This paper presents a deep network based on morphological filters for Gaussian denoising. The morphological filters can be applied with only addition, max, and min functions and require few computational resources. Therefore, the proposed network is suitable for implementation using a small microprocessor. Each layer of the proposed network consists of a top-hat transform, which extracts small peaks and valleys of noise components from the input image. Noise components are iteratively reduced in each layer by subtracting the noise components from the input image. In this paper, the extensions of opening and closing are introduced as linear combinations of the morphological filters for the top-hat transform of this deep network. Multiplications are only required for the linear combination of the morphological filters in the proposed network. Because almost all parameters of the network are structuring elements of the morphological filters, the feature maps and parameters can be represented in short bit-length integer form, which is suitable for implementation with single instructions, multiple data (SIMD) instructions. Denoising examples show that the proposed network obtains denoising results comparable to those of BM3D [1] without linear convolutions and with approximately one tenth the number of parameters of a full-scale deep convolutional neural network [2]. Moreover, the computational time of the proposed method using SIMD instructions of a microprocessor is also presented.

This paper presents non-destructive millimeter-wave (MMW) imaging of sub-millimeter-wide cracks on a concrete surface covered with paper. We measured the near-field scattering of 76.5 GHz-MMW signals at concrete surface cracks for detection of the sub-millimeter-wide cracks. A decrease in the received signal magnitude by near-field scattering at the fine concrete surface crack was slight, which yielded an unclear MMW image contrast of fine cracks at the concrete surface. We have found that the received signal magnitude at concrete surface crack is larger than that at the surface without a crack, when the paper thickness is almost equal to n/4 of the effective wavelength of the MMW signal in the paper (n=1, 3, 5 ...), thus, making MMW image contrast at the surface crack reversed. By calculating the difference of two MMW images obtained from different paper thickness, we were able to improve the MMW image contrast at the surface crack by up to 3.3 dB.

This paper presents convex filter networks that are obtained from extensions of morphological filters. The proposed filter network consists of a convex and concave filter that are extensions of the dilation and erosion of mathematical morphology with the maxout activation function. Maxout can approximate arbitrary convex functions as piecewise linear functions, including the max function. The class of the convex function hence includes the morphological dilation and can be trained for specific image processing tasks. In this paper, the closing filter is extended to a convex-concave filter network with maxout. The convex-concave filter is trained by the stochastic gradient method for noise and mask removal. The examples of noise and mask removal show that the convex-concave filter can obtain a recovered image, whose quality is comparable to inpainting by using the total variation minimization with reduced computational cost without mask information of the corrupted pixels.

In this study, we introduce shift-invariant sparse image representations using tree-structured dictionaries. Sparse coding is a generative signal model that approximates signals by the linear combinations of atoms in a dictionary. Since a sparsity penalty is introduced during signal approximation and dictionary learning, the dictionary represents the primal structures of the signals. Under the shift-invariance constraint, the dictionary comprises translated structuring elements (SEs). The computational cost and number of atoms in the dictionary increase along with the increasing number of SEs. In this paper, we propose an algorithm for shift-invariant sparse image representation, in which SEs are learnt with a tree-structured approach. By using a tree-structured dictionary, we can reduce the computational cost of the image decomposition to the logarithmic order of the number of SEs. We also present the results of our experiments on the SE learning and the use of our algorithm in image recovery applications.

This paper proposes an adaptation method for structuring elements of morphological filters. A structuring element of a morphological filter specifies a shape of local structures that is eliminated or preserved in the output. The adaptation of the structuring element is hence a crucial problem for image denoising using morphological filters. Existing adaptation methods for structuring elements require preliminary training using example images. We propose an adaptation method for structuring elements of morphological opening filters that does not require such training. In our approach, the opening filter is interpreted as an approximation method with the union of the structuring elements. In order to eliminate noise components, a penalty defined from an assumption of image smoothness is imposed on the structuring element. Image denoising is achieved through decreasing the objective function, which is the sum of an approximation error term and the penalty function. In experiments, we use the proposed method to demonstrate positive impulsive noise reduction from images.

In this paper, we propose a method for supervised single-channel speech separation through sparse decomposition using periodic signal models. The proposed separation method employs sparse decomposition, which decomposes a signal into a set of periodic signals under a sparsity penalty. In order to achieve separation through sparse decomposition, the decomposed periodic signals have to be assigned to the corresponding sources. For the assignment of the periodic signal, we introduce clustering using a K-means algorithm to group the decomposed periodic signals into as many clusters as the number of speakers. After the clustering, each cluster is assigned to its corresponding speaker using preliminarily learnt codebooks. Through separation experiments, we compare our method with MaxVQ, which performs separation on the frequency spectrum domain. The experimental results in terms of signal-to-distortion ratio show that the proposed sparse decomposition method is comparable to the frequency domain approach and has less computational costs for assignment of speech components.

