A Compressed Sensing Framework to Recover Cutting Tool Modal Parameters from Aliased Video

Cutting tools vibrate with small motion over frequencies ranging from a few 100 Hz to a few kHz. Estimating small motion over these wide range of frequencies using newer vision-based modal analysis methods requires video to be recorded at high frame rates and resolutions. High frame rates are necessary for proper temporal resolution and high resolution is necessary for properly spatially resolving small motion. However, since most cameras trade resolution for speed, registering high-frequency small motion with video becomes nontrivial. To recover cutting tool modal parameters from high resolution but potentially temporally aliased video, this paper discusses the use of the compressed sensing technique. Compressed sensing enables non-uniform random sampling at sub-Nyquist rates and leverages sparse structures of signals to allow for exact recovery of signals that are not aliased. Though compressed sensing has significant potential, it requires video to be randomly sampled at the time of acquisition. Since existing camera hardware does not allow for this yet, this paper instead demonstrates modal parameter recovery from motion registered from video that is randomly downsampled at non-uniform rates from video that was originally properly and uniformly sampled. Recovered parameters from aliased video agree with those from video sampled properly.