In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the signal-to-noise ratio (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of weather forecasting and economics. == Description == In general, the objective of deconvolution is to find the solution f of a convolution equation of the form: f ∗ g = h {\displaystyle fg=h\,} Usually, h is some recorded signal, and f is some signal that we wish to recover, but has been convolved with a filter or distortion function g, before we recorded it. Usually, h is a distorted version of f and the shape of f can't be easily recognized by the eye or simpler time-domain operations. The function g represents the impulse response of an instrument or a driving force that was applied to a physical system. If we know g, or at least know the form of g, then we can perform deterministic deconvolution. However, if we do not know g in advance, then we need to estimate it. This can be done using methods of statistical estimation or building the physical principles of the underlying system, such as the electrical circuit equations or diffusion equations. There are several deconvolution techniques, depending on the choice of the measurement error and deconvolution parameters: === Raw deconvolution === When the measurement error is very low (ideal case), deconvolution collapses into a filter reversing. This kind of deconvolution can be performed in the Laplace domain. By computing the Fourier transform of the recorded signal h and the system response function g, you get H and G, with G as the transfer function. Using the convolution theorem, F = H / G {\displaystyle F=H/G\,} where F is the estimated Fourier transform of f. Finally, the inverse Fourier transform of the function F is taken to find the estimated deconvolved signal f. Note that G is at the denominator and could amplify elements of the error model if present. === Deconvolution with noise === In physical measurements, the situation is usually closer to ( f ∗ g ) + ε = h {\displaystyle (fg)+\varepsilon =h\,} In this case ε is noise that has entered our recorded signal. If a noisy signal or image is assumed to be noiseless, the statistical estimate of g will be incorrect. In turn, the estimate of ƒ will also be incorrect. The lower the signal-to-noise ratio, the worse the estimate of the deconvolved signal will be. That is the reason why inverse filtering the signal (as in the "raw deconvolution" above) is usually not a good solution. However, if at least some knowledge exists of the type of noise in the data (for example, white noise), the estimate of ƒ can be improved through techniques such as Wiener deconvolution. == Applications == === Seismology === The concept of deconvolution had an early application in reflection seismology. In 1950, Enders Robinson was a graduate student at MIT. He worked with others at MIT, such as Norbert Wiener, Norman Levinson, and economist Paul Samuelson, to develop the "convolutional model" of a reflection seismogram. This model assumes that the recorded seismogram s(t) is the convolution of an Earth-reflectivity function e(t) and a seismic wavelet w(t) from a point source, where t represents recording time. Thus, our convolution equation is s ( t ) = ( e ∗ w ) ( t ) . {\displaystyle s(t)=(ew)(t).\,} The seismologist is interested in e, which contains information about the Earth's structure. By the convolution theorem, this equation may be Fourier transformed to S ( ω ) = E ( ω ) W ( ω ) {\displaystyle S(\omega )=E(\omega )W(\omega )\,} in the frequency domain, where ω {\displaystyle \omega } is the frequency variable. By assuming that the reflectivity is white, we can assume that the power spectrum of the reflectivity is constant, and that the power spectrum of the seismogram is the spectrum of the wavelet multiplied by that constant. Thus, | S ( ω ) | ≈ k | W ( ω ) | . {\displaystyle |S(\omega )|\approx k|W(\omega )|.\,} If we assume that the wavelet is minimum phase, we can recover it by calculating the minimum phase equivalent of the power spectrum we just found. The reflectivity may be recovered by designing and applying a Wiener filter that shapes the estimated wavelet to a Dirac delta function (i.e., a spike). The result may be seen as a series of scaled, shifted delta functions (although this is not mathematically rigorous): e ( t ) = ∑ i = 1 N r i δ ( t − τ i ) , {\displaystyle e(t)=\sum _{i=1}^{N}r_{i}\delta (t-\tau _{i}),} where N is the number of reflection events, r i {\displaystyle r_{i}} are the reflection coefficients, t − τ i {\displaystyle t-\tau _{i}} are the reflection times of each event, and δ {\displaystyle \delta } is the Dirac delta function. In practice, since we are dealing with noisy, finite bandwidth, finite length, discretely sampled datasets, the above procedure only yields an approximation of the filter required to deconvolve the data. However, by formulating the problem as the solution of a Toeplitz matrix and using Levinson recursion, we can relatively quickly estimate a filter with the smallest mean squared error possible. We can also do deconvolution directly in the frequency domain and get similar results. The technique is closely related to linear