https://www.chenk.top/en/tags/sparsity/Recent content in Sparsity on Chen Kai BlogHugoenWed, 19 Mar 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/12-sparse-matrices-and-compressed-sensing/Wed, 19 Mar 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/12-sparse-matrices-and-compressed-sensing/<p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/en/linear-algebra/12-sparse-matrices-and-compressed-sensing/illustration_1.png" alt="Essence of Linear Algebra (12): Sparse Matrices and Compressed Sensing — Less Is More — Chapter overview" loading="lazy" decoding="async" class="content-image"> </figure> </p> <hr> <h2 id="the-less-is-more-miracle" class="heading-anchor">The &ldquo;Less Is More&rdquo; Miracle<a href="#the-less-is-more-miracle" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><p>A raw 24-megapixel photograph weighs in at roughly 70 MB. JPEG compresses it to a few hundred kilobytes — a 100<span class="math-inline">$\times$</span> reduction — and you cannot tell the difference. A traditional MRI scan takes thirty minutes; a modern compressed sensing MRI gets the same image in five.</p>