Discrete tomography studies how to recover structured discrete objects from partial, indirect, or highly compressed measurements. Our group develops mathematical foundations and efficient algorithms for reconstruction when data are scarce, noisy, quantized, or obtained through carefully designed queries. The work sits at the intersection of combinatorics, coding theory, information theory, optimization, signal processing, and machine learning. We study both the fundamental limits of recovery and practical methods for robust inference, with applications in sparse recovery, compressed sensing, neural compression, group testing, distributed learning, and hypothesis testing.
The discrete inverse problem can be formulated as follows:
Recover (or estimate some property of) an unknown object x* sampled from a discrete domain X using observations produced by a noisy channel W.
My research can be broadly categorized into the following themes depending on the assumed model of channel W, and the goal of recovery.
Recovery from queries
Recovery from noise
Optimization Algorithms
Applications
We study how carefully designed queries can reveal hidden discrete structure with minimal measurement cost. This includes adaptive and non-adaptive query models, and recovery with highly constrained observations.
Queries are not always possible, and measurement can be noisy. Our work analyzes recovery under various noise models such as burst noise, deletions, and mixture-based corruption models, with an emphasis on information-theoretic guarantees and robustness.
[C] Homomorphic Error Correcting Codes
(x* = arg min f(x, y, S) over X)
We design fast and principled algorithms for discrete optimization under communication or precision constraints.
We connect discrete tomography ideas to broader settings including compressed learning, neural compression, hypothesis testing, and dimensionality reduction.