- Topics
- Acoustics and Ultrasonics
- Spatial impulse response
- Delay and velocity measurements
- Envelope detection (demodulation)
- Effects of surface roughness
- Nagy, Peter B., and James H. Rose. "Surface roughness and the ultrasonic detection of subsurface scatterers." Journal of applied physics 73.2 (1993): 566-580.
- Especially Eqs. (9), (10) and (11)
- Artificial Neural Networks
- Calculus
- Multivariate calculus
- Calculus of variations
- Computer vision
- Rotation and translation estimation (rigid body)
- Global displacement estimation
- Phase Correlation Algorithm
- Control Theory
- Laplace Transform
Partial Fractions Expansion
for Inverse Laplace Transform
- Modern Control
- System Identification
- Networked Control Systems
- Fourier Analysis
- Fourier Series
- Bode Diagrams
- Image reconstruction
- Regularization
-
- 3.2 Regularização em problemas inversos
- Karl, W. Clem. "Regularization in image restoration and reconstruction." Handbook of Image and Video Processing. Academic Press, 2005. 183-V.
-
- Linear model-based reconstruction in ultrasound
-
- 2.6 Reconstrução por problemas inversos em ultrassom
- 3 Reconstrução de imagens por problemas inversos
- Viola, Francesco, Michael A. Ellis, and William F. Walker. "Time-domain optimized near-field estimator for ultrasound imaging: Initial development and results." IEEE Transactions on Medical Imaging 27.1 (2007): 99-110.
- See Fig. 2
-
- Full Waveform Inversion
- See Optimization > Adjoint State Methods
-
- This is a very didactic, tutorial-like paper that may serve to those giving a first look at FWI
- Matlab
GNU Octave
(Sistema em código aberto compatível com Matlab)
- Optimization
- Adjoint state methods
- Convex optimization
- Greedy algorithms
- Orthogonal Matching Pursuit (OMP)
- Lagrange Multipliers
- Appendix E. Lagrange Multipliers from
Bishop, Christopher M., and Nasser M. Nasrabadi. Pattern recognition and machine learning. Vol. 4. No. 4. New York: springer, 2006.
- Newton's Methods
-
I really like the one-dimensional approach
used in the Wikipedia article about Newton's
method. Then, seeing the Jacobian and thee Hessian
as N-dimensional generalizations of the first
and second derivatives will really make things
easier to swallow.
-
- Quasi-Newton Methods
Section 2.2 "Overview of Algorithms" from
Nocedal & Wright's book provides a smooth
introduction about what quasi-Newton methods
do. Then, chapter 6 dives into the specifics,
but honestly I still didn't take a look at.
Nocedal, J., Wright, S. (2006). Numerical Optimization.
United States: Springer New York.
- BFGS
Some colleagues have been using SciPy's
implementation of L-BFGS-B quite succesfully
for large scale problems (e.g. FWI).
https://docs.scipy.org/doc/scipy/reference/optimize.minimize-lbfgsb.html
- Programmable Logic Controllers
- CodeSys
- Python
- Multithreading
- Python on Android
- Simulation
Discretization of ODE- and
PDE-based systems
For an undergraduate-level introduction
to discretization, see pages 256-269 from Green, R. A., Lathi, B. P. (2018). Linear Systems and Signals. United Kingdom: Oxford University Press.
-
Although this video is about solving PDEs,
it provides a nice hint about how they can
be discretized.