|Using a learned signal model with the robust signal modeling and reconstructions under development produces a sharper reconstruction of the heart image shown above than conventional analytical models like the wavelet or finite differences transform.|
My research focuses on combining mathematical modeling tools, signal processing theory, and estimation techniques into novel image processing and reconstruction methods, for applications like magnetic resonance imaging (MRI). For example, I recently integrated a robust means for constructing mathematical models of signals, called dictionary learning, with an advanced MRI reconstruction method to reproduce high-quality images from much faster scans. Ongoing imaging research is organized into multiple related thrusts:
- Fast reconstruction algorithms
- Reconstruction artifact correction (e.g., motion, inhomogeneity)
- Selecting reconstruction parameters, methods to optimize image quality automatically
More information about current and future research can be found on the Virginia Imaging Theory and Algorithms Laboratory (VITAL) web site.
Fast Reconstruction Algorithms
|Using more advanced variable-splitting techniques, current research is able to significantly improve the reconstruction error after two seconds of processing time using the ADMM algorithm, versus a more conventional Split Bregman approach. The error image (intensity scaled up by a factor of 5) portrays significantly reduced errors in the heart image shown.|
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, will enable rapid reconstruction of images and time series on the fly.
Previous research (in collaboration with Jeffrey Fessler and Sathish Ramani at the University of Michigan, and Yonina Eldar at Technion, supported by NIH F32 EB015914) investigated new combinations of optimization techniques like variable-splitting and majorization-minimization in order to solve these complicated reconstruction problems more quickly. Current efforts in the VITAL laboratory are investigating similar approaches for learned signal models and larger-scale reconstructions.
- Weller, Daniel S. "Robust Phase Retrieval with Sparsity under Nonnegativity Constraints." 2016 IEEE Asilomar Conf. on Signals, Systems, and Computers. Pacific Grove, CA, USA, Nov. 2016, pp. 1043-1047.
- Weller, Daniel S. "Analysis-Form Sparse Phase Retrieval Using Variable-Splitting." 2016 IEEE Southwest Symposium on Image Analysis and Interpretation. Santa Fe, NM, USA, March 2016, pp. 61-64.
- Weller, Daniel S. "Reconstruction with Dictionary Learning for Accelerated Parallel Magnetic Resonance Imaging." 2016 IEEE Southwest Symposium on Image Analysis and Interpretation. Santa Fe, NM, USA, March 2016, pp. 105-108.
- Weller, Daniel S., Pnueli, Ayelet, Divon, Gilad, Radzyner, Ori, Eldar, Yonina C., and Fessler, Jeffrey A. "Undersampled Phase Retrieval with Outliers." IEEE Trans. Comput. Imaging, vol. 1, no. 4, pp. 247-258, December 2015. DOI: 10.1109/TCI.2015.2498402
- Weller, Daniel S., Pnueli, Ayelet, Radzyner, Ori, Divon, Gilad, Eldar, Yonina C., and Fessler, Jeffrey A. "Phase retrieval of sparse signals using optimization transfer and ADMM." 2014 IEEE Int. Conf. on Image Processing. Paris, France, Oct. 2014, pp. 1342-6.
- Weller, Daniel S., Ramani, Sathish, and Fessler, Jeffrey A. "Augmented Lagrangian with Variable Splitting for Faster Non-Cartesian L1-SPIRiT MR Image Reconstruction." IEEE Trans. Med. Imaging, vol. 33, no. 2, pp. 351-361, February 2014. DOI: 10.1109/TMI.2013.2285046
Reconstruction Artifact Correction
|One way to significantly accelerate MRI scans with interleaved spiral measurement patterns is to use fewer interleaves or shots. However, using fewer shots increases susceptibility to nonuniform field distortions. The image on the right has the nonuniformity corrected during the reconstruction process.|
One drawback of MRI is its suspectibility to a range of artifact-inducing phenomena, many of which can distort images to render them no longer useful. A frequent cause of such artifacts is subject motion, either body movements while lying in the scanner, or motion of the internal organs while breathing. Another such challenge, nonuniform magnetic fields can cause unacceptable signal loss or geometric distortions when imaging rapidly. Starting with head motion correction (in collaboration with Jeffrey Fessler and Douglas Noll at the University of Michigan supported by NIH F32 EB015914), previous research investigated new ways for learning and correcting for head motion and nonuniform fields during the reconstruction. Current efforts (with Craig Meyer, John Mugler, and Michael Salerno at the University of Virginia) will address motion in MRI's in young children, who tend to move in the scanner, and in freely-breathing MRI's of cardiac patients, where the heart moves during the breathing cycle.
