import numpy as np
from scipy.stats import skew, kurtosis
from typing import Dict, Any, Optional

def analyze_data(data: np.ndarray) -> Dict[str, Any]:
    """
    Calculates a dictionary of summary statistics for the given NumPy array.

    Args:
        data: The input NumPy array (can be 1D or 2D).

    Returns:
        A dictionary containing various statistical metrics. Returns an
        empty dictionary if the input data is empty.
    """
    if data is None or data.size == 0:
        return {}

    analysis: Dict[str, Any] = {
        "size": data.size,
        "data_type": data.dtype,
        "unique_values": len(np.unique(data)),
        "maximum": np.max(data),
        "minimum": np.min(data),
        "mean": np.mean(data),
        "standard_deviation": np.std(data),
        "sum": np.sum(data),
        "median": np.median(data),
        "percentile_25": np.percentile(data, 25),
        "percentile_75": np.percentile(data, 75),
        "range": np.max(data) - np.min(data),
    }

    if data.ndim > 1:
        analysis["shape"] = data.shape

    # For skewness and kurtosis, the array must be flattened to 1D.
    # These calculations are more meaningful on the flattened data distribution.
    flat_data = data.flatten()
    analysis["skewness"] = skew(flat_data)
    analysis["kurtosis"] = kurtosis(flat_data)

    return analysis


def inverse_fourier_transform(matrix: np.ndarray) -> Optional[np.ndarray]:
    """
    Computes the inverse 2D Fourier Transform of a matrix.

    This function calculates the inverse FFT and returns the absolute
    values of the result, which is suitable for image visualization.

    Args:
        matrix: The input matrix in the frequency domain.

    Returns:
        The resulting real-valued image (as a NumPy array) after the
        inverse transform, or None if an error occurs.
    """
    try:
        # Perform the inverse 2D Fast Fourier Transform
        image = np.fft.ifft2(matrix)
        
        # Return the magnitude (absolute value) of the complex result
        # for visualization purposes.
        return np.abs(image)
    except Exception:
        # The logger will be used here in the future.
        # For now, return None to signal an error to the caller.
        return None