We present a recursive approach to implement the Discrete Hartley Transform in the optical domain by using a passive fiber network of asymmetric couplers, without phase shifters. The optical implementation of Discrete Cosine Transform is also derived, resulting in effective and flexible tools for optical data compression and signal processing.

Ultrasound beams propagating in biological tissues undergo distortions due to local inhomogeneities of the acoustic parameters and the nonlinearity of the medium. The spectral analysis of the radio-frequency (RF) backscattered signals may yield important clinical information in the field of tissue characterization, as well as enhancing the detectability of tissue parenchymal diseases. In this paper, we propose a new tissue spectral imaging technique based on the wavelet packets (WP) decomposition. In a conventional ultrasound imaging system, the received echo-signals are generally decimated to generate a medical image, with a loss of information. With the proposed approach, all the RF data are processed to generate a set of frequency subband images. The ultrasound echo signals are simultaneously frequency decomposed and decimated, by using two quadrature mirror filters, followed by a dyadic subsampling. In addition, to enhance the lesion detectability and the image quality, we apply a nonlinear filter to reduce noise in each subband image. The proposed method requires simple additional signal processing and it can be implemented on any real-time imaging system. The frequency subband images, which are available simultaneously, can be either used in a multispectral display or summed up together to reduce speckle noise. To localize the different frequency response in the tissues, we propose a multifrequency display method where three different subband images, chosen among those available, are encoded as red, green, and blue intensities (RGB) to create a false-colored RGB image. According to the clinical application, different choices can evidence different spectral proprieties in the biological tissue under investigation. To enhance the lesion contrast in a grey-level image, one of the possible methods is the summation of the images obtained from narrow frequency subbands, according to the frequency compounding technique. We show that by adding the denoised subband images created with the WP decomposition, the contrast-to-noise ratio in two phantom images is largely increased.