https://bughht.github.io/tags/optimization/Recent content in Optimization on Bughht BlogHugozh-CNhhong6@mgh.harvard.edu (Haotian Hong)hhong6@mgh.harvard.edu (Haotian Hong)Mon, 15 Dec 2025 15:09:46 +0800https://bughht.github.io/intern_mgh/acdc_optim/Mon, 15 Dec 2025 15:09:46 +0800hhong6@mgh.harvard.edu (Haotian Hong)https://bughht.github.io/intern_mgh/acdc_optim/<h1 id="shim-waveform-optimization-method-notes">Shim Waveform Optimization: Method Notes</h1> <blockquote> <p><strong>GitHub Repository</strong>: <a href="https://github.com/bughht/ACDC_Optim"target="_blank" rel="external nofollow noopener noreferrer">bughht/ACDC_Optim</a></p> </blockquote> <p>We solve for shim coil currents that cancel a measured (or predicted) $B_0$ bias field, subject to per-coil amplitude and total-current hardware limits. The codebase (<code>ACDC_optimization.py</code>) provides <strong>four solvers</strong> for this problem, chosen according to whether the currents are static or time-varying, and whether the amplifier chain&rsquo;s temporal response (SIRF) needs to be modeled:</p> <p>Naming scheme: <code>solve_shim_&lt;scope&gt;_&lt;algorithm&gt;</code>.</p> <table> <thead> <tr> <th>Function</th> <th>Use case</th> <th>Method</th> </tr> </thead> <tbody> <tr> <td><code>solve_shim_static_qp</code></td> <td>Single time frame</td> <td>Exact QP (<code>quadprog</code>, Goldfarb–Idnani)</td> </tr> <tr> <td><code>solve_shim_waveform_qp</code></td> <td>Waveform, <strong>no</strong> SIRF coupling ($\mathbf{C}=\mathbf{I}$)</td> <td>Exact QP per time point, parallelized (<code>joblib</code>)</td> </tr> <tr> <td><code>solve_shim_waveform_fista</code></td> <td>Waveform, <strong>with</strong> SIRF coupling</td> <td>FISTA (NumPy, FFT-based <code>scipy.signal.convolve</code>, or legacy dense $\mathbf{C}$)</td> </tr> <tr> <td><code>solve_shim_waveform_fista_torch</code></td> <td>Waveform, with SIRF, large $T$ / GPU</td> <td>FISTA (PyTorch, FFT-based <code>conv1d</code>, or legacy dense $\mathbf{C}$)</td> </tr> </tbody> </table> <p>When the SIRF convolution can be neglected, per-time-point QP gives the <em>exact</em> convex optimum and is used directly (<code>solve_shim_waveform_qp</code>). FISTA is only needed once the temporal convolution matrix $\mathbf{C}$ couples time points together, since that removes the block-diagonal structure that makes per-frame QP tractable.</p>