Nonlinear Sampling with Application to Imaging Tomer Michaeli
EE Department, Technion
Ph.D. student,EE DepartmentTechnion
Sampling theory is concerned with recovery of continuous-time signals from their samples. Two important aspects of every sampling theorem are the prior on the signal and the sampling mechanism. For example, in the Shannon sampling theorem the prior is that the signal is bandlimited and the measurements are pointwise uniformly spaced samples. Until recently, much of the sampling literature treated linear acquisition devices and linear signal priors, that is, families of signals that form linear subspaces. These include shift-invariant (SI) spaces, of which the bandlimited prior is a special case. Subspace models and linear sampling result in linear recovery algorithms that are often easy to implement. However, many real-world signals do not conform to the subspace model and practical samplers often introduce nonlinear distortions. Nonlinear signal models arise, for example, in communication, radar and ultrasound applications, while nonlinear measurement devices include CCD image sensors and optical modulators. The nonlinearities typically increase the signal's bandwidth, and thus seemingly require sampling at a higher rate. Nevertheless, by exploiting the signal's structure, it is often possible to perform recovery using a low sampling rate. In this talk, we present a unified framework for treating such settings and demonstrate our approach in the context of motion blur removal from an image sequence that was acquired by a sensor with nonlinear response. We show that our method is superior to the naive approaches of applying the inverse of the nonlinearity prior to a standard deblurring stage or following it.
?What is Sub-Nyquist Sampling
We live in an analog world, but data processing is usually performed by digital computers.
The transition from the analog (continuous time) to the digital world is called sampling.
In most analog-to-digital converters (ADCs) today, sampling is based on the Shannon-Nyquist theorem, which requires sampling at a rate that is at least twice the highest signal frequency.
As the bandwidth of the signal increases, it demands the increase in sampling frequency, which raises a number of critical issues that affect system design:
There is a need for expensive wideband ADCs which require excessive hardware solutions and consume a lot of power.
Computer systems need more memory and more computing power in order to process the sampled data. In many cases, much of the sampled information is compressed and reduced in later stages of the processing.
Sub-Nyquist sampling offers a new way of smart and effective sampling of wideband signals by performing analog preprocessing prior to sampling. The idea is to exploit the same structure that is used in the digital chain in order to drastically reduce the sampling rate and only sample the information in the signal that is actually needed. Thus, instead of sampling at a high rate and then compressing the data, it is possible to sample the signal at a low rate to begin with. Low sampling rate also enables low-rate digital processing and reduces required system memory and power.
This technology has many potential applications in a large variety of fields such as communications, radar systems, medical imaging, optical systems, super-resolution microscopy and more.
At the event we will present algorithms and systems developed in the area of sub-Nyquist sampling.