In this paper, we propose a camera calibration method that estimates both intrinsic parameters (perspective and distortion) and extrinsic parameters (rotational and translational). All camera parameters can be determined from one or more images of planar pattern consists of parallelogramatic grid points. As far as the pattern can be visible, the relative relations between camera and patterns are arbitrary. So, we have only to prepare a pattern, and take one or more images changing the relative relation between camera and the pattern, arbitrarily; neither solid object of ground truth nor precise z-stage are required. Moreover, constraint conditions that are imposed on rotational parameters are explicitly satisfied; no intermediate parameter that connected several actual camera parameters are used. Taking account of the conflicting fact that the amount of distortion is small in the neighborhood of the image center, and that small image has poor clues of 3-D information, we adopt iterative procedure. The best parameters are searched changing the size and number of parallelograms selected from grid points. The procedure of the iteration is as follows: The perspective parameters are estimated from the shape of parallelogram by nonlinear optimizations. The rotational parameters are calculated from the shape of parallelogram. The translational parameters are estimated from the size of parallelogram by least squares method. Then, the distortion parameters are estimated using all grid points by least squares method. The computer simulation demonstrates the efficiency of the proposed method. And the results of the implementation using real images are also shown.

For image restoration, an image prior that is obtained from the morphological gradient has been proposed. In the field of mathematical morphology, the optimization of the structuring element (SE) used for this morphological gradient using a genetic algorithm (GA) has also been proposed. In this paper, we introduce a new image prior that is the sum of the morphological gradients and total variation for an image restoration problem to improve the restoration accuracy. The proposed image prior makes it possible to almost match the fitness to a quantitative evaluation such as the mean square error. It also solves the problem of the artifact due to the unsuitability of the SE for the image. An experiment shows the effectiveness of the proposed image restoration method.

Fast wavelet transform is presented for realtime processing of wavelet transforms. A processor for the fast wavelet transform is of the frequency sampling structure in architectural level. The fast wavelet transform owes its parallelism both to the frequency sampling structure and parallel tapping of a series of delay elements. Computational burden of the fast transform is hence independent of specific scale values in wavelets and the parallel processing of the fast transform is readily implemented for real-time applications. This point is quite different from the computation of wavelet transforms by convolution. We applied the fast wavelet transform to detecting detonation in a vehicle engine for precise real-time control of ignition advancement. The prototype wavelet for this experiment was the Gaussian wavelet (i.e. Gabor function) which is known to have the least spread both in time and in frequency. The number of complex multiplications needed to compute the fast wavelet transform over 51 scales is 714 in this experiment, which is less than one tenth of that required for the convolution method. Experimental results have shown that detonation is successfully detected from the acoustic vibration signal picked up by a single knock sensor embedded in the outer wall of a V/8 engine and is discriminated from other environmental mechanical vibrations.

This study proposes a method to decompose a signal into a set of periodic signals. The proposed decomposition method imposes a penalty on the resultant periodic subsignals in order to improve the sparsity of decomposition and avoid the overestimation of periods. This penalty is defined as the weighted sum of the l2 norms of the resultant periodic subsignals. This decomposition is approximated by an unconstrained minimization problem. In order to solve this problem, a relaxation algorithm is applied. In the experiments, decomposition results are presented to demonstrate the simultaneous detection of periods and waveforms hidden in signal mixtures.

In this paper, we propose an image enlargement method by using morphological operators. Our enlargement method is based on the nonlinear frequency extrapolation method (Greenspan et al., 2000) by using a Laplacian pyramid image representation. In this method, the sampling process of input images is modeled as the Laplacian pyramid. A high resolution image is obtained with the finer scale Laplacian that is extrapolated by a nonlinear operation from a low resolution Laplacian. In this paper, we propose a novel nonlinear operation for extrapolation of the finer scale Laplacian. Our nonlinear operation is realized by morphological operators and is capable of generating the finer scale Laplacian, the amplitude of which is proportional to contrasts of edges that appear in the low resolution image. In experiments, the enlargement results given by the proposed method are demonstrated. Compared with the Greenspan's method, the proposed method can recover sharp intensity transients of image edges with small artifacts.