prediction. === Optics and other imaging === In optics and imaging, the term "deconvolution" is specifically used to refer to the process of reversing the optical distortion that takes place in an optical microscope, electron microscope, telescope, or other imaging instrument, thus creating clearer images. It is usually done in the digital domain by a software algorithm, as part of a suite of microscope image processing techniques. Deconvolution is also practical to sharpen images that suffer from fast motion or jiggles during capturing. Early Hubble Space Telescope images were distorted by a flawed mirror and were sharpened by deconvolution. The usual method is to assume that the optical path through the instrument is optically perfect, convolved with a point spread function (PSF), that is, a mathematical function that describes the distortion in terms of the pathway a theoretical point source of light (or other waves) takes through the instrument. Usually, such a point source contributes a small area of fuzziness to the final image. If this function can be determined, it is then a matter of computing its inverse or complementary function, and convolving the acquired image with that. The result is the original, undistorted image. In practice, finding the true PSF is impossible, and usually an approximation of it is used, theoretically calculated or based on some experimental estimation by using known probes. Real optics may also have different PSFs at different focal and spatial locations, and the PSF may be non-linear. The accuracy of the approximation of the PSF will dictate the final result. Different algorithms can be employed to give better results, at the price of being more computationally intensive. Since the original convolution discards data, some algorithms use additional data acquired at nearby focal points to make up some of the lost information. Regularization in iterative algorithms (as in expectation-maximization algorithms) can be applied to avoid unrealistic solutions. When the PSF is unknown, it may be possible to deduce it by systematically trying different possible PSFs and assessing whether the image has improved. This procedure is called blind deconvolution. Blind deconvolution is a well-established image restoration technique in astronomy, where the point nature of the objects photographed exposes the PSF thus making it more feasible. It is also used in fluorescence microscopy for image restoration, and in fluorescence spectral imaging for spectral separation of multiple unknown fluorophores. The most common iterative algorithm for the purpose is the Richardson–Lucy deconvolution algorithm; the Wiener deconvolution (and approximations) are the most common non-iterative algorithms. For some specific imaging systems such as laser pulsed terahertz systems, PSF can be modeled mathematically. As a result, as shown in the figure, deconvolution of the modeled PS
Sports Card Investor
Sports Card Investor is an American sports collectibles media platform and mobile application founded by Geoff Wilson. The platform provides market data, analysis, and editorial content focused on sports trading cards and related collectibles. It operates a website, mobile app, and digital media channels covering developments in the sports card industry. The company posted its first YouTube video in July 2019, shortly before a period of rapid growth in sports card collecting in the early 2020s, which was marked by increased trading volumes and mainstream media attention. == History == Sports Card Investor was founded by Geoff Wilson, an entrepreneur and collector who began publishing sports card–related content online before launching the platform's dedicated app and subscription tools. In February 2020, the company launched Market Movers, the first website and app to chart sports card prices and track card collections. The platform expanded its media presence through partnerships and distribution agreements. In 2023, Yahoo Sports announced a new collectibles coverage initiative that included additional content from Sports Card Investor. In February 2024, the Sports Card Investor studio relocated to CardsHQ in Atlanta, Georgia, and visitors to the facility can watch Sports Card Investor videos being filmed. == Platform and content == The Sports Card Investor app provides users with pricing data, portfolio-tracking tools, and market-trend analysis for trading cards. The company also produces video and editorial content discussing market developments, grading trends, and major card releases. Coverage in industry publications has referenced Sports Card Investor in discussions about shifts in sports card licensing rights and hobby market reactions. == Industry context == The growth of Sports Card Investor coincided with a broader resurgence in trading card markets, including record sales and expanded retail presence. Mainstream outlets have cited the company and its founder in reporting on collectibles investing trends, grading practices, and market volatility. The Sports Card Investor app has attracted over 37,000 reviews on the Apple App Store, reflecting its strong user engagement within the sports card community.
