A near-optimal wavelet-based estimation technique for video sequences

This thesis presents a method for estimation of a video signal given a data set with Poisson noise. The cameras used in creating video sequences are often charge-coupled devices, which produce data by way of a counting process, leading to noise with a Poisson distribution. Because many applications using video require data with less noise, a method of reducing the noise and estimating the original signal is desired. The method presented in this thesis attempts to accomplish this goal without using a Wiener lter, which can de-noise signals and is optimal in the mean-square error sense, but is hard to implement because second-order statistics may be unknown and because of the inversion of a possibly large matrix. Instead, an approximation of the Wiener lter is accomplished by rst performing a one-dimensional discrete Fourier transform in order to decorrelate the video sequence between each two-dimensional frame or across each channel, and then performing a two-dimensional discrete wavelet transform on each of the resulting frames. Thresholding is then implemented, and the inverse transform is applied in order to recover an estimate of the original signal. It is shown that this scheme is e ective in improving signal-to-noise ratio in synthetic video sequences and video captured by a camera