English | 中文说明
Course: Digital Image Processing · Major: Artificial Intelligence (NUIST) · Author: Hossen Md Jisan
This project proposes a deep learning framework for discrete-time LTI system identification using Z-transform pole-zero representations. Each system's pole-zero map is rendered as a 64×64 grayscale image and paired with a 128-dimensional frequency-response magnitude vector. Three neural architectures are designed and compared:
- PoleZeroCNN — image-only CNN over the pole-zero map
- FreqMLP — MLP over the frequency-response vector
- FusionNet — late fusion of both modalities
Systems are classified into five frequency-selective categories: lowpass, highpass, bandpass, bandstop, and allpass.
The work bridges classical digital signal processing theory with modern deep learning and demonstrates that Z-transform pole-zero geometry is a rich, learnable representation for automated filter recognition — with direct applications to image denoising, blind deconvolution, and adaptive image restoration.
Classical discrete-time system identification relies on hand-derived pole-zero analysis and frequency-response inspection — exact, but manual and hard to automate at scale. This project asks whether a filter's identity (lowpass, highpass, bandpass, bandstop, allpass) can instead be learned directly from its Z-transform geometry, treating the pole-zero map as an image and the frequency response as a vector. It is a small, controlled test of whether deep networks can read classical DSP representations, with downstream relevance to image denoising, blind deconvolution, and adaptive restoration.
Trained on 5,000 balanced samples (1,000 per class) and evaluated on 750 held-out test samples:
| Model | Accuracy | Precision | Recall | F1-Score | Parameters |
|---|---|---|---|---|---|
| PoleZeroCNN | 99.73% | 99.76% | 99.73% | 99.74% | 421,861 |
| FreqMLP | 100.00% | 100.00% | 100.00% | 100.00% | 75,269 |
| FusionNet | 100.00% | 100.00% | 100.00% | 100.00% | 455,077 |
All random seeds are fixed at 42; the full pipeline is reproducible end-to-end in ≈224 s on GPU.
DIP_ZTransform_DL/
├── src/
│ ├── 01_dataset_generation.py # Synthetic pole-zero dataset (5000 samples, 5 classes)
│ ├── 02_dataset_visualization.py # Dataset visualization (6 figures auto-saved)
│ ├── 03_model.py # CNN, MLP, FusionNet model definitions
│ ├── 04_train.py # Training loop, checkpoints, LR scheduling
│ ├── 05_evaluate.py # Test evaluation, confusion matrices, metrics
│ └── 06_run_all.py # One-command full pipeline
├── dataset/ # Auto-populated on run
├── output/
│ ├── figures/ # Training curves, confusion matrices, predictions (12 PNG)
│ ├── dataset_viz/ # Dataset visualizations (6 PNG)
│ └── test_metrics/ # Metrics CSV, JSON, comparison chart (1 PNG)
├── paper/
│ ├── main.tex # Complete LaTeX paper source (1257 lines)
│ └── figures/ # Paper figures directory (copy from output/)
├── requirements.txt
├── .gitignore
└── README.md
Python 3.9 or higher recommended:
pip install -r requirements.txtCore dependencies: PyTorch 2.0+, NumPy, SciPy, Matplotlib, scikit-learn, scikit-image, Pillow, pandas, seaborn, tqdm.
# Option 1: One-command full pipeline (recommended)
python src/06_run_all.py
# Option 2: Step by step
python src/01_dataset_generation.py # ~96s on CPU
python src/02_dataset_visualization.py
python src/03_model.py # Architecture verification
python src/04_train.py # ~110s on GPU
python src/05_evaluate.pyoutput/dataset_viz/ (6 figures)
- fig01_sample_pz_maps.png — Sample pole-zero map images per class
- fig02_mean_freq_response.png — Mean frequency response per class
- fig03_class_distribution.png — Class balance bar chart
- fig04_freq_response_heatmap.png — Frequency response heatmap
- fig05_pixel_distribution.png — Pixel intensity distributions
- fig06_pz_scatter.png — Pole-zero scatter on Z-plane
output/figures/ (12 figures)
- fig_train_curves_{cnn,mlp,fusion}.png — Training and validation curves
- fig_confusion_{cnn,mlp,fusion}.png — Normalized confusion matrices
- fig_f1_per_class_{cnn,mlp,fusion}.png — Per-class F1 score bar charts
- fig_pz_predictions_{cnn,mlp,fusion}.png — Prediction panels (GT vs predicted)
output/test_metrics/ (1 figure)
- fig_model_comparison.png — Side-by-side model comparison
paper/main.tex contains the complete LaTeX source (1,257 lines):
- Abstract (with quantitative results)
- Introduction (background, problem statement, research objectives)
- Related Work (classical system ID, deep learning for signals, multi-modal fusion — references 2015–2022)
- Dataset Construction (Z-transform theory, conjugate pair generation, class placement rules, two feature representations)
- Model Architectures (shared ConvBlock derivation; PoleZeroCNN and FreqMLP layer tables with forward-pass equations; FusionNet TikZ diagram and mathematical forward pass; label smoothing, Adam, cosine annealing)
- Experiments and Discussion (all 19 figures, 5 data tables, error analysis, relevance to image processing)
- Conclusion and Future Work
- References (18 references, 2015–2022)
To compile:
# Step 1: Copy figures into paper directory
mkdir -p paper/figures
cp output/dataset_viz/*.png paper/figures/
cp output/figures/*.png paper/figures/
cp output/test_metrics/fig_model_comparison.png paper/figures/
# Step 2: Compile (run twice for correct cross-references)
cd paper
pdflatex main.tex
pdflatex main.tex- The
.npzand.ptfiles indataset/are excluded from git via.gitignore; they are regenerated automatically by running the pipeline. - The code falls back to CPU automatically if no GPU is available.
