validation.