Research

Other Previous Research

Fast Reconstruction Algorithms

Joint work with Sathish Ramani, Jon-Fredrik Nielsen, and Jeffrey Fessler at University of Michigan, and Yonina Eldar at Technion, supported by NIH F32 EB015914

High quality model-based reconstructions from incomplete measurements are necessary to enable faster, more robust MRI scans. However, such processing generally requires time-consuming iterative algorithms, which limits the image quality readily available to MRI users during a scan. For physicians and other users to integrate new advanced image reconstructions into their scanning protocols, faster implementations are needed. The algorithmic improvements made possible in this research, coupled with parallel and cloud computing capababilities, enable rapid reconstruction of images and time series on the fly. This research investigated new combinations of optimization techniques like variable-splitting and majorization-minimization in order to solve these complicated reconstruction problems more quickly.

Selected Publications:

1. Daniel S. Weller. "Robust Phase Retrieval with Sparsity under Nonnegativity Constraints." IEEE Asilomar Conference on Signals, Systems, and Computers. Pacific Grove, CA, USA, November 2016, pp. 1043-1047. DOI: 10.1109/ACSSC.2016.7869528

2. Daniel S. Weller. "Analysis-Form Sparse Phase Retrieval Using Variable-Splitting." IEEE Southwest Symposium on Image Analysis and Interpretation. Santa Fe, NM, USA, March 2016, pp. 61-64. DOI: 10.1109/SSIAI.2016.7459175

3. Daniel S. Weller, Ayelet Pnueli, Gilad Divon, Ori Radzyner, Yonina C. Eldar, and Jeffrey A. Fessler. "Undersampled Phase Retrieval with Outliers." IEEE Transactions on Computational Imaging, vol. 1, no. 4, pp. 247-258, December 2015. DOI: 10.1109/TCI.2015.2498402

4. Daniel S. Weller, Ayelet Pnueli, Ori Radzyner, Gilad Divon, Yonina C. Eldar, and Jeffrey A. Fessler. "Phase retrieval of sparse signals using optimization transfer and ADMM." IEEE International Conference on Image Processing. Paris, France, October 2014, pp. 1342-1346. DOI: 10.1109/ICIP.2014.7025268

5. Daniel S. Weller, Sathish Ramani, and Jeffrey A. Fessler. "Augmented Lagrangian with Variable Splitting for Faster Non-Cartesian L1-SPIRiT MR Image Reconstruction." IEEE Transactions on Medical Imaging, vol. 33, no. 2, pp. 351-361, February 2014. DOI: 10.1109/TMI.2013.2285046

Reconstruction Parameter Selection

Joint work with Sathish Ramani, Jon-Fredrik Nielsen, and Jeffrey Fessler at University of Michigan, supported by NIH F32 EB015914

Another hurdle to overcome with advanced reconstruction techniques for MRI and other applications is the selection of the numerical parameters that control the signal models used in the reconstruction. Using too large or too small a value can over-emphasize or under-regularize a reconstruction, yielding unacceptable image quality. Manual parameter tuning is too time-consuming and unreliable for widespread practical application, so automatic methods aim to adjust these parameters to optimize some measure of reconstructed image quality. We applied an automatic squared-error measure of image quality to choose regularization parameter values for advanced MRI reconstruction algorithms.

Selected Publications:

1. Daniel S. Weller, Sathish Ramani, Jon-Fredrik Nielsen, and Jeffrey A. Fessler. "Monte Carlo SURE-Based Parameter Selection for Parallel Magnetic Resonance Imaging Reconstruction." Magnetic Resonance in Medicine, vol. 71, no. 5, pp. 1760-1770, May 2014. DOI: 10.1002/mrm.24840

2. Sathish Ramani, Daniel S. Weller, Jon-Fredrik Nielsen, and Jeffrey A. Fessler. "Non-Cartesian MRI Reconstruction With Automatic Regularization Via Monte-Carlo SURE." IEEE Transactions on Medical Imaging, vol. 32, no. 8, pp. 1411-1422, August 2013. DOI: 10.1109/TMI.2013.2257829

3. Daniel S. Weller, Sathish Ramani, Jon-Fredrik Nielsen, and Jeffrey A. Fessler. "Automatic L1-SPIRiT Regularization Parameter Selection Using Monte-Carlo SURE." ISMRM 21st Scientific Meeting. Salt Lake City, USA, April 2013, p. 2602. (preprint)

4. Daniel S. Weller, Sathish Ramani, Jon-Fredrik Nielsen, and Jeffrey A. Fessler. "SURE-Based Parameter Selection for Parallel MRI Reconstruction using GRAPPA and Sparsity." IEEE International Symposium on Biomedical Imaging. San Francisco, USA, April 2013, pp. 954-957. DOI: 10.1109/ISBI.2013.6556634

Accelerating MRI by Unifying Sparse Models and Multiple Receivers

Joint work with Vivek Goyal (thesis advisor, now at Boston University) and Elfar Adalsteinsson at the Massachusetts Institute of Technology, Lawrence Wald and Jonathan Polimeni at the A. A. Martinos Center, and Leo Grady at Siemens Corporate Research (now at Paige.ai)

