Analytic Design Technique for 2D FIR Circular Filter Banks and Their Efficient Implementation Using Polyphase Approach

This paper proposes an analytical design procedure for 2D FIR circular filter banks and also a novel, computationally efficient implementation of the designed filter bank based on a polyphase structure and a block filtering approach. The component filters of the bank are designed in the frequency domain using a specific frequency transformation applied to a low-pass, band-pass and high-pass 1D prototype with a specified Gaussian shape and imposed specifications (peak frequency, bandwidth). The 1D prototype filter frequency response is derived in a closed form as a trigonometric polynomial with a specified order using Fourier series, and then it is factored. Since the design starts from a 1D prototype with a factored transfer function, the frequency response of the designed 2D filter bank components also results directly in a factored form. The designed filters have an accurate shape, with negligible distortions at a relatively low order. We present the design of two types of circular filter banks: uniform and non-uniform (dyadic). An example of image analysis with the uniform filter bank is also provided, showing that the original image can be accurately reconstructed from the sub-band images. The proposed implementation is presented for a simpler case, namely for a smaller size of the filter kernel and of the input image. Using the polyphase and block filtering approach, a convenient implementation at the system level is obtained for the designed 2D FIR filter, with a relatively low computational complexity.

High-Performance Deep Neural Network-Based Tomato Plant Diseases and Pests Diagnosis System With Refinement Filter Bank

A fundamental problem that confronts deep neural networks is the requirement of a large amount of data for a system to be efficient in complex applications. Promising results of this problem are made possible through the use of techniques such as data augmentation or transfer learning of pre-trained models in large datasets. But the problem still persists when the application provides limited or unbalanced data. In addition, the number of false positives resulting from training a deep model significantly cause a negative impact on the performance of the system. This study aims to address the problem of false positives and class unbalance by implementing a Refinement Filter Bank framework for Tomato Plant Diseases and Pests Recognition. The system consists of three main units: First, a Primary Diagnosis Unit (Bounding Box Generator) generates the bounding boxes that contain the location of the infected area and class. The promising boxes belonging to each class are then used as input to a Secondary Diagnosis Unit (CNN Filter Bank) for verification. In this second unit, misclassified samples are filtered through the training of independent CNN classifiers for each class. The result of the CNN Filter Bank is a decision of whether a target belongs to the category as it was detected (True) or not (False) otherwise. Finally, an integration unit combines the information from the primary and secondary units while keeping the True Positive samples and eliminating the False Positives that were misclassified in the first unit. By this implementation, the proposed approach is able to obtain a recognition rate of approximately 96%, which represents an improvement of 13% compared to our previous work in the complex task of tomato diseases and pest recognition. Furthermore, our system is able to deal with the false positives generated by the bounding box generator, and class unbalances that appear especially on datasets with limited data.

Systematic Construction of Real Lapped Tight Frame Transforms

We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.