Median filtering is commonly used to reduce noise in an image. It replaces each pixel value with the median value in a local neighborhood, making it effective for removing salt-and-pepper noise and preserving the edges and features in the image.

To address the performance deterioration of a deployed Gradient Boosting model, it's crucial to regularly update the model with new data (option D). Data drift is common, and updating the model ensures it adapts to the changing environment. While re-training with additional data (option A) may help, regularly updating the model with new data is more sustainable. Increasing the learning rate (option B) or reducing model complexity (option C) may not be effective in addressing performance deterioration over time.

The technique used to prevent overfitting in neural networks is called "Dropout." During training, dropout randomly removes a fraction of neurons, helping to prevent overreliance on specific neurons and improving generalization.

In time series analysis, a sequence of data points measured at successive points in time is called "time series data." This data structure is used to analyze and forecast trends, patterns, and dependencies over time. It's fundamental in fields like finance, economics, and climate science.

"Backpropagation" in neural networks refers to the process of updating the model's weights based on the computed errors during the forward pass. It's a key step in training neural networks and involves minimizing the loss function.

A document database, like MongoDB, is well-suited for storing unstructured data with variable schemas, making it an ideal choice for use cases involving user posts, images, and comments.

Homomorphic Encryption allows computation on encrypted data without the need for decryption. It's a significant advancement in data privacy because it ensures that sensitive data remains encrypted during processing, reducing the risk of data exposure and breaches while still enabling useful computations.

Transfer learning benefits deep learning models by decreasing training time and data requirements. It allows models to leverage pre-trained knowledge, saving time and reducing the need for large datasets. The model starts with knowledge from a source task and fine-tunes it for a target task, which is often faster and requires less data than training from scratch.

Memorization indicates overfitting. Applying dropout regularization (Option C) is a suitable approach to prevent overfitting in deep neural networks. Increasing the learning rate (Option A) can lead to convergence issues. Adding more layers (Option B) can worsen overfitting. Decreasing the batch size (Option D) may not directly address memorization.

In a resource-constrained environment, one major challenge is the high memory and processing demands of deep learning models. They can be computationally expensive. A potential solution could be model optimization techniques like quantization, pruning, or using smaller network architectures to reduce memory and processing requirements.