The ubiquity of integrating detectors in scientific and engineering applications suggests that a variety of real-world measurements are high-dimensional count data. Count data, however, is usually an indirect means of measuring the underlying vector-valued signal of interest—whether it be light intensity in a pixel sensor, energy in charged gas particles, or energy in inelastic scattering detected by scanning electron microscope—that cannot be measured directly. As such, the estimation of this signal from the observed count data therefore plays a prominent role across diverse applications. We developed a technique to recover the signal intensity with only handful of photons by carefully modeling the real image sensor noise in the wavelet domain. Because of the manner in which it is derived, the proposed denoising algorithm is guaranteed to be the optimum wavelet-denoising algorithm—meaning there are no other wavelet-based methods that yield a higher image quality.
Image blur is a phenomenon caused by pixel sensors recording light from multiple sources. Defocus and object motion blurs are spatially varying because they depend on depth or the speed of the object, respectively. For these reasons, blur may be seen as a visual cue for scene understanding. The technique we developed to estimate the degree of blur at each pixel location is so precise that it can be used to infer object speed and depth from a single image. Our image deblurring method recovers an unprecedented level of image details. In a related work, we developed a blur-invariant representation of image structures useful for feature extraction. It gives rise to the possibility that objects in a blurry image can be recognized—an autofocus algorithm may bring a face into focus quickly by detecting the faces before the camera is in focus, for example. The proposed blur-invariant image representation may also be used to extract edge information, when ordinary edge detection methods on blurred images would clearly fail.