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# CondatTV Cython wrapper for the efficient TV denoising algorithm by [Laurent Condat](https://lcondat.github.io/). This wrapper wraps Condats C implementation of the algorithm for use with NumPy. The algorithm this code uses is the improved fast total variation algorithm. The original C and MATLAB code is available on the [software page](https://lcondat.github.io/software.html) of Laurent Condat's [webpage](https://lcondat.github.io/). ## Installation instructions To install these bindings, you should have a C-compiler installed on your system. Make sure you have [NumPy](https://numpy.org/install/) and [Cython](https://cython.readthedocs.io/en/latest/src/quickstart/install.html) installed beforehand (both packages come with Anaconda by default) and write ``` pip install condat-tv ``` in your terminal window. In case that does not work, you can install it directly from github by running the command ``` pip install git+https://github.com/yngvem/condat_tv.git ``` ## Example of denoising with total variation minimization The following example is inspired by the experiments on syntetic data in [[1]](#[1]) ```python import condat_tv import numpy as np import matplotlib.pyplot as plt ``` ### Generate syntetic data ```python np.random.seed(0) N = 500 # number of samples # Generate a sparse "derivative" vector signal_derivative = np.random.standard_normal(N)*4 for k in range(N): signal_derivative[k] = signal_derivative[k]*(np.random.uniform(0,1)>0.95) # Integrate the sparse derivative vector to obtain a piecewise constant vector signal = np.cumsum(signal_derivative) # Add noise noisy_signal = signal + np.random.standard_normal(signal.shape) ``` ### Plot the syntetic data ```python plt.figure(figsize=(12, 4)) plt.plot(signal, label="Signal") plt.plot(noisy_signal, label="Noisy signal") plt.xlim(0, N) plt.legend() plt.title("Plot showing the signal with and without the added noies") plt.show() ```  ### Denoise and visualize the results ```python plt.figure(figsize=(12, 4)) plt.plot(signal, label="Signal") for reg_strength in [0.5, 2, 8, 32]: # Denoise the signal with total variation minimization denoised_signal = condat_tv.tv_denoise(noisy_signal, reg_strength) # Visualize denoised signal plt.plot(denoised_signal, label=f"Reg strength: {reg_strength}") # Calculate and print RMSE RMSE = np.linalg.norm(denoised_signal-signal)/np.sqrt(N) print(f"Regularisation strength: {reg_strength:.1e}, RMSE: {RMSE:.2e}") plt.xlim(0, N) plt.legend(ncol=5) plt.title("Visualisation of denoising results for different regularisation strengths") plt.show() ``` Regularisation strength: 5.0e-01, RMSE: 5.70e-01 Regularisation strength: 2.0e+00, RMSE: 3.56e-01 Regularisation strength: 8.0e+00, RMSE: 5.89e-01 Regularisation strength: 3.2e+01, RMSE: 1.52e+00  # References <p id="[1]"> <b>[1]</b> Condat L. A direct algorithm for 1-D total variation denoising. IEEE Signal Processing Letters. 2013 Aug 15;20(11):1054-7. <a href="https://ieeexplore.ieee.org/abstract/document/6579659">(link)</a> <p>