Contents

A reading map of the whole book. Page-level navigation lives in the sidebar; this page is for stepping back and seeing the arc.

Preface¶

Why this book exists, and three suggested reading paths.

Chapter 0 — From Measurements to Meaning¶

The clean world, mathematical modelling, where noise comes from, why it’s Gaussian, the inverse problem, and the three attacks (signal processing / parametric fitting / machine learning) that organise the rest of the book.

Part I — Math Foundations¶

Probability, statistics, and linear algebra developed at the level needed for the rest of the book. Three levels, plus an independent linear-algebra track. See Part I overview.

0.1Level 1 — Foundations (interleaved probability ↔ statistics)¶

• Probability — overview

• What is a distribution?

• Bernoulli

• Statistics — overview

• Ch 1 — Exploratory data analysis

• Ch 2 — Distributions

0.2Level 2 — Distributions (probability deep dive)¶

• Binomial

• Poisson

• Normal

• Central Limit Theorem

• Putting it together

• Exercises

• Applied — From photons to pixel noise (capstone — applies the distribution chain to the sensor model)

0.3Level 3 — Inference (statistics deep dive)¶

• Ch 3 — PMFs

• Ch 4 — CDFs

• Ch 5 — Modelling

• Ch 6 — PDFs

• Ch 7 — Relationships between variables

• Ch 8 — Estimation

• Ch 9 — Hypothesis testing

• Ch 10 — Least squares

• Ch 11 — Regression

• Ch 12 — Time series

• Ch 13 — Survival analysis

• Ch 14 — Analytic methods

• Exercises

0.4Linear Algebra (independent track)¶

• Linear algebra — overview

• Part 1 — Vectors and the dot product

• Part 2 — Norms and similarity

• Part 3 — Orthogonality and projection

• Part 4 — Linear transforms

• Exercises

• Applied — Images as vectors, patches as points (capstone — applies the linear algebra to image-patch comparison)

Part II — Signals and Measurement¶

How a continuous physical scene becomes a finite grid of pixel numbers.

• Ch 1 — Digitisation: sampling, Nyquist, aliasing

• Ch 2 — The sensor

• Ch 3 — Pixels

• Ch 4 — Contrast

• Ch 5 — Colour

Part III — Why Raw Signals Fail¶

What pixels alone can and cannot tell you, and why we need higher-level representations.

• Ch 6 — Pixel problems

Part IV — Learning from Signals¶

From convolutions to trained networks.

• Ch 9 — Convolutions

• Ch 10 — Backpropagation

• Ch 11 — CNNs

• Ch 12 — Training

Part V — Attention and Beyond¶

Self-attention, vision transformers, and multimodal models.

• Ch 13 — Attention

• Ch 14 — Vision Transformer

• Ch 15 — Vision-Language Models

Start → Chapter 0 — From Measurements to Meaning