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Key Changes:
Simplified Comments: I removed verbose explanations to focus on the essential details.
Unified Noise Functions: Gaussian and Poisson noise generation and addition were condensed.
Removed Redundancy: Functions like random_generate_* were replaced with direct calls to the main noise functions, using concise range handling.
Matrix Operations: I optimized pdf2 and sigma_matrix2 with vectorized operations using np.einsum and np.dot.