The time required to scan using magnetic resonance (MR) technology is a fundamental limiting factor of image quality and affordability and impedes the development of novel applications of MR imaging in clinical diagnostics. One popular method for accelerating the acquisition process in MR imaging include partial reconstructions from data acquired using multiple receiver coils. Recently, compressed sensing (CS) has been applied successfully to highly undersampled MR data, both of the single and multiple coil varieties. However, despite the intuitive complementary nature of using multiple coils and CS, only limited improvement has been attained by combining these methods, and the most successful methods involve non-standard acquisition parameters or sampling patterns. I am examining the problem of combining sparsity models and accelerated parallel imaging and exploring novel algorithms for their combination suitable for conventional MR imaging using uniformly-spaced undersampling patterns. A significant reduction in scan time will open up whole new possibilities for MR imaging, including real-time high-resolution MR video and rapid scanning for dynamic imaging.

Selected Publications:

1. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Sparsity-Promoting Calibration for GRAPPA Accelerated Parallel MRI Reconstruction." IEEE Transactions on Medical Imaging, vol. 32, no. 7, pp. 1325-1335, July 2013. DOI: 10.1109/TMI.2013.2256923

2. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Denoising Sparse Images from GRAPPA Using the Nullspace Method." Magnetic Resonance in Medicine, vol. 68, no. 4, pp. 1176-1189, October 2012. DOI: 10.1002/mrm.24116

3. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Accelerated Parallel Magnetic Resonance Imaging Reconstruction Using Joint Estimation with a Sparse Signal Model." IEEE Statistical Signal Processing Workshop. Ann Arbor, USA, August 2012, pp. 221-224. DOI: 10.1109/SSP.2012.6319666

4. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Greater Acceleration Through Sparsity-Promoting GRAPPA Kernel Calibration." ISMRM 20th Scientific Meeting. Melbourne, Australia, May 2012, p. 3354.

5. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Regularizing GRAPPA using simultaneous sparsity to recover de-noised images." SPIE Wavelets and Sparsity XIV, vol. 8138, August 2011, pp. 81381M-1-9. DOI: 10.1117/12.896655

6. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Combined compressed sensing and parallel MRI compared for uniform and random cartesian undersampling of k-Space." IEEE International Conference on Acoustics, Speech, and Signal Processing. Prague, Czech Republic, May 2011, pp. 553-556. DOI: 10.1109/ICASSP.2011.5946463

7. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "SpRING: sparse reconstruction of images using the nullspace method and GRAPPA." ISMRM 19th Scientific Meeting. Montreal, Canada, May 2011, p. 2861.

8. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Evaluating sparsity penalty functions for combined compressed sensing and parallel MRI." IEEE International Symposium on Biomedical Imaging. Chicago, USA, March-April 2011, pp. 1589-1592. DOI: 10.1109/ISBI.2011.5872706 Finalist, Student Paper Competition.

9. Daniel S. Weller, Jonathan R. Polimeni, Leo Grady, Lawrence L. Wald, Elfar Adalsteinsson, and Vivek K Goyal. "Combining nonconvex compressed sensing and GRAPPA using the nullspace method." ISMRM 18th Scientific Meeting. Stockholm, Sweden, May 2010, p. 4880.

Sampling Jitter in Analog-to-Digital Converters (ADCs)

Joint work with Vivek Goyal (thesis advisor) at the Massachusetts Institute of Technology (now at Boston University)

The sampling process of acquiring discrete-time (digital) signals from continuous-time (analog) signals used in analog-to-digital converters (ADCs) is highly susceptible to timing noise, or inaccuracy in the phase of the clock controlling the sampling process. Current methods involve designing analog clock circuitry with very nearly exact clock phase, at the expense of component cost, power consumption, and component size. As devices that interact with the analog world get smaller and have more stringent power requirements, ADCs have become a significant limiting factor. I am looking at signal processing alternatives for reducing the effect of timing noise, particularly non-linear algorithms for signal post-processing and am comparing these novel algorithms to those linear algorithms already developed. This work will enable significant advances in sensors, medical equipment, and scientific instrumentation. The sampling jitter problem also has higher-dimensional analogues in image-acquisition and microscopy.

Selected Publications:

1. Daniel S. Weller and Vivek K Goyal. "Bayesian post-processing methods for jitter mitigation in sampling." IEEE Transactions on Signal Processing, vol. 59, no. 5, pp. 2112-2123, May 2011. DOI: 10.1109/TSP.2011.2108289

2. Daniel S. Weller and Vivek K Goyal. "On the estimation of nonrandom signal coefficients from jittered samples." IEEE Transactions on Signal Processing, vol. 59, no. 2, pp. 587-597, February 2011. DOI: 10.1109/TSP.2010.2090347

3. Daniel S. Weller and Vivek K Goyal. "Jitter compensation in sampling via polynomial least squares estimation." IEEE International Conference on Acoustics, Speech, and Signal Processing. Taipei, Taiwan, April 2009, pp. 3341-3344. DOI: 10.1109/ICASSP.2009.4960340