Clubhouse (app)
Clubhouse is an American social audio app for iOS and Android developed by Alpha Exploration Co. that enables users to participate in real-time, audio-only communication within virtual "rooms". Launched in March 2020 by Paul Davison and Rohan Seth, the platform is characterized by its "drop-in" nature, where users can join live discussions on a wide range of topics as either listeners or speakers. The application gained attention in early 2021, operating on an invite-only model and featuring appearances from public figures such as Elon Musk, Oprah Winfrey, and Mark Zuckerberg. During this period, Clubhouse reached a reported valuation of approximately $4 billion and contributed to the expansion of similar social audio features like Twitter Spaces and Spotify Greenroom. The app later expanded to Android in May 2021 and removed its waitlist in July 2021, opening access to the general public. == History == Clubhouse began as an invite only social media startup by Paul Davison and Rohan Seth in Fall 2019. Originally designed for podcasts with the name Talkshow, the app was rebranded as "Clubhouse" and officially released for the iOS operating system in March 2020 and as of May 2021 the Android systems as well. Clubhouse was valued at $100 million after receiving funding from notable angel investors. These investors included Ryan Hoover (Founder, Product Hunt), Balaji Srinivasan (Former CTO, Coinbase), James Beshara (Co-Founder, Tilt.com), and several venture capitalists, including a $12 million Series A investment from the venture capital firm, Andreessen Horowitz, in May 2020. The app gained popularity in the early months of the COVID-19 pandemic. It had 600,000 registered users by December 2020. In January 2021, CEO Paul Davison announced that the active weekly user base on the app consisted of approximately 2 million individuals. The company announced that it would start working on an Android version of the app. In that month, the app became widely used in Germany when German podcast hosts Philipp Klöckner and Philipp Gloeckler began an invite-chain over a Telegram group. It brought German influencers, journalists, and politicians to the platform. Clubhouse raised their Series B at a $1 billion valuation. On February 1, 2021, Clubhouse had an estimated 3.5 million downloads on a global level which grew rapidly to 8.1 million downloads by February 15. This significant growth in popularity was because celebrities such as Elon Musk and Mark Zuckerberg made appearances on the app. In the same month, Clubhouse hired an Android Software Developer. A year after the app's release, the number of weekly active users was greater than 10 million, but the user base declined 21% during three weeks from late February to early March. This decline was reportedly caused by a decrease in the number of Clubhouse users after its initial release. During its initial roll out, the app was accessible only by invitation, and invitation codes on eBay were selling at up to $400. On April 5, 2021, Clubhouse partnered with Stripe to launch its first monetizing feature called Clubhouse Payments. Although testing began with only 1,000 users, after a week, the company rolled out the functionality to another 60,000 or more users in the US. In the same month, Twitter entered in discussions to purchase Clubhouse for $4 billion. The talks ended with no acquisition. Later, the company raised their Series C round of funding at a $4 billion valuation. The app also received interest in a partnership, with the National Football League announcing a content deal that month; Twitter Spaces later poached Clubhouse's exclusive NFL deal with 20 official NFL Spaces scheduled for the 2021-22 season. Finally, On May 9, 2021, Clubhouse launched a beta version of the Android app for users in the US, and on May 21, 2021, Clubhouse became available worldwide for Android users. In July 2021, Clubhouse announced a partnership with TED to offer exclusive talks. and on July 21, 2021, the company discarded its invitation system and made the application available to all, though a wait list for registration was still applied in order to manage new traffic. As of the time of the announcement, the company stated it had 10 million users on the wait list. On September 23, 2021, the company announced a new feature named "Wave". In October 2021, Clubhouse rolled out new features called "Replays and Clips". In April 2023, the company announced it was reducing its staff by half amid a "resetting" due to post-pandemic market shifts. == Features == === Rooms === The primary feature of Clubhouse is real-time virtual "rooms" in which users can communicate with each other via audio. Rooms are divided into different categories based on levels of privacy. Moderator roles are denoted by a green star that appears next to the user's name. When a user joins a room, they are initially assigned to the role of a "listener" and cannot unmute themselves. Listeners can notify the moderators of their intent to join the stage and speak by clicking on the "raise hand" icon. Users who are invited to the stage become "speakers" and can unmute themselves. Users can exit a room by tapping the "leave quietly" button or with the help of peace sign emoji. === Houses === In August 2022, Clubhouse announced a feature called Houses, an invite-based version of the rooms. === Events === A lot of conversations in Clubhouse are of spontaneous nature. However, users can schedule conversations by creating events. While scheduling an event, users can first name the event and then set the date and time at which the conversation will begin. Users can also add co-hosts to help moderate the event. Once the event has been created, it is added to the Clubhouse "bulletin". The bulletin shows upcoming scheduled events and allows users to set notifications for events by clicking the bell icon corresponding to the event. Users can access the bulletin by clicking on the calendar icon at the top of the home page. === Clubs === At the Clubhouse, clubs are user communities that regularly discuss a common interest. Many clubs are present in Clubhouse which represents a wide array of topics. Users can find clubs by name under the search tab. A club consists of three categories of users: "Admin", "Leader", and "Member". Members can create private rooms and invite more users into the club. Leaders have all the privileges of a member. Apart from that, they are authorized to create/schedule club-branded open rooms. An admin can modify club settings, add/delete users, change user privileges and create/schedule any type of room. There are three types of clubs: "Open", "By Approval", and "Closed" for