In this paper, a new image synthesis model based on a set of wavelet bases is proposed. In the proposed model, images are approximated by the sum of synthesis functions that are translated to image edge positions. By applying the proposed model to sketch-based image coding, no iterative image recovery procedure is required for image decoding. In the design of the synthesis functions, we define the synthesis functions as a linear combination of wavelet bases. The coefficients for wavelet bases are obtained from an iterative procedure. The vector quantization is applied to the vectors of the coefficients to limit the number of the synthesis functions. We apply the proposed synthesis model to the sketch-based image coding. Image coding experiments by eight synthesis functions and a comparison with the orthogonal transform methods are also given.

This paper presents a deep network based on unrolling the diffusion process with the morphological Laplacian. The diffusion process is an iterative algorithm that can solve the diffusion equation and represents time evolution with Laplacian. The diffusion process is applied to smoothing of images and has been extended with non-linear operators for various image processing tasks. In this study, we introduce the morphological Laplacian to the basic diffusion process and unwrap to deep networks. The morphological filters are non-linear operators with parameters that are referred to as structuring elements. The discrete Laplacian can be approximated with the morphological filters without multiplications. Owing to the non-linearity of the morphological filter with trainable structuring elements, the training uses error back propagation and the network of the morphology can be adapted to specific image processing applications. We introduce two extensions of the morphological Laplacian for deep networks. Since the morphological filters are realized with addition, max, and min, the error caused by the limited bit-length is not amplified. Consequently, the morphological parts of the network are implemented in unsigned 8-bit integer with single instruction multiple data set (SIMD) to achieve fast computation on small devices. We applied the proposed network to image completion and Gaussian denoising. The results and computational time are compared with other denoising algorithm and deep networks.

In this paper, an image prior based on soft-morphological filters and its application to image recovery are presented. In morphological image processing, a gray-scale image is represented as a subset in a three-dimensional space, which is spanned by spatial and intensity axes. Morphological opening and closing, which are basic operations in morphological image processing, respectively approximate the image subset and its complementary images as the unions of structuring elements that are translated in the three-dimensional space. In this study, the opening and closing filters are applied to an image prior to resolve the regularization problem of image recovery. When the proposed image prior is applied, the image is recovered as an image that has no noise component, which is eliminated by the opening and closing. However, the closing and opening filters are less able to eliminate Gaussian noise. In order to improve the robustness against Gaussian noise, the closing and opening filters are respectively approximated as soft-closing and soft-opening with relaxed max and min functions. In image recovery experiments, image denoising and deblurring using the proposed prior are demonstrated. Comparisons of the proposed prior with the existing priors that impose a penalty on the gradient of the intensity are also shown.

In this paper, we propose an ECG waveform compression technique based on the matching pursuit. The matching pursuit is an iterative non-orthogonal signal expansion technique. A signal is decomposed to atoms in a function dictionary. The constraint to the dictionary is only the over-completeness to signals. The function dictionary can be defined to be best match to the structure of the ECG waveform. In this paper, we introduce the multiscale analysis to the implementation of inner product computations between signals and atoms in the matching pursuit iteration. The computational cost can be reduced by utilization of the filter bank of the multiscale analysis. We show the waveform approximation capability of the matching pursuit with multiscale analysis. We show that a simple 4-tap integer filter bank is enough to the approximation and compression of ECG waveforms. In ECG waveform compression, we apply the error feed-back procedure to the matching pursuit iteration to reduce the norm of the approximation error. Finally, actual ECG waveform compression by the proposed method are demonstrated. The proposed method achieve the compression by the factor 10 to 30. The compression ratio given by the proposed method is higher than the orthogonal wavelet transform coding in the range of the reconstruction precision lower than 9% in PRD.

We introduce an image contour clustering method based on a multiscale image representation and its application to image compression. Multiscale gradient planes are obtained from the mean squared sum of 2D wavelet transform of an image. The decay on the multiscale gradient planes across scales depends on the Lipshitz exponent. Since the Lipshitz exponent indicates the spatial differentiability of an image, the multiscale gradient planes represent smoothness or sharpness around edges on image contours. We apply vector quatization to the multiscale gradient planes at contours, and cluster the contours in terms of represntative vectors in VQ. Since the multiscale gradient planes indicate the Lipshitz exponents, the image contours are clustered according to its gradients and Lipshitz exponents. Moreover, we present an image recovery algorithm to the multiscale gradient planes, and we achieve the skech-based image compression by the vector quantization on the multiscale gradient planes.