An image contrast based algorithm for 2-D ISAR image autofocusing is proposed. The problem of ISAR image autofocusing is formulated analytically by defining geometry and dynamics of the radar-target system and by assuming a mathematical model for the received signal. The image focusing is then achieved by estimating the model parameters through the maximisation of the image contrast. The problem of the maximum search is solved numerically by means of an iterative search method. An algorithm able to produce an accurate initial guess is also developed by using the radon transform. The good accuracy of the initial guess guarantees the convergence of the optimisation problem solution to the global maximum. The performance of the proposed autofocusing technique is tested by comparing it to the point prominent processing (PPP) algorithm, the phase gradient algorithm (PGA) and the image entropy based technique (IEBT), through the use of real data. Results confirm the effectiveness of the proposed algorithm. 2 Mathematical aspects of signal modelling and ISAR processing Let the system geometry be represented by Fig. 1 where the radar is located at ð0; 0; h r Þ in the system of coordinates

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Key words: 50 dB acoustic noise reduction; acoustic gradient pulse; EPI; gradient coils Acoustic noise from MRI machines has always been a problem. This noise results from the switching of current in gradient wires within the main field that effectively turns the MRI system into a giant loudspeaker. With the recent increase in main field strengths (i.e., whole-body systems of 7 T), and the ever greater demands placed upon gradient coil currents and switching rates by high-speed imaging, the problem of noise has reached the point where it poses a significant health risk to the subject. Various passive approaches have been proposed to ameliorate the acoustic noise. Currently, the most common approach is the use of vacuum technology to isolate the subject from the source of the noise (1,2).Recently, Mansfield and Haywood (3) introduced the novel concept of active acoustically controlled gradient coils to reduce the acoustic output arising directly from gradient coil vibration. This has been demonstrated to greatly reduce the noise generated at the source within the coil structure. Typical reductions in acoustic noise output from a continuous monotone are ϳ30 dB (4). This method depends upon the physical characteristics of the gradient coil support structure, and functions optimally at harmonics of the resonant frequencies of the structure related to these physical characteristics as it relies upon cancellation of standing compressional waves. Off-resonance, there are residual effects that do not respond to control in this manner. Given the high velocity of sound in solids, a single operating frequency was adopted close to the fundamental plate frequency (Fig. 1). By selecting the plate material, this frequency can be conveniently chosen to correspond to the highest operating frequency of the MRI system. In this study we developed a switched gradient pulse for use in EPI that employs only frequency components within a relatively narrow band near the resonance for optimum active acoustic control.Gradient EPI requires a rapidly switched gradient in the read direction. For the purposes of both electrical generation and minimum noise production, this is most conveniently achieved with a simple sinusoidal waveform, in which one k-space line of data is acquired in each half cycle. Ideally, for active acoustic control, this read gradient pulse would consist of a sine wave of appropriate frequency modulated with a top-hat function. Unfortunately, this introduces an infinite range of frequencies to the spectrum of the gradient pulse in the form of a sinc function with significant energy beyond the narrow operational band of active acoustic control, which compromises the effectiveness of the control process.We propose the use of a modulated read gradient pulse that consists of a finite number of frequencies within the narrow band for which active acoustic control is highly effective. A preliminary account of the results of this work has been presented elsewhere (5). METHOD Pulse DesignConsider a series of regularly repeating ...