membership. Any user can join an open club by pressing the "Join The Club" button on the club profile. In case of approval, users need to apply and wait for membership by clicking the "Apply To Join" button on the club profile. The admins of the respective club are privileged to accept or reject the user's request. In a closed club, membership is limited to users selected by the club admin. All users of a club will be notified when a public room within the club is created. The club creation is restricted to active users and whoever creates the club will become the club admin. Eligible users can create a club by going to their profile, press the "+" sign present in the "Member of" section. Clubs in which a user is a member are shown on their profile page. The first club to half a million members was the Human Behavior Club founded by The Digital Doctor (Dr. Sohaib Imtiaz). === Backchannel === Backchannel is the messaging function which allows users to interact individually or within a group via text. The Backchannel feature was initially leaked on June 18, 2021, in response to the launch of Spotify Greenroom. This is notable step because, until this point, Clubhouse was voice only with no way to hyperlink or message. It was entirely dependent on Instagram and Twitter for text messaging. The feature was initially leaked in the App Store, which the company says was an accident on Twitter. A month later, after multiple failed attempts, the Clubhouse Backchannel finally launched on July 14, 2021. === Explore === The homepage of Clubhouse provides access to ongoing chat rooms, which are recommended based on the people and clubs that are followed by the user. As the users tap on the magnifying glass icon, they will be redirected to the explore page. On that page, users can search for people and clubs to follow and also find conversations categorized by topics. === Clubhouse Payments === This is the direct payment service provided by the app, which allows users to send money to content creators. It includes those users who had enabled this functionality in their profile. Money can be sent from users to the creator by clicking on their profile. Press "Send Money" then enter the amount you want to send. When a user does this for the first time, they'll be prompted to reg
Stairstep interpolation
In the field of image processing, stairstep interpolation is a widely employed method technique for interpolating pixels after enlarging an image. The fundamental concept is to interpolate multiple times, in small increments, using any interpolation algorithm that is better than nearest-neighbor interpolation such as; bilinear interpolation, and bicubic interpolation. A common scenario is to interpolate an image by using a bicubic interpolation which increases the image size by no more than 10% (110% of the original size) at a time until the desired size is reached. Fred Miranda, a developer, popularized this method by creating and developing several Photoshop plug-ins that incorporate this technique. == Example ==
CatDV
CatDV is a media asset manager program for handling multimedia production workflows developed by Square Box Systems. Quantum Corporation acquired Square Box Systems in 2020. == Versions == The full family of CatDV Products is as follows: CatDV Standalone Products CatDV Professional Edition CatDV Pegasus CatDV Networked Products CatDV Essential - entry level server product CatDV Enterprise Server - for MySQL databases and most common server platforms including Linux, Windows and Mac OS X CatDV Pegasus Server - adds features such as high performance full-text indexing, access control lists, and more CatDV Worker Node - automated workflow and transcoding engine CatDV Web Client - provides access to the CatDV database via a web browser. There is no need to install special software on the desktop, making it easy to deploy to a large number of users. CatDV Professional Edition & Pegasus Clients - designed to support the multi-user capabilities of the CatDV Enterprise and Workgroup Servers from the desktop Using plugins and scripting, which often require additional professional services support to set up, complex integrations with a wide variety of third party systems (including archive, cloud storage, and artificial intelligence) are possible. == Awards == CatDV won two awards in 2010, a blue ribbon from Creative COW Magazine and a "Best of Show Vidy Award" from Videography. In April 2012 Square Box won a Queen's Award for Enterprise for CatDV.
ConEmu
ConEmu (short for Console emulator) is a free and open-source tabbed terminal emulator for Windows. ConEmu presents multiple consoles and simple GUI applications as one customizable GUI window with tabs and a status bar. It also provides emulation for ANSI escape codes for color, bypassing the capabilities of the standard Windows Console Host to provide 256 and 24-bit color in Windows. The program has a large range of customization, including custom color palettes for the standard 16 colors, hotkeys, transparency, an auto-hideable mode (similar to the way Quake originally displayed its developer console). Initially, the program was created as a companion to Far Manager, bringing some features common for graphical file managers to this console application (thumbnails and tiles, drag and drop with other windows, true color interface, and others). As of 2012, ConEmu could be used with any other Win32 console application or simple GUI tool (such as Notepad, PuTTY or DOSBox). ConEmu doesn't provide any shell itself, but rather allows using any other shell. It does provide a limited macro language, to control the hosted applications startup.
Drops (app)
Drops is a language learning app that was created in Estonia by Daniel Farkas and Mark Szulyovszky in 2015. It is the second product from the company, after their first app, LearnInvisible, had issues in retaining a user's engagement over the required time period. The languages available include Native Hawaiian and Māori, and was classified as one of the fifty "Most Innovative Companies" for 2019 by Fast Company. The company partnered with Global Eagle Entertainment to include Travel Talk, a feature intended to focus on words and phrases frequently used by travelers. At the beginning of the COVID-19 pandemic in March 2020, the number of users increased by 55 percent in the United States and 92 percent in the United Kingdom. Droplets, a language app for children, includes profiles for multiple teachers working with remote students. The company also produces an app called Scripts, intended to help users learn to write alphabets. The app was purchased by the Norwegian company Kahoot! on 24 November 2020.