Considerable interest has arisen in recent years regarding wavelet analysis as a new transform technique for speech- and image-processing applications. This technique has shown effective results in several applications such as image compression, edge detection, feature extraction, and nonlinear noise filtering. Now, Yousef Hawwar and Ali Rex of the University of Wisconsin-Milwaukee (Milwaukee, WI) and Robert Turnery of Xilinx (San Jose, CA) have used the technique as the basis for filtering noise in real-time image-processing applications.
"In traditional Fourier-based signal processing," says Turney, " the spectrum of the signal is assumed to have little overlap with the noise spectrum and, therefore, linear time-invariant filtering is employed." However, this linear filtering approach cannot separate noise from signal where their Fourier spectra overlap. "In discrete-wavelet-transform [DWT] analysis, the method is different," he explains.
"Here, it is assumed that the amplitude, rather than the location, of the spectra of the signal is as different as possible for that type of noise." This allows clipping, thresholding, and shrinking of the amplitude of the coefficients to separate signals or to remove noise. The localizing or concentrating properties of the wavelet transform make the algorithm particularly effective for such applications.
Using available Virtex FPGA technology from Xilinx, Turney and his colleagues have hardwired a filtering algorithm based on the wavelet transform that operates at 80 MHz. In this approach, the DWT of a signal is calculated, and the resultant wavelet coefficients are passed through a threshold. Next, the coefficients that are smaller than a certain value are removed. Then, the resultant coefficients are used to reconstruct the signal.
With this method, it is possible to remove noise with little loss of details. If a signal has its energy concentrated in a small number of wavelet coefficients, then its coefficient values will be relatively large compared to the noise that has its energy spread over a large number of coefficients. According to Turney, system clock rates of 100 and 120 MHz are also available for more-aggressive system-bandwidth requirements.
