Why Read This Book

You will get a rigorous, DSP-centered treatment of multidimensional signals that connects 2-D Fourier theory to practical image filtering and restoration methods. The book emphasizes mathematical foundations and gives you the tools to analyze and design 2-D filters and frequency-domain image-processing algorithms.

Who Will Benefit

Advanced undergraduates, graduate students, and practicing engineers working on image processing or multidimensional signal problems who need a solid theoretical foundation and practical filtering/restoration techniques.

Level: Advanced — Prerequisites: Undergraduate signals and systems, 1-D DSP (Fourier transforms, convolution), linear algebra, and basic calculus; familiarity with MATLAB is helpful for implementing examples.

Key Takeaways

• Apply the 2-D Fourier transform and its properties to analyze images and other multidimensional signals
• Analyze and mitigate sampling and aliasing effects in two dimensions and design correct reconstruction schemes
• Design and implement 2-D spatial and frequency-domain filters (separable and nonseparable FIR/IIR)
• Perform image restoration and enhancement using inverse filtering, Wiener filtering, and other frequency-domain methods
• Use correlation and spectral analysis tools for detection, pattern matching, and texture analysis in images

Topics Covered

1. Introduction and basic concepts of 2-D signals and systems
2. The two-dimensional continuous- and discrete-time Fourier transforms
3. Sampling and reconstruction in two dimensions; aliasing and sampling lattices
4. The 2-D discrete Fourier transform, periodicity, and computational issues
5. Spatial-domain filtering: convolution, separable and nonseparable filters
6. Frequency-domain filtering and implementation techniques
7. Design of 2-D FIR and IIR filters
8. Image restoration: inverse filtering, Wiener filtering, and constrained methods
9. Homomorphic and nonlinear enhancement techniques
10. Correlation, pattern matching, and spectral estimation in 2-D
11. Practical considerations and examples; brief treatment of multiresolution/transform methods

Languages, Platforms & Tools

How It Compares

More theory-focused and DSP-centric than Gonzalez & Woods' Digital Image Processing (which is more application and example oriented); similar in spirit to Oppenheim-style rigorous treatments but specialized to multidimensional signals.