Direct binary search (DBS) produces the images of the best quality among half-toning algorithms. The reason is that it minimizes the total squared perceived error instead of using heuristic approaches. The search for the optimal solution involves two operations: (1) toggle and (2) swap. Both operations try to find the binary states for each pixel to minimize the total squared perceived error. This error energy minimization leads to a conjecture that the absolute value of the filtered error after DBS converges is bounded by half of the peak value of the autocorrelation filter. However, a proof of the bound's existence has not yet been found. In this paper, we present a proof that shows the bound existed as conjectured under the condition that at least one swap occurs after toggle converges. The theoretical analysis also indicates that a swap with a pixel further away from the center of the autocorrelation filter results in a tighter bound. Therefore, we propose a new DBS algorithm which considers toggle and swap separately, and the swap operations are considered in the order from the edge to the center of the filter. Experimental results show that the new algorithm is more efficient than the previous algorithm and can produce half-toned images of the same quality as the previous algorithm.

Frequency estimation of a complex sinusoidal signal is a fundamental problem in signal processing. In this regard, Aboutanios and Mulgrew (A&M) proposed an iterative frequency estimator which can approach the theoretical bound in two iterations, thus, made it one of the best iterative estimators. In this paper, we theoretically analyze the two versions of the A&M estimator and show that the estimation biases of the two versions are not equivalent. The results of the theoretical analysis indicate that the bias of the first iteration can be accurately predicted by a polynomial equation. We then propose to use the roots of the polynomial equation to improve the estimation and reduce the bias. Experiments show that the proposed new estimator can significantly reduce the bias.

In this paper, we developed a new virtual output queue (VOQ) scheduling algorithm called “longest queue first in round-robin matching” (LQFRRM) for input-queued switches. Based on the well-known iSLIP algorithm, we proposed a new update policy for the output round robin pointers. That is, when a grant is not accepted, all the output round robin pointers are updated to the longest queue. The rationale is that a grant not accepted will leave an output port idle and that means a less than optimal solution. Therefore, a better alternative is to give priority to the longest queue, especially under non-uniform traffic. The simulation results showed that LQFRRM was better than iSLIP in non-uniform traffic and was comparable to iSLIP in uniform traffic.

Because spiral magnetic resonance imaging (MRI) is more robust to motion artifacts than echo planar imaging (EPI), spiral imaging method is more suitable in real-time imaging applications where dynamic processes are to be observed. The major hurdle to use spiral imaging method in real-time applications is its slow reconstruction speed. Since spiral trajectories do not sample data on rectilinear grids, raw data must be regridded before inverse fast Fourier transform (FFT). At present, the computational cost for the spiral reconstruction algorithm is still too high and it is not fast enough to achieve the minimum speed requirement of 20 frames/s for real-time imaging applications. In this paper, we propose to replace floating-point calculations with fixed-point calculations in the reconstruction algorithm to remove the computational bottlenecks. To overcome the quantization and round-off errors introduced by fixed-point calculations, we devise a method to find the optimal precision for the fixed-point representation. Adding with a highly efficient vector-radix two-dimensional (2-D) FFT algorithm and modifications to speed up the gridding convolution, we have cut the reconstruction time by 42% and achieved real-time reconstruction at 30 frames/s for 128 x 128 matrices on low-cost PC's.