Full-Field Mode Shape Identification of Vibrating Structures from Compressively Sampled Video
Video-based techniques for structural dynamics have shown great potential for identifying full-field, high-resolution modal properties. One significant advantage of these techniques is that they lend themselves to being applied to structures at very small
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Full-Field Mode Shape Identification of Vibrating Structures from Compressively Sampled Video Bridget Martinez, Yongchao Yang, Ashlee Liao, Charles Farrar, Harshini Mukundan, Pulak Nath, and David Mascareñas
Abstract Video-based techniques for structural dynamics have shown great potential for identifying full-field, highresolution modal properties. One significant advantage of these techniques is that they lend themselves to being applied to structures at very small length scales such as MEMS devices and living cells. These small structures typically will have resonant frequencies greater than 1 Khz, thus requiring the use of high-speed photography to capture their dynamics without aliasing. High speed photography generally requires the structure-under-test (e.g. living cell) to be exposed to high levels of illumination. It is well-known that exposing delicate structures such as living cells to these high levels of light energy can result in damage to their structural integrity. It is therefore desirable to develop techniques to minimize the amount of illumination that is required to capture the modal properties of interest. This is particularly important given that the mechanical properties of living cells have recently been found to be of interest to the biomedical community. For example, it is known that changes in cell stiffness are correlated with grade of metastasis in cancer cells. Compressive sensing techniques could help mitigate this problem, particularly in fluorescence microscopy applications where cells are illuminated using a laser light source. Compressive sampling would allow for the cells to be exposed to the laser light with a significantly lower duty cycle, thus resulting in less damage to the cells. As a result the structural dynamics of the cells can be measured at increasingly high frequencies yielding new information about cellular material properties that can be coupled with biochemical cues to yield new therapeutic strategies. Furthermore, video-based techniques would benefit from the reductions in memory, bandwidth and computational requirements normally associated with compressive sampling. In this work we present a technique that intimately combines solutions to the blind-source separation problem for video-based, high-resolution operational modal analysis with compressive sampling. Keywords Compressive sensing · Operational modal analysis · Imager · Microscopy · Cancer
10.1 Introduction Since its introduction to the field of signal processing in 2004, compressed sensing (CS) has enabled many applications which allow for the recovery of sparse or compressible signaling. Following the famous Shanon sampling theorem, CS has proven a great triumph in the field of signal processing [1–4]. As abovementioned, CS is useful in the acquisition of signals which are either spare or compressible; both compressibility and sparsity are properties that can be assigned to information which can be represented in its entirety, or completeness with only a few, key components of data. Furthermore, these
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