Low-complexity three-dimensional discrete Hartley transform approximations for medical image compression.

The discrete Hartley transform (DHT) is a useful tool for medical image coding. The three-dimensional DHT (3D DHT) can be employed to compress medical image data, such as magnetic resonance and X-ray angiography. However, the computation of the 3D DHT involves several multiplications by irrational quantities, which require floating-point arithmetic and inherent truncation errors. In recent years, a significant progress in wireless and implantable biomedical devices has been achieved. Such devices present critical power and hardware limitations. The multiplication operation demands higher hardware, power, and time consumption than other arithmetic operations, such as addition and bit-shifts. In this work, we present a set of multiplierless DHT approximations, which can be implemented with fixed-point arithmetic. We derive 3D DHT approximations by employing tensor formalism. Such proposed methods present prominent computational savings compared to the usual 3D DHT approach, being appropriate for devices with limited resources. The proposed transforms are applied in a lossy 3D DHT-based medical image compression algorithm, presenting practically the same level of visual quality (>98% in terms of SSIM) at a considerable reduction in computational effort (100% multiplicative complexity reduction). Furthermore, we implemented the proposed 3D transforms in an ARM Cortex-M0+ processor employing the low-cost Raspberry Pi Pico board. The execution time was reduced by ∼70% compared to the usual 3D DHT and ∼90% compared to 3D DCT.

Process monitoring using inflated beta regression control chart.

This paper provides a general framework for controlling quality characteristics related to control variables and limited to the intervals (0, 1], [0, 1), or [0, 1]. The proposed control chart is based on the inflated beta regression model considering a reparametrization of the inflated beta distribution indexed by the response mean, which is useful for modeling fractions and proportions. The contribution of the paper is twofold. First, we extend the inflated beta regression model by allowing a regression structure for the precision parameter. We also present closed-form expressions for the score vector and Fisher's information matrix. Second, based on the proposed regression model, we introduce a new model-based control chart. The control limits are obtained considering the estimates of the inflated beta regression model parameters. We conduct a Monte Carlo simulation study to evaluate the performance of the proposed regression model estimators, and the performance of the proposed control chart is evaluated in terms of run length distribution. Finally, we present and discuss an empirical application to show the applicability of the proposed regression control chart.

Low-Complexity Multidimensional DCT Approximations for High-Order Tensor Data Decorrelation.

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. 3D DCT approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless 8×8 ×8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.