While bandwidth and storage capabilities are increasing with advances in technology, so are the demands of users as
quantities of data to transmit and store grow simultaneously. The need for effective signal compression is always
present, as reduction in data size is required while maintaining minimal signal destruction. This paper presents a new
signal compression scheme that uses coordinate logic transforms in combination with Boolean minimized
representations. The processing of the coordinate logic transforms on signal data helps reduce unnecessary signal
complexity allowing more effective data reduction during the Boolean minimized form encoding. The coordinate logic
transforms are an alternate method for calculating coordinate logic filters which simplify the computational complexity
through algorithmic parallelism. In this work, the combination of coordinate logic transforms with a Boolean minimized
form encoding scheme allows for a new compression technique that is applicable to both binary and grayscale input images.
The resizing of data, either upscaling or downscaling based on need for increased or decreased resolution, is an
important signal processing technique due to the variety of data sources and formats used in today's world. Image
interpolation, the 2D variation, is commonly achieved through one of three techniques: nearest neighbor, bilinear
interpolation, or bicubic interpolation. Each method comes with advantages and disadvantages and selection of the
appropriate one is dependent on output and situation specifications. Presented in this paper are algorithms for the
resizing of images based on the analysis of the sum of primary implicants representation of image data, as generated by
a logical transform. The most basic algorithm emulates the nearest neighbor technique, while subsequent variations
build on this to provide more accuracy and output comparable to the other traditional methods. Computer simulations
demonstrate the effectiveness of these algorithms on binary and grayscale images.
This paper presents a novel method for edge detection within two-dimensional signals (images). Using Boolean partial derivatives calculated quickly through a logical transform, the algorithm generates a binary edge map. The process is initially described for binary data and then extended for multi-bit (grayscale) images. Computer simulations demonstrate the procedure for three classes of signals: synthetic images (where actual edge maps are known), natural images, and cell-phone images (those taken by a low-resolution, low-quality camera). Results are compared quantitatively (when possible with Pratt's figure of merit) and visually with six common edge detection techniques: Sobel, Prewitt, Roberts, Laplacian of Gaussian, zero-cross and Canny methods. Comparison with these methods demonstrates that the algorithm presented here is able to consistently perform competitively in the numerical sense, while also detecting major edges and fine details simultaneously. Both of these latter aspects are visually apparent in the binary output image maps produced.
During critical situations, the precise digital processing of medical signals such as heartbeats is essential. Outside noise introduced into this data can lead to misinterpretation. Thus, it is important to be able to detect and correct the signal quickly and efficiently using digital filtering algorithms. With filtering, the goal is to remove noise locations by correctly identify the corrupted data points and replacing these locations with acceptable estimations of the original values. However, one has to be careful throughout the filtering process not to also eliminate other important detailed information from the original signal. If the filtered output is to be analyzed post-filtering, say for feature recognition, it is important that both the structure and details of the original clean signal remain. This paper presents an original algorithm and two variations, all using the logical transform, that strive to do this accurately and with low levels of computation. Using real heartbeat signals as test sets, the output is compared to that produced by median type filters, and results demonstrated over a variety of noise levels.
Median filters excel at removing impulse noise from digital signals, with high accuracy and quick running-times. However, they have limitations if the resulting signals are to be used for feature recognition purposes, as they often remove crucial details and add unwanted noise. In this paper, an algorithm for digital filtering using the logical transform is proposed. This method is able to achieve mean-squared-error results similar to median type filters while maintaining image details. Variations of the algorithm allow for greater noise reduction, but at the cost of increased computation.