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The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to the Karhunen-Lo\`eve transform (KLT), which is the optimal transform in terms of retained transform coefficients and data…

The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…

With the integration of communication and computing, it is expected that part of the computing is transferred to the transmitter side. In this paper we address the general problem of Frequency Modulation (FM) for function approximation…

An orthogonal 16-point approximate discrete cosine transform (DCT) is introduced. The proposed transform requires neither multiplications nor bit-shifting operations. A fast algorithm based on matrix factorization is introduced, requiring…

An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior…

Self-attention is central to the success of Transformer architectures; however, learning the query, key, and value projections from random initialization remains challenging and computationally expensive. In this paper, we propose two…

Discrete transforms play an important role in many signal processing applications, and low-complexity alternatives for classical transforms became popular in recent years. Particularly, the discrete cosine transform (DCT) has proven to be…

To achieve higher accuracy in machine learning tasks, very deep convolutional neural networks (CNNs) are designed recently. However, the large memory access of deep CNNs will lead to high power consumption. A variety of hardware-friendly…

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

Visual tracking usually requires an object appearance model that is robust to changing illumination, pose and other factors encountered in video. In this paper, we construct an appearance model using the 3D discrete cosine transform…

A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of particular interest in image processing. The main features of the algorithm are regularity of the graph and very low arithmetic complexity. The 16-point version…

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing…

Since their introduction the Trasformer architectures emerged as the dominating architectures for both natural language processing and, more recently, computer vision applications. An intrinsic limitation of this family of "fully-attentive"…

In this paper, we propose Dynamic Compressive Transformer (DCT), a transformer-based framework for modeling the unbounded sequence. In contrast to the previous baselines which append every sentence representation to memory, conditionally…

In this paper, we propose a collection of approximations for the 8-point discrete cosine transform (DCT) based on integer functions. Approximations could be systematically obtained and several existing approximations were identified as…

The expressiveness of neural networks highly depends on the nature of the activation function, although these are usually assumed predefined and fixed during the training stage. Under a signal processing perspective, in this paper we…

Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. We propose to learn these filters as combinations of preset spectral filters defined by the Discrete Cosine Transform (DCT).…

The discrete cosine transform (DCT) is a widely-used and important signal processing tool employed in a plethora of applications. Typical fast algorithms for nearly-exact computation of DCT require floating point arithmetic, are multiplier…

Due to its remarkable energy compaction properties, the discrete cosine transform (DCT) is employed in a multitude of compression standards, such as JPEG and H.265/HEVC. Several low-complexity integer approximations for the DCT have been…