Project Grant 2237538

CAREER: THEORETICAL FRAMEWORK FOR DESIGN AND ANALYSIS OF SNAPSHOT COMPRESSIVE IMAGING SYSTEMS -CAPTURING HIGH-RESOLUTION 3D DATA CUBES, SUCH AS VIDEO FILES OR HYPERSPECTRAL IMAGES, IS A KEY REQUIREMENT IN MANY MODERN APPLICATIONS, RANGING FROM MEDICINE TO ROBOTICS. HOWEVER, SINCE SENSOR ARRAYS CAN TYPICALLY ACQUIRE ONLY 2D IMAGES, CAPTURING SUCH DATA CUBES OFTEN REQUIRES SCANNING ALONG THE THIRD DIMENSION, WHICH MAKES THE PROCESS TIME-CONSUMING, COSTLY, AND INEFFECTIVE. ONE EMERGING SOLUTION TO ADDRESS THIS CHALLENGE AND ENABLE EFFICIENT 3D IMAGING IS THE SO-CALLED SNAPSHOT COMPRESSIVE IMAGING (SCI). IN SCI SOLUTIONS, THE DATA-ACQUISITION HARDWARE IS DESIGNED TO CAPTURE AN ENCODED 2D IMAGE THAT SUMMARIZES THE FULL INFORMATION CONTAINED IN THE 3D DATA CUBE. THE DESIRED 3D DATA CUBE IS LATER RECONSTRUCTED FROM A SINGLE 2D PROJECTION USING COMPLEX COMPUTATIONAL DECODING ALGORITHMS. MOST THEORETICAL AND ALGORITHMIC QUESTIONS RELATED TO SUCH DECODING PROBLEMS ARE STILL WIDELY OPEN. IN THE ABSENCE OF A SOLID THEORETICAL UNDERSTANDING OF THE PROBLEM, EXISTING SOLUTIONS ARE GENERALLY HEURISTIC METHODS THAT ARE COMPUTATIONALLY VERY INTENSIVE, INEFFICIENT, AND SUB-OPTIMAL. THE GOAL OF THIS PROJECT IS TO ENABLE COST-EFFECTIVE, RELIABLE, AND EFFICIENT SCI IMAGING BY ADDRESSING THE RELATED FUNDAMENTAL QUESTIONS. SUCH SOLUTIONS CAN IMPACT A WIDE RANGE OF APPLICATIONS, FROM MEDICAL DIAGNOSIS TO ROBOTICS TO AGRICULTURE. TO DEVELOP FULLY PRACTICAL AND ROBUST SCI SOLUTIONS APPLICABLE IN A WIDE RANGE OF APPLICATIONS, A NOVEL THEORETICAL FRAMEWORK IS REQUIRED THAT ENABLES RESEARCHERS TO DESIGN AND OPTIMIZE I) THE 3D TO 2D PROJECTION STEP SUBJECT TO THE HARDWARE CONSTRAINTS OF THE SYSTEM, AND II) COMPUTATIONALLY EFFICIENT RECOVERY ALGORITHMS THAT CAN REPRODUCE A HIGH-QUALITY 3D DATA CUBE FROM A SINGLE 2D MEASUREMENT. THE MAIN GOAL OF THIS PROPOSAL IS TO PROVIDE SUCH A THEORETICAL PLATFORM THAT ENABLES RESEARCHERS TO DESIGN, ANALYZE, AND OPTIMIZE SCI SYSTEMS. TO ACHIEVE THIS GOAL, THE TEAM OF RESEARCHERS AIM AT I) CHARACTERIZING THE FUNDAMENTAL TRADE-OFFS BETWEEN THE PARAMETERS OF SCI SYSTEMS, SUCH AS PROJECTION MAPPING, 3D DATA-CUBE STRUCTURE, AND ACHIEVABLE RECONSTRUCTION QUALITY AND RESOLUTION; II) DEVELOPING AN AUTOMATED, THEORETICALLY-FOUNDED, AND EFFICIENT APPROACH TO STRUCTURE LEARNING THAT IS APPLICABLE TO VARIOUS TYPES OF 3D DATA CUBES ENCOUNTERED IN SCI APPLICATIONS; AND III) DESIGNING DISRUPTIVE SCI SOLUTIONS THAT INCORPORATE THE DEVELOPED AUTOMATED STRUCTURE-LEARNING METHOD INTO AN EFFICIENT NEAR-OPTIMAL SCI RECOVERY ALGORITHM THAT PERFORMS CLOSE TO THE CHARACTERIZED FUNDAMENTAL LIMITS. THIS AWARD REFLECTS NSF'S STATUTORY MISSION AND HAS BEEN DEEMED WORTHY OF SUPPORT THROUGH EVALUATION USING THE FOUNDATION'S INTELLECTUAL MERIT AND BROADER IMPACTS REVIEW CRITERIA.