Enhancing Ultrasound Images Using Hybrid FIR Structures

Abstract

The problem of saving a sharp edge with a simultaneous enhancing in the image is typical for ultrasound applications. Ultrasound imaging is a technique that is widely used in a variety of clinical applications, such as cardiology (Najarian & Splinter, 2007), obstetrics and gynecology (Jan, 2006), and others. Due to the blur and typically non Gaussian noise, an origin ultrasound image has a poor resolution. That forces researches to create image processing algorithms having a contradictive ability of cleaning the image of noise but saving its sharp edge. An overall panorama of nonlinear filtering following the median strategy has been presented by Pitas and Venetsanopoulos (Pitas & Venetsanopoulos, 1990) along with important modifications for a large class of nonlinear filters employing the order statistics. The algorithm issues for the filter design have been discussed in (Kalouptsidis & Theodoridis, 1993). In (Astola & Kuosmanen, 1997), the finite impulse response (FIR) median hybrid filters (MHF) strategy has been proposed with applications to image processing. An important step ahead has been made in (Heinonen & Neuvo, 1987; 1988), where the FIR MHF structures have been designed. In the sequel, the MHF structures have extensively been investigated, developed, and used by many authors. Basically, hybrid FIR structures can be designed using different types of estimators. Among possible solutions, the polynomial estimators occupy a special place, since the polynomial models often well formalize a priori knowledge about different processes. Relevant signals are typically represented with degree polynomials to fit a variety of practical needs. Examples of applications of polynomial structures can be found in signal processing (Dumitrescu, 2007; Mathews & Sicuranza, 2001), timescales and clock synchronization (Shmaliy, 2006), image processing (Bose, 2004), speech processing (Heinonen & Neuvo, 1988), etc. The polynomial estimators suitable for such structures can be obtained from the generic form of the p-step predictive unbiased FIR filter proposed in (Shmaliy, 2006; 2009). Such estimators usually process data on finite horizons of N points that typically obtain a nice restoration. In this Chapter, we first give the theory of the p-step smoothing unbiased FIR estimator of polynomial signals viewing an image as a multistate space model. We then use the polynomial solutions in the design of FIR MHF structures and justify optimal steps p from the standpoint of minimum produced errors. We show advantages of the approach employing the three generic ramp FIR solutions. Namely, we exploit the 1-step predictive