Signal Transformation and Information Representation Group :: Professor Vivek K Goyal
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Group Overview – appropriate c. 2012

The recent and ongoing work of the STIR group has included key innovations in a broad range of fields. Our work is generally organized around conceptual themes, including quantization, sampling, and sparsity. Alongside the invention of theoretical frameworks for source coding, we work with great collaborators to maximize our technological impact in several areas of information acquisition.

Optical Imaging

The newest focus area for the STIR group is optical imaging. We have invented new ways to relate optical imaging to spatiotemporal sampling, and this has led to some surprising new capabilities.

  • Demonstrated that the capture of transient light field properties, beyond mere time of flight, enables dramatic effects such as forming an image of a surface that is in the line of sight of neither the illumination source nor the sensor—without a mirror.
  • Introduced a new architecture for forming depth maps with a single optical sensor: the Compressive Depth Acquisition Camera (CoDAC). This concept is at the center of a winning proposal in the 2011 Qualcomm Innovation Fellowship contest.

Magnetic Resonance Imaging

MRI requires sophisticated signal processing both to create the magnetization conditions needed to reveal tissue properties and to encode and interpret the magnetization. MRI measurements are essentially uninterpretable without firm grounding in both signal processing and physics. The STIR group has made contributions to both excitation design and image reconstruction.

  • Introduced a new formulation for slice-selective excitation design through simultaneous sparse approximation (IEEE Trans. Medical Imaging paper).
  • Demonstrated that our formulation enables B1+ inhomogeneity mitigation for 7T brain imaging, reducing a major impediment to clinical use of ultra-high main field MRI (Mag. Res. Med. paper)
  • Provided a method to analyze and minimize specific absorption rate, providing optimum imaging under safety constraints (J. MRI paper)
  • Introduced a joint reconstruction technique for multiple contrast preparations using a hierarchical Bayesian model (Mag. Res. Med. paper)
  • Introduced the SpRING algorithm to improve upon GRAPPA and compressed sensing used separately for image construction from multiple receive coils (ISMRM paper; full paper in revision)

Sparse Signal Estimation and Detection (Including Compressed Sensing)

Exploiting sparsity has become a central theme in signal processing over the past two decades, and this trend has accelerated greatly with the introduction of compressed sensing. The STIR group has made foundational contributions in understanding the limits of estimation and detection and the performances of algorithms.

  • Proved necessary and sufficient conditions for sparse signal support recovery that were the first to establish the importance of signal-to-noise ratio and dynamic range in understanding the relative performance of the (intractable) optimal detector, lasso, and a (very simple) thresholding-based detector (IEEE Trans. Inform. Theory paper).
  • Provided the first analytical framework to enable computation of the exact asymptotic performance of a large class of estimators, including the lasso estimator. This is based on generalizing Guo and Verdú's replica method analysis of high-dimensional estimation problems with linear mixing (full paper).
  • Presented a new class of simultaneous sparsity problems, along with a variety of algorithms for solving these problems; these arise in MRI excitation design (SIAM J. Sci. Comput. paper).
  • Constructively demonstrated that conditional rank information (the relative sizes of the nonzero entries of a sparse vector) is tremendously valuable by proving that a simple algorithm using conditional ranks can have performance approaching maximum likelihood at high SNR. This is presented in the context of random access communication, where the interpretation is that knowledge of conditional ranks mitigates the near-far effect and can in the best case asymptotically eliminate multiple access interference. This work also supports previously-unproven observations in sparse Bayesian learning (full paper).

Source Coding and Quantization

The STIR group has introduced several new ways to think about fundamental limits of source coding and the effects of quantization, as well as new techniques for source coding.

  • Initiated theoretical study of compression of nonsequential data, as a foundation for compression of databases and other data that can be reordered (DCC paper won the 2006 Capocelli Prize and Lav Varshney's SM thesis won the 2006 Ernst A. Guillemin Thesis Prize).
  • Introduced a theory for quantization of data that will be used in computations, showing in particular that the improvement over quantizing for low error in the input data can be arbitrarily large (Vinith Misra's MEng thesis won the 2008 David Adler Memorial Prize; see full paper).
  • Developed optimal quantizer designs for low relative error, which has self-evident importance but is often less convenient than absolute error (DCC paper won the 2011 Capocelli Prize).
  • Introduced a framework for understanding team decision making on ensembles of problems, where optimal categorization of hypothesis testing problems can be seen as quantization of the prior probabilities of the hypotheses. This has many intriguing implications for human decision making, apparent statistical biases, and team or committee formation (DCC paper 1, DCC paper 2).
  • Introduced a theoretical framework for malleable coding, where compression is balanced against the cost of editing the compressed data (edit-distance version, fixed reuse version).
  • Introduced theory and efficient algorithms for sorting-based sensors, through a generalization of permutation source codes (ACHA paper).
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