- Jeelani, Haris, Yang, Yang, Salerno, Michael, and Weller, Daniel S. "Evaluation of k-Space and Image-Space Motion Correction Schemes for CMR Perfusion." 20th Annual SCMR Scientific Sessions, Washington, DC, USA, February 2017, in press.
- Luonan Wang and Weller, Daniel S. "Joint Motion Estimation and Image Reconstruction Using Alternating Minimization." ISMRM 24nd Scientific Meeting. Singapore, May 2016, p. 1800.
- Weller, Daniel S. and Fessler, Jeffrey A. "Fast non-Cartesian L1-SPIRiT with Field Inhomogeneity Correction." ISMRM 22nd Scientific Meeting. Milan, Italy, May 2014, p. 84. Summa cum laude award.
- Weller, Daniel S., Noll, Douglas C., and Fessler, Jeffrey A. "Prospective Motion Correction for Functional MRI Using Sparsity and Kalman Filtering." Proc. SPIE Wavelets and Sparsity XV, vol. 8858, pp. 885823-1-10, Aug. 2013. DOI: 10.1117/12.2023074
Reconstruction Parameter Selection and Image Quality
|A computed tomography (CT) heart image is shown reconstructed with three levels of noise suppression, an essential step of reproducing images from X-ray CT images acquired with lower X-ray dose. This research is concerned with how to automatically distinguish the best quality image (center) from the noisy (left) and oversmoothed (right) images.|
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. Previous work (with Sathish Ramani, Jon-Fredrik Nielsen, and Jeffrey Fessler at University of Michigan) applied an automatic squared-error measure of image quality to choose regularization parameter values for advanced MRI reconstruction algorithms. Current efforts use new ideas in image quality perception to more robustly compare pairs of images to account for structural differences. When combined with a "parameter trimming" framework for efficiently predicting converged image quality from early steps of an iterative algorithm, these automatic methods can be used to rapidly select reconstruction parameters for the iterative reconstructions described previously.
- Haoyi Liang and Weller, Daniel S. "Comparison-based Image Quality Assessment for Selecting Image Restoration Parameters." IEEE Trans. Image Process., vol. 25, no. 11, pp. 5118-5130, Nov. 2016. DOI: 10.1109/TIP.2016.2601783
- Haoyi Liang and Weller, Daniel S. "Denoising method selection by comparison-based image quality assessment." 2016 IEEE Int. Conf. on Image Processing. Phoenix, AZ, USA, Sep. 2016, pp. 3106-3110.
- Haoyi Liang and Weller, Daniel S. "Regularization Parameter Trimming for Iterative Image Reconstruction." 2015 IEEE Asilomar Conf. on Signals, Systems, and Computers. Pacific Grove, CA, USA, Nov. 2015, pp. 755-759.
- Weller, Daniel S., Ramani, Sathish, Nielsen, Jon-Fredrik, and Fessler, Jeffrey A. "Monte Carlo SURE-Based Parameter Selection for Parallel Magnetic Resonance Imaging Reconstruction." Magn. Reson. Med., vol. 71, no. 5, pp. 1760-1770, May 2014. DOI: 10.1002/mrm.24840
- Ramani, Sathish, Weller, Daniel S., Nielsen, Jon-Fredrik, and Fessler, Jeffrey A. "Non-Cartesian MRI Reconstruction With Automatic Regularization Via Monte-Carlo SURE." IEEE Trans. Med. Imag., vol. 32, no. 8, pp. 1411-1422, August 2013. DOI: 10.1109/TMI.2013.2257829
- Weller, Daniel S., Ramani, Sathish, Nielsen, Jon-Fredrik, and Fessler, Jeffrey A. "Automatic L1-SPIRiT Regularization Parameter Selection Using Monte-Carlo SURE." ISMRM 21st Scientific Meeting. Salt Lake City, USA, April 2013, p. 2602.
