A noise-ranking switching filter for images with general fixed-value impulse noises

doi:10.1016/j.sigpro.2014.07.015

Signal Processing

Volume 106, January 2015, Pages 198-208

https://doi.org/10.1016/j.sigpro.2014.07.015 Get rights and content

Highlights

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A novel and general fixed-value impulse noise model is studied.
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A noise-ranking switching filter (NRSF) is proposed for suppressing the noises.
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Three modified detections are applied in the first stage of NRSF.
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The NRSF employs the directional convolution to restore the corrupted pixels.

Abstract

Impulse noise is generally classified into random-value and fixed-value types. However, most of the previous literatures recognized salt and pepper (S&P) noise as the fixed-value impulse noise because it is easily detected and recovered. This article studies a general fixed-value impulse noise in which the corrupted pixels are set to not only the minimum–maximum values but also any fixed intensities. A novel noise-ranking switching filter (NRSF) is proposed for suppressing these tough noise types. In order to clearly distinguish the noise-free pixels from noisy pixels having the same gray value, the detection stage of NRSF consists of three modified methodologies, named global–local statistics analysis, sectional boundary discriminative noise detection, and a directional test. Once a corrupted pixel has been identified, the same matrix convolution technique used in the last test is employed again in the second NRSF stage to recover the noise. Additionally, it is suggested that the corrupted pixels are processed via the rank of noise density for improving the suppression capability at very high noise ratio. Although the NRSF is driven for a new impulse noise model, it outperforms several state-of-the-art algorithms in terms of noise suppression and detail preservation even for images with the traditional S&P noise.

Introduction

During the acquisition, transmission and storage processes, images are often corrupted by impulse noises that occur primarily due to hardware imperfections. Corrupted pixel recovery is an essential part of any image processing job with numerous proposed denoising methods [1]. Nonlinear filters have been developed for noise removal due to the nonlinear characteristics of impulse noises. One of the most popular non-linear filters is the median filter with good denoising capability, simple implementation and high computational efficiency. However, the median filter will not perform well enough in high noise density cases. Various median-based filter modifications have been proposed to improve its performance. Nevertheless, those methods still process the whole image in spite of whether the current pixel may be noise-free. As a result, it would inevitably change undamaged pixels and cause image quality degradation. To overcome this drawback one solution is to introduce a noise-detection mechanism for determining damaged pixels first, then replace them with estimated values while leaving the remaining pixels unchanged [2]. It is obvious that the denoising capability of the switching median filter depends on the noise-detection performance [3]. A variety of filters with different noise detectors have been proposed in recent years. The more sophisticated median filters include the vector median filter [4], [5], directional weighted filter [6], [7], decision-based algorithm [8], [9], fuzzy switching median filter [10], [11], and so on.

Generally, impulse noise is classified into two types: random-value impulse noise and fixed-value impulse noise. The gray level of random-value impulse noises are uniformly distributed in the [0–255] interval. Filters that can remove random-value impulse noise or any mixture thereof have also been proposed. For example, the signal-dependent rank ordered mean (SDROM) [12], directional weighted median (DWM) [6], [13], [14], bilateral filter [15], [16], minimum–maximum exclusive mean (MMEM) [17], [18] filters, the fuzzy impulse noise detection and reduction method (FIDRM) [19], [20] and the improved decision-based method [21], [22]. Basically, researchers can use the cluster test to separate a noise and its uncorrupted neighbors based on the assumption that the probability of noises with the same gray level is small. Nevertheless, it is known that random-value impulse noise removal is more difficult because the intensity value of the corrupted pixel and that of its uncorrupted neighbors can be quite close. This statement works on the assumption that in most of the literature the fixed-value impulse noise is just assumed to be the maximum or minimum gray level (0 or 255) which is also known as “salt and pepper” (S&P) noise. This is certainly not the only case while equipment is partially imperfect or corrupted by some fixed disturbances [19], [23]. For example, if a data bus has a few central bits been flipped over, say, “xx0000xx”, where “x” may be “1” or “0”. The value of pixels will fixedly be corrupted as {0–3, 64–67, 128–131, 192–195}. In order to extend the scope of application, Ng and Ma proposed four general fixed-value impulse noise models [24]. However, these models still limit the intensity value of corrupted pixels close to the extreme values to facilitate the detection and removal of noise. A more general noise model is also studied in FIDRM [19], but it can only deal with the single beam type and low-density noises.

