I. Background and introduction
Deep learning is a genre of computational methods for artificial intelligence (AI) that use neural network with multiple layers to learn complex data patterns. Deep learning excels at tasks like image recognition, natural language processing, and speech recognition. It powers most of the AI applications at present.
Although its applicability remains an issue, compressed sensing (or called computational imaging) theory aroused the fantasy of scientists worldwide: the initial paper (Donoho, 2006) was cited over 37,000 times in only 20 years (2006-2026), and the initial authors have reaped many prestigious honors including Gauss Prize 2018 and IEEE Kilby Medal 2021, despite the intense contentions over its mathematical correctness, and especially over the authenticity of its technical claims ever since.
Maximum Accuracy Computing (MAC) is a new mathematical theory supplying a novel computational method for data prediction (extrapolation, interpolation, approximation, or reconstruction). It purports to predict the unknown elements of a data set, given a small portion (say, 25% or even less) of data samples, always attaining the maximum accuracy that the data samples can possibly provide.
II. Rapid: rationale and performance
1. Ingeniously Innovated Mathematical Rationale
Rapid implements our new mathematical theory and method: Maximum Accuracy Computing (MAC), which only entails rudimentary knowledge in linear algebra. The mathematical rationale is simple yet powerful. Insights into mathematical defects in existing methods prompted us to probe the issue in new directions, blossoming into a series of crucial discoveries of new mathematical phenomena, which constitute a new mathematical theory, and culminate in the novel computational method.
MAC fulfills a new philosophy of data pattern. It first learns the varying pattern of data samples with a mathematical transform, and then precisely predicts the unknown data in conformation to the pattern. Both the value and the pattern of data samples remain intact, resulting in the maximum accuracy with 40 times more accurate data, which leap from utterly inapplicable to perceptually identical, compared with deep learning (CNN): mse(CNN) = mse(MAC) x 40.18 (mse: mean squared error), equivalent to the speed change from horse wagon to jet engine, i.e., from 15 mph to 600 mph. Meanwhile, its extremely simple algorithm only employs one single matrix multiplication, leading to millions of times faster computation.
2. Immensely Improved Technical Performance
A revolutionary innovation, Rapid improves data accuracy from utterly inapplicable to visually identical, compared with both deep learning and compressed sensing (computational imaging). The most successful deep learning algorithm in image and speech recognition, Convolutional Neural Networks (CNN) remains the state-of-the-art method, confirmed by the ubiquitous survey conducted by Alina Machidon and Veljko Pejović. Likewise, the comprehensive review conducted by Elaine Marques, et al. concludes that Orthogonal Matching Pursuit (OMP) remains the state-of-the-art method for compressed sensing (computational imaging). Reported by MIT News multiple times, the MIT thesis of Radu Berinde (page 90) provides the performance of OMP in all due terms of actual image, PSNR, and running time, and hence it remains a rare, if not unique, presumably trustworthy source to assess the authentic technical performance of compressed sensing (computational imaging). The CVPR paper by Kuldeep Kulkarni et al. provides the technical performance of CNN on image data, but only in terms of PSNR.
To date, most publications on compressed sensing (computational imaging) failed to present experimental results in all the three due terms. Even worse, although utterly inapplicable, those experimental results are not supported by verifiable software implementation, in blatant violation of the principle of reproducibility. For example, the most famous product on compressed sensing (computational imaging), Rice University DSP Lab’s “single-pixel camera” is not supported by any downloadable software ever since, but still is crowned with the IEEE Best Paper Award for 2020, signifying it remains the state of the art in compressed sensing, though its paper by Richard Baraniuk et al. was published in 2008, and even after its website was removed entirely around 2018, which should have rendered the paper retracted instead.
As shown below, Rapid runs hundreds of thousands of times faster in computation than compressed sensing (computational imaging). More importantly, Rapid distantly surpasses both deep learning and compressed sensing (computational imaging) in data accuracy. For instance, Rapid achieves 42.58dB in PSNR (visually identical) in predicting the large data set “Lena” with 25% samples, in stark contrast to the 26.54dB (utterly inapplicable) by deep learning (CNN), implying that mse(CNN) = mse(MAC) x 40.18 (mse: mean squared error). It is 40 times more accurate data, equivalent to the speed change from horse wagon to jet engine, i.e., from 15 mph to 600 mph. This vast leap in data accuracy conspicuously manifests that MAC far surpasses deep learning in terms of the capacity to learn and apply complex data patterns.
For the visual quality and applicability of images at about 26dB or less in PSNR, refer to the below images (b), (e), (h), and (k), examples of severely distorted data, utterly inapplicable for any application: the drastic distortions starkly disprove any brazen claim of their applicability, which is tantamount to the claim of capability to weave beautiful but invisible cloth. Exploiting mass ignorance, absurdity may often produce popularity, but never provides applicability. It turns out, the beauty of compressed sensing is only audible, not visible: everybody says, but nobody sees, repeating the story of Emperor’s New Clothes, including the final episode that the Emperor proceeds with his nude procession despite a child’s revelation of his nudity, and as a result the swindlers continue to profit from their fraud.
Rapid is too good, and is true. To verify, click here to download Rapid Demo (Windows) and test data. Normally, it takes the credential of having innovated a comparable mathematical method to qualify as a peer. Thus are the adherents of compressed sensing distantly ineligible to comment on MAC.
40% samples
25% samples
III. Conclusion
With enormously enhanced capacity to learn and apply complex data patterns, equivalent to the speed change from horse wagon to jet engine, plus millions of times faster computation, Maximum Accuracy Computing (MAC) bears the potential to displace neural network as the core computing engine for AI technologies, especially when it involves image, video, audio, or other signals.