- Weller, Daniel S., Ramani, Sathish, Nielsen, Jon-Fredrik, and Fessler, Jeffrey A. "SURE-Based Parameter Selection for Parallel MRI Reconstruction using GRAPPA and Sparsity." 2013 IEEE Int. Symp. on Biomedical Imaging. San Francisco, USA, April 2013, pp. 954-957.
Accelerating MRI by Unifying Sparse Models and Multiple Receivers
Joint work with Vivek Goyal (thesis advisor) and Elfar Adalsteinsson at the Massachusetts Institute of Technology, Lawrence Wald and Jonathan Polimeni at the A. A. Martinos Center, and Leo Grady now at HeartFlow, Inc. (formerly with Siemens Corporate Research)
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.
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "Sparsity-Promoting Calibration for GRAPPA Accelerated Parallel MRI Reconstruction." IEEE Trans. Med. Imag., vol. 32, no. 7, pp. 1325-1335, July 2013. DOI: 10.1109/TMI.2013.2256923
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "Denoising Sparse Images from GRAPPA Using the Nullspace Method." Magn. Reson. Med., vol. 68, no. 4, pp. 1176-1189, Oct. 2012. DOI: 10.1002/mrm.24116
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "Accelerated Parallel Magnetic Resonance Imaging Reconstruction Using Joint Estimation with a Sparse Signal Model." 2012 IEEE Statist. Signal Process. Workshop. Ann Arbor, USA, August 2012, pp. 221-224.
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "Greater Acceleration Through Sparsity-Promoting GRAPPA Kernel Calibration." ISMRM 20th Scientific Meeting. Melbourne, Australia, May 2012, p. 3354.
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "Regularizing GRAPPA using simultaneous sparsity to recover de-noised images." Proc. SPIE Wavelets and Sparsity XIV, vol. 8138, pp. 81381M-1-9, Aug. 2011. DOI: 10.1117/12.896655
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "Combined compressed sensing and parallel MRI compared for uniform and random cartesian undersampling of k-Space." 2011 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing. Prague, Czech Republic, May 2011, pp. 553-556. DOI: 10.1109/ICASSP.2011.5946463
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "SpRING: sparse reconstruction of images using the nullspace method and GRAPPA." ISMRM 19th Scientific Meeting. Montreal, Canada, May 2011, p. 2861.
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "Evaluating sparsity penalty functions for combined compressed sensing and parallel MRI." 2011 IEEE Int. Symp. on Biomedical Imaging. Chicago, USA, March-April 2011, pp. 1589-1592. DOI: 10.1109/ISBI.2011.5872706 Finalist, Student Paper Competition.
- Weller, Daniel S., Polimeni, Jonathan R., Grady, Leo, Wald, Lawrence L., Adalsteinsson, Elfar, and Goyal, Vivek K. "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
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.
- Weller, Daniel S. and Goyal, Vivek K. "Bayesian post-processing methods for jitter mitigation in sampling." IEEE Trans. Signal Process., vol. 59, no. 5, pp. 2112-2123, May 2011. DOI: 10.1109/TSP.2011.2108289
- Weller, Daniel S. and Goyal, Vivek K. "On the estimation of nonrandom signal coefficients from jittered samples." IEEE Trans. Signal Process., vol. 59, no. 2, pp. 587-597, Feb. 2011. DOI: 10.1109/TSP.2010.2090347
- Weller, Daniel S. and Goyal, Vivek K. "Jitter compensation in sampling via polynomial least squares estimation." 2009 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing. Taipei, Taiwan, April 2009, pp. 3341-3344. DOI: 10.1109/ICASSP.2009.4960340