This article studies a novel and more general fixed-value impulse noise model. The impulse noise discussed here may fixedly occur at any range in [0–255]. Thus the difference between the noise and its neighbor may not be as significant as that of S&P noise. Different from the random-value impulse noise, noise repetition with the same gray-level is quite usual and the random-value impulse noise detection method will be not applicable for this new noise model. Therefore, it is clear that the object of how to interleave the noise and the true image is tougher than both the classical impulse noise.

In this paper we present a novel method to solve the above obstacle. Based on the switching- filter idea the NRSF consists of two stages. However, as mentioned, the key issue in NRSF is good ability of general fixed-value impulse noise detection and these two stages will all serve the detection object more or less. Several novel and/or modified techniques are proposed to improve the detection capability. The first NRSF stage considers both the global histogram and local statistics for discriminating the candidate noise. Then a sectional boundary discriminative noise detection (SBDND) technique is applied again. The second NRSF stage employs a multiple matrix convolution to final confirm the true noise and then yield a directional mean to recover it. For improving the suppression capability at very high noise values, the sparse matrix transformation is used to determine the processing sequence of the corrupted pixels via the noise-density rank in the working window. Extensive simulations show that the NRSF outperforms several state-of-the-art algorithms, in terms of noise suppression and detail preservation, no matter for images with the new impulse noise or the traditional S&P noise.

The rest of this paper is organized as follows: Section 2 defines the novel general fixed-value impulse noise. Section 3 introduces the proposed NRSF algorithm for impulse noise. Section 4 presents some simulation results. Conclusions are presented in Section 5.

Section snippets

The general noise model

The novel fixed-value impulse noise model is introduced in (1) for examining the performance of our proposed filter. The intensity is stored as an 8-bit integer giving 256 possible different shades of gray going from black to white, which can be represented as a [0,255] integer interval. In this interval we consider several gray-level values g₁, g₂, …, g_n with (g_b−1≠g_b) and n are a small number for fixed-value impulse noises. The reasonable assumption on n is without loss of generality since

The NRSF design

We focus on gray-scale images that are corrupted by fixed-value impulse noises. Our filtering scheme is divided into two stages but both stages performing more or less detection because the switching filter performance is greatly affected by the detector efficiency. Since the intensity value of a general fixed-value noise and that of its uncorrupted neighbors can be quite close to each other, the core object is that the detector is expected to have good ability to discriminate noise-free pixels

Simulation results

Simulations were carried out on well-known Matlab R2010A environment images to verify the efficiencies of the proposed algorithm. The NRSF thresholds were determined using experiments as: percentage of maximum intensity α=0.6, minimum noise ratio p_min=0.03, maximum width H_w=25, maximum group count n_max=10, local density bound β=2.5, ranking trigger δ=0.4 and similarity τ=11. The noise densities in these images varied widely from 10% to 90% with increments of 10%. A comparison of the noise

Conclusions

This paper proposed a novel algorithm for fixed-value impulse noise removal from an image. The noise models considered here were more general than those discussed in previous literature. As a result the existing methods could not perform well in removing this novel noise. The proposed method is simple, easier to implement and the algorithm efficiency was tested using a wide-range of noise densities on several representative images. Both visual and quantitative results demonstrated that the

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In progressive switching median filter (PSMF) [10], both the noise detection and filtering technique are recursively applied through iterations. The noise-ranking switching filter [11] studies a general fixed-value impulse noise where the corrupted pixels are set to not only the minimum–maximum values within the processing kernel but also any fixed intensities. In the first stage of removal of high-density impulse noise based on switching morphology-mean filter [12], impulse noise is detected in an image.
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View full text

A noise-ranking switching filter for images with general fixed-value impulse noises

Highlights

Abstract

Introduction

Section snippets

The general noise model

The NRSF design

Simulation results

Conclusions

Pattern Recognit. Lett.

Signal Process.

Pattern Recognit.

Signal Process.

Pattern Recognit. Lett.

Pattern Recognit. Lett.

Digit. Signal Process.

Signal Process.

A fast two-dimensional median filtering algorithm

IEEE Trans. Acoust. Speech Signal Process.

A new fast and efficient decision-based algorithm for removal of high-density impulse noises

IEEE Signal Process. Lett.

Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter

IEEE Signal Process. Lett.

Salt-and-pepper noise detection and reduction using fuzzy switching median filter

IEEE Trans. Consum. Electron.

Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction

IEEE Signal Process. Lett.

A new directional weighted median filter for removal of random-valued impulse noise

IEEE Signal Process. Lett.