v2.2

v2.2

Every figure and table is now numbered and can be referred to from the text, and the MATLAB listings have been cut back to the algorithm itself.

Added

• Captions and labels for all 23 figures and tables.
• 25 in-text references using the class's own \figref and \tabref, which print "Figure 1.10" with the label typeset bold.
• A short passage at the end of Section 2.1 explaining where the 1KB to 0.6KB saving comes from, why 205 coefficients are enough, and how this differs from sample-then-compress.

Changed

• The MATLAB listings now show only the algorithm. Setup, signal generation, plotting and the fprintf statistics are gone, which takes the listings from 896 lines to 227. The code still reads as runnable MATLAB and the step comments match the prose.
• The three greedy pursuit figures (OMP, CoSaMP, SAMP) went from 0.8\textwidth to 0.58, and the Mallat filter bank from 1\textwidth to 0.7. They previously occupied a nearly empty page each.
• Section 2.2 no longer starts after a half-empty page. The added passage pushes the break to a natural point, so the page now ends mid-sentence instead of 170 points early.

Fixed

• Figures printed without numbers. The preamble carried \captionsetup[figure]{labelformat=empty}, which suppressed the "Figure N:" prefix, so a cross-reference would have pointed at a number that appeared nowhere on the page. The line and the now-redundant \usepackage{caption} are removed.
• The table in Section 3.1 used \caption*, which produces no number and therefore cannot be referenced. It is a normal numbered caption now.
• Section 1.5 referred to two figures by hardcoded number ("Figure 1 chooses a small s and figure 2 chooses a large s"). Once figures are numbered per chapter those references point at the wrong figures, so they are real cross-references now.
• Two occurrences of the Greek letter sigma in Section 1.2 were Unicode characters inside math mode. The math font has no such glyph, so both printed as blank and LaTeX logged "Missing character: There is no σ in font cmmi10". They use \sigma now.
• A bibliography entry used fullwidth full stops (U+FF0E) instead of ordinary ones.

v2.1

v2.1

A full retypesetting. The tutorial moves to the same document class as the other tutorials, and the whole book is rebuilt around it.

Added

• A short overview at the start of every chapter — four of them, one per part: Signal Transformation, Basic Concepts, Compressed Sensing, and Image processing.
• A cover image on the title page, showing the measurement equation Y = Φ·Ψᵀ·X.
• elegantbook.cls is now bundled. It was not included before and is not installed by default, so a fresh clone could not be built at all.
• .latexmkrc and .gitignore. A bare latexmk now selects XeLaTeX and runs as many passes as the cross-references need.

Changed

• Migrated from ctexart to the elegantbook document class. The hand-rolled heading sizes, the page border, the custom title page and the manual section dividers are gone, along with more than a dozen redundant packages.
• Headings no longer carry a redundant \textbf{} wrapper (89 of them). ElegantBook already sets headings in bold, so they were being bolded twice.
• Figures now float. All 22 were pinned with [H]; they use [htbp], which packs pages instead of leaving large gaps. The one figure referred to as "the figure below" keeps its pinned placement.
• Figure captions lost their "Figure N:" prefix. No figure is cross-referenced anywhere, so the numbers carried no information.
• The table of contents, the Preface and the Afterword are set with wider spacing.
• The README has been rewritten.

Fixed

• Typo in the source filename: Introdution → Introduction. The same typo was in one of the section headings too.
• Eighteen grammar slips, mostly articles: a observation → an observation (three places), a orthogonal, a equivalent, a equation, a optimization, a all-zero; an proper → a proper; all we uses → all we use.

Removed from version control

• Introdution to Compressed Sensing.synctex.gz was a tracked build artifact. It is regenerated at build time and is now ignored.

v2.0

v2.0

Three additions, one of them a whole new chapter.

Added

• Curvelet transforms, continuous and discrete, added to the Signal Transformation chapter. Curvelets handle edges better than wavelets do, and the two sections follow the same shape as the wavelet ones: definition first, then the algorithm.
• Image Quality Assessment and BayesShrink, added to the Basic Concepts chapter. Both are tools for judging how good a reconstruction is, and the later chapters use them.
• A new chapter, Image processing, covering total variation regularization and ADMM.

Changed

• The first chapter's title is now capitalised "Signal Transformation", matching the other three.

v1.0

v1.0

The first release.

A tutorial on compressed sensing, written as a single LaTeX document. It answers one question: if a signal is sparse in some basis, how few measurements does it take to recover it exactly? The Nyquist rate is the classical answer for band-limited signals, and compressed sensing shows that sparsity buys far more.

The tutorial builds up in three parts. It begins with the transforms that make sparsity meaningful, then develops the concepts the theory needs, and only then reaches compressed sensing itself.

Contents

• Signal transformation — the discrete Fourier transform and its non-uniform variant, the discrete cosine transform, the short time Fourier transform, and the continuous and discrete wavelet transforms.
• Basic Concepts — sparsity, norms, convex optimization, and the projection matrix.
• Compressed Sensing — the definition, the observation matrices that make recovery possible, and greedy pursuit.
• Afterword and References.

Building

Requires a TeX distribution with XeLaTeX, and a full TeX Live installation rather than a minimal one. elegantbook.cls is bundled in the repository, so there is nothing extra to install.