- All random seeds are fixed at 42 for full reproducibility.
- Figure paths in the LaTeX source are relative to
paper/figures/; the copy step above must be completed before compilation.
- Extend beyond five canonical classes to continuous filter-parameter regression (e.g., predicting cutoff frequency and filter order)
- Test robustness to noisy or incomplete frequency-response vectors, closer to real identification conditions
- Add a held-out generalization split over unseen pole-zero configurations rather than random samples of the same generator
- Apply the trained models to a downstream image-restoration task (selecting a filter from a degraded image) to demonstrate the stated applications
English | 中文说明
课程名称： 数字图像处理 专业： 人工智能 姓名： Hossen Md Jisan 学号： 202353460019 研究主题： 基于Z变换极点与零点的深度学习系统辨识
在本项目中，我提出了一种基于深度学习的离散时间LTI系统辨识框架。我将每个系统的Z变换极零点分布图渲染为64x64的灰度图像，并结合128维频率响应幅度向量，构建三种神经网络架构：卷积网络PoleZeroCNN、多层感知机FreqMLP和后期融合网络FusionNet，将系统分类为低通、高通、带通、带阻与全通五类。
该框架将经典数字信号处理与现代深度学习相结合，在数字图像处理领域的滤波器识别、图像去噪、盲目反卷积等任务中具有直接应用价值。
我在5000个样本（每类1000个）的均衡数据集上训练并评估三个模型，测试集750个样本：
| 模型 | 准确率 | 精确率 | 召回率 | F1分数 | 参数量 |
|---|---|---|---|---|---|
| PoleZeroCNN | 99.73% | 99.76% | 99.73% | 99.74% | 421,861 |
| FreqMLP | 100.00% | 100.00% | 100.00% | 100.00% | 75,269 |
| FusionNet | 100.00% | 100.00% | 100.00% | 100.00% | 455,077 |
DIP_ZTransform_DL/
├── src/
│ ├── 01_dataset_generation.py # 合成极零点数据集（5000样本，5类）
│ ├── 02_dataset_visualization.py # 数据集可视化（6张图自动保存）
│ ├── 03_model.py # CNN、MLP、FusionNet架构定义
│ ├── 04_train.py # 训练、检查点、学习率调度
│ ├── 05_evaluate.py # 测试评估、混淆矩阵、指标输出
│ └── 06_run_all.py # 一键运行完整流程
├── dataset/ # 运行后自动生成
├── output/
│ ├── figures/ # 训练曲线、混淆矩阵、预测面板（12张）
│ ├── dataset_viz/ # 数据集可视化（6张）
│ └── test_metrics/ # 测试指标CSV、JSON、对比图（共19张PNG）
├── paper/
│ ├── main.tex # LaTeX论文完整源码
│ └── figures/ # 论文图像目录（从output/复制）
├── requirements.txt
├── .gitignore
└── README.md
我建议使用Python 3.9及以上版本：
pip install -r requirements.txt主要依赖：PyTorch 2.0+、NumPy、SciPy、Matplotlib、scikit-learn、scikit-image、Pillow、pandas、seaborn、tqdm。
# 一键运行（推荐）
python src/06_run_all.py
# 分步运行
python src/01_dataset_generation.py # 约96秒（CPU）
python src/02_dataset_visualization.py
python src/03_model.py # 架构验证
python src/04_train.py # 约110秒（GPU）
python src/05_evaluate.py在GPU环境下完整流程约耗时224秒。
output/dataset_viz/（6张）
- fig01_sample_pz_maps.png
- fig02_mean_freq_response.png
- fig03_class_distribution.png
- fig04_freq_response_heatmap.png
- fig05_pixel_distribution.png
- fig06_pz_scatter.png
output/figures/（12张）
- fig_train_curves_cnn.png
- fig_train_curves_mlp.png
- fig_train_curves_fusion.png
- fig_confusion_cnn.png
- fig_confusion_mlp.png
- fig_confusion_fusion.png
- fig_f1_per_class_cnn.png
- fig_f1_per_class_mlp.png
- fig_f1_per_class_fusion.png
- fig_pz_predictions_cnn.png
- fig_pz_predictions_mlp.png
- fig_pz_predictions_fusion.png
output/test_metrics/（1张）
- fig_model_comparison.png
paper/main.tex 包含完整LaTeX论文（1257行），结构如下：
- 摘要（含定量结果）
- 引言（背景、问题定义、研究目标）
- 相关工作（2018-2022年文献）
- 数据集构建（Z变换原理、共轭对生成、两种特征表示）
- 模型架构（ConvBlock公式、PoleZeroCNN逐层规格、FreqMLP逐层规格、FusionNet架构图与数学推导、训练目标与优化策略）
- 实验与讨论（全部19张图、5张数据表、误分析）
- 结论与未来工作
- 参考文献（18篇，均为2015-2022年期刊与会议论文）
编译步骤：
# 第一步：复制图像到论文目录
mkdir -p paper/figures
cp output/dataset_viz/*.png paper/figures/
cp output/figures/*.png paper/figures/
cp output/test_metrics/fig_model_comparison.png paper/figures/
# 第二步：编译（运行两次生成正确引用编号）
cd paper
pdflatex main.tex
pdflatex main.tex- dataset/ 中的 .npz 和 .pt 文件已通过 .gitignore 排除，在本地运行代码后自动生成。
- 若无GPU，代码自动回退到CPU，训练时间相应增加。
- 所有随机种子固定为42，确保完全可复现。
- 论文图像引用路径为 figures/，编译前必须先执行上述复制命令。