CSD573_lecture_3_ex_2.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPWAMEtQYwUsQLFebjAe+vG",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/gtsagkatakis/OptimizationMethods_2023/blob/main/CSD573_lecture_3_ex_2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "TOtcNQPUMazz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a simple sky image with a point source\n",
        "sky_size = 64\n",
        "sky = np.zeros((sky_size, sky_size))\n",
        "sky[sky_size//2, sky_size//2] = 1  # A point source in the center\n",
        "\n",
        "#sky[12, 24] = 1  # A point source in the center"
      ],
      "metadata": {
        "id": "h4f1qJ-xMcFh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Simulate the Measurement Matrix A as a Fourier Transform matrix\n",
        "F = np.fft.fftshift(np.fft.fft2(np.eye(sky_size**2).reshape(sky_size, sky_size, sky_size, sky_size)))\n",
        "\n",
        "# Flatten the 2D sky image to 1D\n",
        "sky_flat = sky.flatten()\n",
        "\n",
        "# Simulate observed visibilities\n",
        "v = (F.reshape(sky_size**2, sky_size**2) @ sky_flat)\n",
        "\n",
        "# Add some noise (optional, to simulate real-world observations)\n",
        "noise_level = 1\n",
        "v += noise_level * (np.random.randn(sky_size**2))"
      ],
      "metadata": {
        "id": "IHJ0yVr_MfZq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Reconstruct the sky by matrix inversion\n",
        "s_reconstructed = np.linalg.inv(F.reshape(sky_size**2, sky_size**2)) @ v\n",
        "reconstructed_sky = s_reconstructed.reshape(sky_size, sky_size)"
      ],
      "metadata": {
        "id": "1PrRmoiqMiGn"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "id": "t32x8DtO9QMT",
        "outputId": "3d953691-83d1-41de-d3c4-78d4c36e1aa2"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 3 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plotting\n",
        "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
        "\n",
        "ax[0].imshow(sky, cmap='gray')\n",
        "ax[0].set_title('Original Sky')\n",
        "ax[0].axis('off')\n",
        "\n",
        "ax[1].imshow(np.abs(v.reshape(sky_size, sky_size)), cmap='gray')\n",
        "\n",
        "ax[1].set_title('Simulated Visibilities')\n",
        "ax[1].axis('off')\n",
        "\n",
        "ax[2].imshow(reconstructed_sky.real, cmap='gray')\n",
        "ax[2].set_title('Reconstructed Sky')\n",
        "ax[2].axis('off')\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ]
    }
  ]
}